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ILOG CPLEX 8.1 User's Manual

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2. Concert Type Callable Library Interactive Optimizer IRCuts Int CPX PARAM MIRCUTS IP CUTS MIRCUT NetDisplay Int CPX PARAM NETDISPLAY NETWORK DISPLAY NetEpOpt Num CPX PARAM NETEPOPT NETWORK TOLERANCES OPTIMALITY NetEpRHS Num CPX PARAM NETEPRHS NETWORK TOLERANCES FEASIBILITY NetFind Int CPX PARAM NETFIND NETWORK NETFIND NetItLim Int CPX PARAM NETITLIM NETWORK ITERATIONS NetPPrilnd Int CPX PARAM NETPPRIIND NETWORK PRICING NodeAlg Int CPX PARAM SUBALG IP STRATEGY SUBALGORITHM NodeFileInd Int CPX PARAM NODEFILEIND IP STRATEGY FILE NodeLim Int CPX PARAM NODELIM IP LIMITS NODES NodeSel Int CPX PARAM NODESEL IP STRATEGY NODESELECT NzGrowth Int CPX PARAM NZGROWTH READ NONZEROS Ob3jDif Num CPX PARAM OBJDIF IP TOLERANCES OBJDIFFERENCE ObjLLim Num CPX PARAM OBJLLIM SIMPLEX LIMITS LOWEROBJ ObjULim Num CPX PARAM OBJULIM SIMPLEX LIMITS UPPEROBJ PerInd Bool CPX_PARAM_PERIND SIMPLEX PERTURBATIO PerLim Int CPX PARAM PERLIM SIMPLEX LIMITS PERTURBATION PPriInd Int CPX PARAM PPRIIND SIMPLEX PGRADIEN PreCompress Int CPX PARAM PRECOMPRESS PREPROCESSING COMPRESS PreDual Int CPX PARAM PREDUAL PREPROCESSING DUAL PreInd Bool CPX_PARAM_PREIND PREPROCESSING PRESOLVE PreLinear Int CPX PARAM PRELINEAR PREP
3. netex2 c Reading and optimizing a network problem Transforming to LP to find IIS Import the CPLEX function declarations and the C library header file stdio h with the following single include finclude ilcplex cplex h Import the declarations for the string functions include string h irit main int argc char argwv Declare variables and arrays for retrieving problem data and solution information later on int status 0 CPXENVptr env NULL CPXNETptr net NULL CPXLPptr lp NULL Check command line if arge 2 fprintf stderr Usage s network file gt n argv 0 fprintf stderr Exiting n goto TERMINATE Initialize the CPLEX environment env CPXopenCPLEX amp status ILOG CPLEX 8 1 USER S MANUAL EXAMPLE NETWORK TO LP TRANSFORMATION If an error occurs the status value indicates the reason for failure A call to CPXgeterrorstring will produce the text of the error message Note that CPXopenCPLEX produces no output so the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines the errors will be seen if the CPX PARAM SCRIND indicator is set to CPX ON if env NULL char errmsg 1024 fprintf stderr Could not open CPLEX environment Mn CPXgeterrorstring env status errmsg fprintf stderr s errmsg
4. n 261 NOMIDEX2 COP E E 269 MIPEXZG oaee hea E A EE AEE wa eor A ctae dene 271 HOMMIP CXS COP A T E E E T 275 MIPEXI Ci E 277 PEX Ceroii e a e O E a Ea a S a 299 STE e E E E r E EE E 310 ILOG CPLEX 8 1 USER S MANUAL 19 LIST OF EXAMPLES NOQOAlEXM CDP pr Es 321 illogoalex2 cpp e AEE Mec T 328 HOGOAIEXS COP e 335 NOIPOX4 CPP M s 347 Jor Ae ME 352 HOACITMIPSXD CPP ses sce 365 20 ILOG CPLEX 8 1 USER S MANUAL Meet ILOG CPLEX ILOG CPLEX offers C C and Java libraries that solve linear programming LP and related problems Specifically it solves linearly constrained optimization problems where the objective to be optimized can be expressed as a linear function or a convex quadratic function The variables in the model may be declared as continuous or further constrained to take only integer values ILOG CPLEX comes in three forms to meet a wide range of users needs The ILOG CPLEX Interactive Optimizer is an executable program that can read a problem interactively or from files in certain standard formats solve the problem and deliver the solution interactively or into text files The program consists of the file cplex exe on Windows platforms or cplex on UNIX platforms Concert Technology is a set of libraries offering an API that includes model
5. Command Options Example add baropt page 374 baropt dualopt baropt primopt baropt stop change bounds change coefficient change delete change name change objective ILOG CPLEX 8 1 USER S MANUAL 393 Interactive Optimizer Commands 394 Command Options Example change problem type page 243 page 198 page 202 change qpterm page 200 change rhs change sense change type page 228 display iis page 143 display problem all display problem binaries page 226 display problem bounds display problem constraints display problem generals page 226 display problem histogram page 167 display problem integers page 226 display problem names display problem qpvariables display problem semi continuous display problem sos display problem stats page 121 page 226 display problem variable display sensitivity display settings display settings all display settings changed display solution basis ILOG CPLEX 8 1 USER S MANUAL Interactive Optimizer Commands Command Options Example display solution bestbound display solution dual display solution kappa page 137 display solution objective display solution quality page 141 page 163 display solution reduced display solution slacks display solution variables enter help mipopt p
6. Here is an example of a log file for a barrier optimization without crossover Tried aggregator 1 time LP Presolve eliminated 9 rows and 11 columns Aggregator did 6 substitutions Reduced LP has 12 rows 15 columns and 38 nonzeros Presolve time 0 00 sec Number of nonzeros in lower triangle of A A 26 Using Approximate Minimum Degree ordering Total time for automatic ordering 0 00 sec Summary statistics for Cholesky factor Rows in Factor 12 Integer space required 12 Total non zeros in factor 78 Total FP ops to factor 650 Itn Primal Obj Dual Obj Prim Inf Upper Inf Dual Inf QO 1 3177911e401 1 2600000e 03 6 55e 02 0 00e 00 3 92e 01 1 4 8683118e401 5 4058675e 02 3 91le 01 0 00e 00 1 18e 01 2 1 6008142e 02 3 5969226e 02 1 35e 13 7 11le 15 5 81e 00 3 3 5186681le 02 6 1738305e 02 1 59e 10 1 78e 15 5 16e 01 4 4 5808732e 02 4 7450513e 02 5 08e 12 1 95e 14 4 62e 02 5 4 6435693e 02 4 6531819e 02 1 66e 12 1 27e 14 1 59e 03 6 4 6473085e 02 4 6476678e 02 5 53e 11 2 17e 14 2 43e 15 7 4 6475237e 02 4 6475361e 02 5 59e 13 2 99e 14 2 19e 15 8 4 6475312e 02 4 6475316e 02 1 73e 13 1 55e 14 1 17e 15 9 4 6475314e 02 4 6475314e 02 1 45e 13 2 81e 14 2 17e 15 Barrier Optimal Objective 4 6475314194e 02 Solution time 0 01 sec terations 9 Preprocessing in the Log File The opening lines of that log file record information about preprocessing by the ILOG CPLEX presolve
7. Now read the file and copy the data into the created lp status CPXreadcopyprob env lp argv 1 NULL if status fprintf stderr Failed to read and copy the problem data n goto TERMINATE if CPXgetprobtype env lp CPXPROB_OP fprintf stderr Input file is not a QP Exiting n goto TERMINATE Optimize the problem and obtain solution switch argv 2 0 case o ILOG CPLEX 8 1 USER S MANUAL 217 EXAMPLE 218 READING A QP FROM A FILE method break case p method break case d method break case n method break case b method break default method break PX PX PX PX ALG AUTOMATIC PX PX ALG BARRIER ALG PRIMAL ALG DUAL ALG NET ALG NONE status CPXsetintparam env if status fprintf stderr Failed to set the optimization method goto TERMINATE status CPXqpopt if status fprintf stderr goto TERMINATE env 1p CPX PARAM OPMETHOD method Failed to optimize QP n solnstat CPXgetstat env lp Xf solnstat CPX STA printf Model is unbounded n goto TERMINATE else if solnstat CPX STA printf Model is infeasibl print goto TERMINAT Model goto TERMINAT else if solnstat CPX STAT f L is infeasibl status CPXsolninfo env lp if status fpr
8. Performing Sensitivity Analysis The availability of a basis for an LP allows you to perform sensitivity analysis for your model if it is an LP Such analysis tells you by how much you can modify your model without affecting the solution you found The modifications supported by the sensitivity analysis function include bound changes changes of the right hand side vector and changes of the objective function They are analyzed by methods IloCplex getBoundSA IloCplex getRHSSA and IloCplex getObjSA respectively Analyzing Infeasible Problems An important feature of ILOG CPLEX is that even if no feasible solution has been found that is if cplex solve returns IloFalse some information about the problem can be queried when solving LPs or QPs All the methods discussed so far may successfully return information about the current infeasible solution which ILOG CPLEX maintains Unfortunately there is no simple comprehensive rule about whether or not current solution information can be queried This is because by default ILOG CPLEX uses a presolve procedure to simplify the model If for example the model is proven to be infeasible during the presolve no current solution is generated by the optimizer If in contrast infeasibility is only proven by the optimizer current solution information is available to be queried The status returned by calling cplex getCplexStatus may help to determine which case you are fac
9. 168 Table 5 13 BarAlg Parameter Values for Barrier Optimizer Algorithm luus 170 Table 7 1 RootAlg Parameter Values 0 0000 cece eee lees 201 Table 8 1 Interactive Optimizer Display Options for MIP Problems sss 226 Table 8 2 Problem Type Definitions lseeeee IR 227 Table 8 3 Parameters for Controlling Branch amp Cut Strategy 00 00 eee eee eee 232 Table 8 4 NodeSel Parameter Values for Node Search Type 0 0c eee eee ee eee 233 Table 8 5 VarSel Parameter Values for Branching Variable Choice 2 00 234 Table 8 6 BrDir Parameter Values for Branching Direction Choice lulu 234 Table 8 7 Parameters for Controlling Cuts lsleesee I 237 Table 8 8 Parameters for Controlling MIP Preprocessing selle 239 Table 8 9 Parameters for Branching Priority Order 0 000 cece eee eee eee 241 Table 8 10 Parameters to limit MIP optimization lel 242 Table 8 11 Values of the MIP Display Parameter 0 c eee sns 246 Table 8 12 Values for the Node File Storage Parameter 0 000 e cece eee ee eee 255 Table 8 13 Values of RootAlg and NodeAlg Parameters 0 cece ee eee eee ee 258 Table 9 1 Options for the convert Utility and Corresponding File Extensions 295 Table 9 2 Options for the Output Channel Command 0000 eee eee eens 296 Table 9 3 Channels Directing O
10. which means the current working directory ILOG CPLEX creates the temporary directory by means of system calls If the system environment variable is set on Windows platforms the environment variable TMP on UNIX platforms the environment variable TMPDIR then the system ignores the ILOG CPLEX node file directory parameter and creates the temporary node file directory in the location indicated by its system environment variable Furthermore if the directory specified in the ILOG CPLEX node file directory parameter is invalid for example if it contains illegal characters or if the directory does not allow write access then the system chooses a location according to its own logic i zal e ES o di Bulnjos The temporary directory created for node file storage will have a name prefixed by cpx The files within it will also have names prefixed by cpx ILOG CPLEX automatically removes the files and their temporary directory when it frees the branch amp cut tree in the Interactive Optimizer e at problem modification e at normal termination from the Concert Technology Library e when you call env end e When you modify the extracted model ILOG CPLEX 8 1 USER S MANUAL 255 TROUBLESHOOTING MIP PERFORMANCE PROBLEMS 256 from the Callable Library e when you call a problem modification routine e when you call CPX reeprob If a program terminates abnormally the files are not r
11. PXcheckvals CPXcheckcopyctype CPXcheckcopysos 9 99999999 CPXNETcheckcopynet Each of those routines performs a series of diagnostic tests of the problem data and issues warnings or error messages whenever it detects a potential error To use them you must compile and link the file check c After compiling and linking that file you will be able to step through the source code of these routines with a debugger to help isolate problems If you have observed anomalies in your application you can exploit this diagnostic capability by calling the appropriate routines just before a change or copy routine The diagnostic routine may then detect errors in the problem data that could subsequently cause inexplicable behavior Those checking routines send all messages to one of the standard ILOG CPLEX message channels You capture that output by setting the parameter CPX PARAM SCRIND if you want messages directed to your screen or by calling the routine CPXsetlogfile Callbacks The Callable Library supports callbacks so that you can define functions that will be called at crucial points in your application during the presolve process once per iteration in a linear programming or quadratic programming routine and at various points such as before each node is processed in a mixed integer optimization In addition callback functions can call CPXgetcallbackinfo to retrieve information
12. 9 9 9 Using Parallel Optimizers ILOG CPLEX 8 1 USER S MANUAL 289 4 E O 2 og vs a UE z To MANAGING INPUT amp OUTPUT Managing Input amp Output 290 This section tells you about input to and output from ILOG CPLEX It contains the following subsections gt Understanding File Formats Managing Log Files the Log File Parameter Handling Message Channels the Output Channel Parameter Handling Message Channels Callable Library Routines Example Using the Message Handler Understanding File Formats The ZLOG CPLEX Reference Manual documents the file formats that ILOG CPLEX supports Here is a brief description of these file formats BAS files are text files governed by MPS conventions that is they are not binary for saving a simplex basis BIN files are binary files ILOG CPLEX uses this format when it writes solution files containing the binary representation of real numbers DPE is the format ILOG CPLEX uses to write a problem in a binary SAV file after the objective of a problem has been perturbed for use with the dual simplex optimizer DUA format governed by MPS conventions writes the dual formulation of a problem currently in memory so that the MPS file can later be read back in and the dual formulation can then be optimized explicitly This file format is largely obsolete now since you can set the PreDual parameter to tell ILOG CPLEX to solve the d
13. cerr lt lt Error lt lt ex lt lt endl env end return 0 ILOG CPLEX 8 1 USER S MANUAL A COMPARISON OF GOALS AND CALLBACKS A Comparison of Goals and Callbacks Goals and callbacks both provide an API within 11oCplex to allow you to take control over the branch amp cut search for solving MIP models With one exception the same functionality is available in both APIs In fact the goal API is built on top of callbacks As a consequence you cannot use callbacks and goals at the same time To help you choose which API is more suited to your needs this section examines commonalities and differences between both As pointed out previously both APIs allow you to control the branch amp cut search used by IloCplex to solve MIP models The following points distinguish specific features of this control Checking feasibility e With goals you can discontinue the search at a node by returning a Fail goal Alternatively you can continue searching even though an integer feasible solution has been found by returning another nonempty goal e With callbacks you can use method prune of the branch callback to discontinue the search and an incumbent callback to accept or reject integer feasible solutions Creating branches e With goals you create branches by using by using Or goals with local cut goals as parameters e With callbacks you create branches by using a branch callback Adding local or gl
14. else printf No basis available n Retrieve solution vector x double malloc cur_numcols sizeof double if x NULL fprintf stderr No memory for solution n goto TERMINATE status CPXgetx env lp x 0 cur numcols 1 if status fprintf stderr Failed to obtain primal solution Wn goto TERMINATE Write out the solution for j 0 J lt cur numcols J printf Column d Value 17 10g j x j1 if cstat NULL switch cstat j ILOG CPLEX 8 1 USER S MANUAL 219 EXAMPLE 220 READING A QP FROM A FILE case CPX_AT_LOWER basismsg Nonbasic at lower bound break case CPX_BASIC basismsg Basic break case CPX_AT_UPPER basismsg Nonbasic at upper bound break case CPX_FREE_SUPER basismsg Superbasic or free variable at zero break default basismsg Bad basis status break printf s basismsg print Xn s Display the maximum bound violation status CPXgetdblquality env lp amp maxviol CPX_MAX_PRIMAL_INFEAS if status fprintf stderr Failed to obtain bound violation Mn goto TERMINATE printf Maximum bound violation 17 10g n maxviol TERMINATE Free up the basis and solution free and null char amp cstat free and null char amp rstat free and null char amp x Free up the problem if necessary if
15. e nFoods foodMax length 9 throw new IloException inconsistent data in file filename 9 if nNutrs nutrMin length B 5T nNutrs nutrPerFood length S a throw new IloException inconsistent data in file filename c 2 for int i 0 i lt nNutrs i A 2 if nutrPerFood i length nFoods i o Co lt static void buildModelByRow IloModeler model Data data IloNumVar Buy IloNumVarType type throws IloException int nFoods data nFoods int nNutrs data nNutrs for int j 0 j lt nFoods j Buy j model numVar data foodMin j data foodMax j type model addMinimize model scalProd data foodCost Buy for int i 0 i lt nNutrs i model addRange data nutrMin i model scalProd data nutrPerFood i Buy data nutrMax i static void buildModelByColumn IloMPModeler model Data data IloNumVar Buy IloNumVarType type throws IloException int nFoods data nFoods int nNutrs data nNutrs IloObjective cost model addMinimize ILOG CPLEX 8 1 USER S MANUAL 79 SOLVING THE DIET MODEL WITH THE JAVA API IloRange constraint new IloRange nNutrs for int i 0 i lt nNutrs i constraint i model addRange data nutrMin i data nutrMax i for int j 0 J lt nFoods j IloColumn col model column cost data foodCost j for int i 0 i lt nNutrs i col col and model column constraint i
16. return status END populatebycolumn Solving LP Problems with the Barrier Optimizer This section tells you more about solving linear programming problems using the ILOG CPLEX Barrier Optimizer It includes sections on 156 ILOG CPLEX 8 1 USER S MANUAL SOLVING LP PROBLEMS WITH THE BARRIER OPTIMIZER Identifying LPs for Barrier Optimization Interpreting the Barrier Log File Understanding Solution Quality from the Barrier LP Optimizer Overcoming Numerical Difficulties 9 99 Diagnosing Barrier Optimizer Infeasibility Identifying LPs for Barrier Optimization The ILOG CPLEX Barrier Optimizer is well suited to large sparse problems An alternative to the simplex optimizers it exploits a primal dual logarithmic barrier algorithm to generate a sequence of strictly positive primal and dual solutions to a problem Like the simplex optimizers it is not really necessary to understand the internal workings of barrier in order to obtain its performance benefits However for the interested reader we first pause to give an outline of how it works ILOG CPLEX finds the primal solutions conventionally denoted x s from the primal formulation Minimize cx subject to Ax b with these bounds x s u and x 21 where A is the constraint matrix including slack and surplus variables u is the upper and the lower bounds on the variables Simultaneously ILOG CPLEX automatically finds the dual solutions c
17. 198 Concert Technology 11oCplex programs treat all models as capable of containing quadratic coefficients in the objective function These coefficients can therefore be added or deleted at will When extracting a model with a quadratic objective function IloCplex will automatically detect it as a QP and make the required adjustments to data structures ILOG CPLEX 8 1 USER S MANUAL CHANGING QUADRATIC TERMS However the other ways of using ILOG CPLEX the Callable Library and the Interactive Optimizer require an explicit notion of a Problem Type to distinguish Linear Programs LPs from QPs This subsection discusses the topic for these users When you enter a problem ILOG CPLEX determines the Problem Type from the available information When read from a file LP MPS or SAV format for example or entered interactively a continuous optimization problem is treated as being of Type qp if quadratic coefficients are present in the objective function Otherwise the Problem Type is 1p The issue of Problem Types that support integer restrictions in conjunction with quadratic variables is discussed in Chapter 8 Solving Mixed Integer Programming Problems If you enter a problem that lacks any quadratic coefficients its Problem Type is initially 1p If you then wish to modify the problem to contain quadratic coefficients you do this by first changing the Problem Type to qp Conversely if you have entered a QP model and wish to rem
18. 274 ILOG CPLEX 8 1 USER S MANUAL EXAMPLE USING SOS AND PRIORITY free ptr ptr NULL END free_and_null static void usage char progname fprintf stderr Usage s filename n progname fprintf stderr where filename is a file with extension Mn fprintf stderr MPS SAV or LP lower case is allowed Nin fprintf stderr This program uses the CPLEX MIP optimizer n fprintf stderr Exiting n END usage Example Using SOS and Priority This example illustrates how to use SOS and priority orders Complete Program ilomipex3 cpp It derives from i lomipex1 cpp The differences between that simpler MIP example and this one are The problem solved is slightly different so the output is interesting The actual SOS and priority order that the example implements are arbitrary they do not necessarily represent good data for this problem v A fej ES D di Buinjos The routine setPriorities sets the SOS and priority order a C File examples src ilomipex3 cpp Version 8 1 Copyright C 1999 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products a ilomipex3 cpp Entering and optimizing a MIP problem with SOS sets Pi and priority orders Is a modification of ilomipexl cpp Note that the problem solved is
19. IloCplex Callback MyCallback IloEnv env IloInt num return new env MyCallbackI num It is not customary to write such a function for Java but new is called explicitly for creating a callback object when needed Once an implementation object of your callback is created either with the constructor function in C or by directly calling the new operator for Java use it with 11oCplex by calling cplex use with the callback object as parameter In C to remove a callback that is being used by a cplex object call callback end on the IloCplex Callback handle callback In java there is no way of removing individual callbacks from your 11oCplex object Instead you can remove all callbacks by calling cplex clearCallbacks Since Java uses garbage collection for memory management there is nothing equivalent to the end method for callbacks in the Java API One object of a callback implementation class can be used with only one 11oCplex object at a time Thus when you use a callback with more than one cplex object a copy of the implementation object is created every time cplex use iscalled except for the first time In C the method IloCplex use returns a handle to the callback object that has actually been installed to enable calling end on it To construct the copies of the callback objects in C class IloCplex CallbackI defines another pure virtual method virtual IloCplex CallbackI IloCplex CallbackI
20. NULL fprintf stderr No memory for solution values n goto TERMINATE ILOG CPLEX 8 1 USER S MANUAL 273 i AS fej ES D diIN Buinjos EXAMPLE READING A MIP PROBLEM FROM A FILE status CPXgetmipx env lp x 0 cur numcols 1 if status 1 fprintf stderr Failed to obtain solution n goto TERMINATE Write out the solution for j 0 j lt cur numcols j printf Column d Value 17 10g n j xI j TERMINATE Free up the solution free_and_null char amp x Free up the problem as allocated by CPXcreateprob if necessary if lp NULL status CPXfreeprob env amp lp if status fprintf stderr CPXfreeprob failed error code d n status Free up the CPLEX environment if necessary if env NULL status CPXcloseCPLEX amp env Note that CPXcloseCPLEX produces no output so the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines the errors will be seen if the CPX PARAM SCRIND indicator is set to CPX ON if status char errmsg 1024 fprintf stderr Could not close CPLEX environment Nn CPXgeterrorstring env status errmsg fprintf stderr s errmsg return status END main This simple routine frees up the pointer ptr and sets ptr to NULL static void free and null char ptr if ptr NULL
21. Then call CPXgetobjval in this way status CPXgetobjval env lp amp objval In contrast here is the synopsis of the routine CPXgetx int CPXgetx CPXENV env CPXLPptr lp double x int begin int end You call it by creating a double precision array by means of either one of two methods The first method dynamically allocates the array like this double x NULL x double malloc 100 sizeof double The second method declares the array as a local variable like this double x 100 Then to see the optimal values for columns 5 through 104 for example you could write this status CPXgetx env lp x 5 104 The parameter objval_p in the synopsis of CPXgetobjval and the parameter x in the synopsis of CPXgetx are both of type double However the suffix _p in the ILOG CPLEX 8 1 USER S MANUAL ILOG CPLEX PROGRAMMING PRACTICES parameter objval_p indicates that you should use an address of a single variable in one call while the lack of _p in x indicates that you should pass an array in the other For guidance about how to pass values to ILOG CPLEX routines from application languages such as FORTRAN or BASIC that conventionally call by reference see Call by Reference on page 97 in this manual and consult the documentation for those languages Data Types In the Callable Library ILOG CPLEX defines a few special data types for specific ILOG CPLEX objects as you see in Table
22. To formulate a full optimization problem the objects that are part of it need to be selected This is done by adding them to an instance of 11oMode1 the class used to represent optimization problems For instance IloModel model env model add obj model add rl defines a model consisting of the objective obj constraint x1 and all the variables they use Notice that variables need not be added to a model explicitly as they are implicitly considered if any of the other modeling objects in the model use them However variables may be explicitly added to a model if desired ILOG CPLEX 8 1 USER S MANUAL 35 MODELING AN OPTIMIZATION PROBLEM WITH CONCERT TECHNOLOGY 36 For convenience Concert Technology provides the functions IloMinimize and IloMaximize to define minimization and maximization objective functions Also operators lt and lt are overloaded to create IloRange constraints This allows us to rewrite the above examples in a more compact and readable way TloModel model env model add IloMinimize env 1 x 1 2 x 2 3 x 3 model add x 1 x 2 3 0 With this notation the C variables obj and r1 need not be created The 11oModel class is itself a class of modeling objects Thus one model can be added to another A possible use of this is to capture different scenarios in different models all of which are extensions to a core model The core model could be represented as an IloModel obje
23. amp zobj free and null char amp zrhs free and null char amp zsense free and null char amp zmatbeg free and null char amp zmatcnt free and null char amp zmatind free and null char amp zmatval free and null char amp zlb free and null char amp zub free and null char amp zctype else numcols_p NUMCOLS numrows_p NUMROWS objsen_p CPX_MAX The problem is maximization probname_p zprobname obj p zobj rhs p zrhs sense p Zsense matbeg p zmatbeg matcnt p zmatcnt matind p zmatind matval_p zmatval lb_p zlb ub p zub ctype p zctype return status END setproblemdata This simple routine frees up the pointer ptr and sets ptr to NULL static void free and null char ptr if ptr NULL free ptr ptr NULL END free_and_null 268 ILOG CPLEX 8 1 USER S MANUAL EXAMPLE READING A MIP PROBLEM FROM A FILE Example Reading a MIP Problem from a File This example shows you how to solve a MIP with the Component Libraries when the problem data is stored in a file Complete Program ilomipex2 cpp This example derives from ilolpex2 cpp an LP example explained in the manual ILOG CPLEX Getting Started manual That LP example differs from this MIP example in these ways This example solves only MIPs so it calls only IloCplex solve
24. and for Java looks like this return cplex and cplex or cplex leGoal var Math floor val cplex geGoal var Math floor val 1 this For the C case note that since this statement would be called from the execute method of a subclass of I1oCplex GoallI the full method name IloCplex GoalI OrGoal can be abbreviated to OrGoal and likewise AndGoal This return statement returns an And goal that first executes the Or goal and then the current goal itself specified by the this parameter When the Or goal is executed next it will create two subnodes In the first subnode the first local cut goal representing var val where va1 denotes the floor of va1 will be executed thus adding the constraint var val forthe subtree of this node Similarly the second subnode will be created and when executing its constraint goal the constraint var 2 val 1 will be added for the subtree this is then executed on each of the nodes that have just been created the same goal is used for both subtrees Further details on how goals are processed will be discussed later We will discuss the execution of goals in the branch amp cut search tree in more detail below Before doing so let us go through a first example This example is available as file ilogoalex1 cpp in the examples src subdirectory of your ILOG CPLEX distribution The equivalent Java version can be found as GoalEx1 java in the same location ff M M M SS
25. and its command line does not require the user to indicate an optimizer This example does not generate or print a basis Like other applications based on the ILOG CPLEX Concert Technology Library this one uses IloEnv env to initialize the Concert Technology environment and IloModel model env to create a problem object Before it ends it calls env end to free the environment FM ee se i e i i See eS Ss k C K File examples src ilomipex2 cpp Version 8 1 Copyright C 1999 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products v AS faj ES D diIN Buinjos ilomipex2 cpp Reading in and optimizing a problem To run this example command line arguments are required i e ilomipex2 filename Example ilomipex2 mexample mps finclude lt ilcplex ilocplex h gt ILOSTLBEGIN static void usage const char progname int main int argc char argv IloEnv env ILOG CPLEX 8 1 USER S MANUAL 269 EXAMPLE READING A MIP PROBLEM FROM A FILE try IloModel model env IloCplex cplex env if arge 2 usage argv 0 throw 1 IloObjective obj IloNumVarArray var env IloRangeArray rng env cplex importModel model argv 1 obj var rng cplex extract model cplex solve env out lt lt Solution status lt lt c
26. break status 1 goto TERMINATE for i 0 i lt nmin i if status readarray in amp n nutrper_p i goto TERMINATE af m l neost status 1 goto TERMINATE fscanf in c amp ch if i lt nmin 1 amp amp ch status 1 goto TERMINATE if ch t 7 1 status 1 goto TERMINATE TERMINATE return status END readdata 2 D ie D D D o A 5 lt ILOG CPLEX 8 1 USER S MANUAL 111 EXAMPLE DIETARY OPTIMIZATION 112 ILOG CPLEX 8 1 USER S MANUAL Further Programming Considerations This chapter offers suggestions for improving application development and debugging completed applications It includes sections on Tips for Successful Application Development Using the Interactive Optimizer for Debugging Eliminating Common Programming Errors Tips for Successful Application Development In the previous chapters we indicated briefly the minimal steps to use the Component Libraries in an application This section offers guidelines for successfully developing an application that exploits the ILOG CPLEX Component Libraries according to those steps These guidelines aim to help you minimize development time and maximize application performance e e 2 ee Q D A e 2 7 BuruiuejBoJg 1ou1nJ Prototype the Model We strongly recommend that you begin by creating a small scale ve
27. goto TERMINATE v BS fej ES 3 MO 4 4JOMJON Hulajos Turn on output to the screen status CPXsetintparam env CPX PARAM SCRIND CPX ON if status fprintf stderr Failure to turn on screen indicator error d n status goto TERMINATE Create the problem net CPXNETcreateprob env amp status netex2 A returned pointer of NULL may mean that not enough memory was available or there was some other problem In the case of failure an error message will have been written to the error channel from inside CPLEX In this example the setting of the parameter CPX_PARAM_SCRIND causes the error message to appear on stdout if net NULL fprintf stderr Failed to create network object n goto TERMINATE Read network problem data from file with filename given as command line argument status CPXNETreadcopyprob env net argv 1 if status fprintf stderr Failed to build network problem n goto TERMINATE Optimize the problem status CPXNETprimopt env net if status fprintf stderr Failed to optimize network n goto TERMINATE ILOG CPLEX 8 1 USER S MANUAL 191 EXAMPLE NETWORK TO LP TRANSFORMATION Check network solution status if CPXNETgetstat env net CPX_STAT_INFEASIBLE Create LP object used for invoking infeasibility finder lp CPXcreateprob env amp status netex2
28. int status 0 double obj NUMCOLS double 1b NUMCOLS double ub NUMCOLS char colname NUMCOLS int matbeg NUMCOLS int matind NUMNZ double matval NUMNZ double rhs NUMROWS char sense NUMROWS char rowname NUMROWS To build the problem by column create the rows and then o 2 Q T U Uv E e D 3 7 ILOG CPLEX 8 1 USER S MANUAL 155 SOLVING LP PROBLEMS WITH THE BARRIER OPTIMIZER add the columns CPXchgobjsen env lp CPX_MAX Problem is maximization Now create the new rows First populate the arrays rowname 0 c1 sense 0 L rhs 0 20 0 rowname 1 c2 sense 1 L rhs 1 30 0 status CPXnewrows env lp NUMROWS rhs sense NULL rowname if status goto TERMINATE Now add the new columns First populate the arrays obj 0 1 0 obj 1 2 0 obj 2 3 0 matbeg 0 0 matbeg 1 2 matbeg 2 4 matind 0 0 matind 2 0 matind 4 0 matval 0 1 0 matval 2 1 0 matval 4 1 0 matind 1 1 matind 3 1 matind 5 1 matval 1 1 0 matval 3 3 0 matval 5 1 0 lb 0 0 0 lb 1 0 0 lb 2 0 0 ub 0 40 0 ub 1 CPX INFBOUND ub 2 CPX INFBOUND colname 0 x1 colname 1 x2 colname 2 x3 status CPXaddcols env lp NUMCOLS NUMNZ obj matbeg matind matval lb ub colname if status goto TERMINATE TERMINATE
29. EXAMPLE READING A MIP PROBLEM FROM A FILE A returned pointer of NULL may mean that not enough memory was available or there was some other problem In the case of failure an error message will have been written to the error channel from inside CPLEX In this example the setting of the parameter CPX PARAM SCRIND causes the error message to appear on stdout Note that most CPLEX routines return an error code to indicate the reason for failure x if lp NULL fprintf stderr Failed to create LP n goto TERMINATE Now read the file and copy the data into the created lp Status CPXreadcopyprob env lp argv 1 NULL if status fprintf stderr Failed to read and copy the problem data n goto TERMINATE Optimize the problem and obtain solution status CPXmipopt env lp if status fprintf stderr Failed to optimize MIP n goto TERMINATE solstat CPXgetstat env 1p printf Solution status d n solstat status CPXgetmipobjval env lp amp objval if status 1 fprintf stderr Failed to obtain objective value Wn goto TERMINATE printf Objective value 10g n objval The size of the problem should be obtained by asking CPLEX what the actual size is cur_numcols stores the current number of columns cur numcols CPXgetnumcols env 1p Allocate space for solution x double malloc cur numcols sizeof double if x
30. IA IA 20 A network flow model is an LP model with special structure The ILOG CPLEX Network Optimizer is a highly efficient implementation of the primal simplex technique adapted to take advantage of this special structure In particular no basis factoring occurs However it is possible to solve network models using any of the ILOG CPLEX LP optimizers if first you convert the network data structures to those of an LP model To convert the network data structures to LP data structures in the Interactive Optimizer use the command change problem 1p from the Callable Library use the routine CPXcopynettolp The LP formulation of our example from Figure 6 1 on page 178 looks like this 84 ILOG CPLEX 8 1 ag ag 2ag 6849 5ayy ag ag all 810 a12 844 812 USER S MANUAL 8453 48412 3843 6844 814 814 20 10 0 lt a 0 lt aig 0 lt ayy 0 lt aq 0 lt a3 0 lt ayy 15 11 EXAMPLE NETWORK TO LP TRANSFORMATION In that formulation in each column there is exactly one coefficient equal to 7 one exactly one coefficient equal to and all other coefficients are 0 zero Since a network flow problem corresponds in this way to an LP problem you can indeed solve a network flow problem by means of a ILOG CPLEX LP optimizer as well If you read a network flow problem into the Interactive Optimizer you can transform it into its LP formulation with the comman
31. ILOG CPLEX 8 1 User s Manual December 2002 Copyright 2001 2002 by ILOG This document and the software described in this document are the property of ILOG and are protected as ILOG trade secrets They are furnished under a license or non disclosure agreement and may be used or copied only within the terms of such license or non disclosure agreement No part of this work may be reproduced or disseminated in any form or by any means without the prior written permission of ILOG S A Printed in France Table of Contents Listof Flg reS 2 2 22 rg cR I Rex RR eee rx eee Rome eee eee 15 Listof Tabl s ACD 17 List of Examples 2222 42 scel or rm ccm RR ccna dra S 19 Preface Meet ILOG CPLEX oreille RE ER xU RE eR Pa eee Ee eec 21 What Is ILOG CPLEX iiesaueu cur rr rea eee eee tees eee iR EEN 22 What You Need to KNOW 1 cc cece cee n n hh hh n nnn 23 In This Manual 5 52 ax rar tr acm ex nhan wi o rae RR ROC ane KORR 8a 24 Examples Online eona 2 RI enn p ERR qo ERRARE PROF IC rd US kom RE UR 25 Notation in This Manual lesser RR Rh Rh tn 26 Related Documentation lese ehh n n nnn n 27 For More Information 2 4 sias hannah rh rra haha ER ERR RACER ee 29 Customer Support ssssseselsleeleeeee mer hen 29 WebSite a bch eere dcm et amc tid es ee ob deg et Mete E wies E ee sio del 29 Chapter 1 ILOG Concert Technology for C Users 000 e cece eee 31 The Design of the ILOG CP
32. Reduced MIP has 2 rows 3 columns and 6 nonzeros dp Presolve time 0 00 sec y 2 Clique table 0 GUB 0 GUBEQ 0 two covers 0 probed S ImplBd table 0 bounds a Root relaxation solution time 0 00 sec 32 7 Nodes Cuts U Node Left Objective IInf Best Integer Best Node ItCnt Gap 0 0 125 2083 1 125 2083 3 122 5000 0 122 5000 Cuts 2 4 Mixed integer rounding cuts applied 1 Integer optimal solution Objective 1 2250000000e 002 Solution time 0 02 sec Iterations 4 Nodes 0 These additional items appear only in the node log file not on screen Variable records the name of the variable where ILOG CPLEX branched to create this node If the branch was due to a special ordered set the name listed here will be the right most variable in the left subset B indicates the branching direction e D means the variables was restricted to a lower value e U means the variable was restricted to a higher value ILOG CPLEX 8 1 USER S MANUAL 249 TROUBLESHOOTING MIP PERFORMANCE PROBLEMS e L means the left subset of the special ordered set was restricted to 0 zero e R means the right subset of the special ordered set was restricted to O zero Parent indicates the node number of the parent Depth indicates the depth of this node in the branch amp cut tree Troubleshooting MIP Performance Problems 250 Even the most sophisticated methods currently available to solve pure integer and mixed
33. The ZLOG CPLEX Reference Manual documents the type of each parameter bool int num string along with the Concert Technology enumeration value symbolic constant and reference number representing the parameter The method setDefaults resets all parameters except the log file to their default values including the ILOG CPLEX callback functions This routine resets the callback functions to NULL When solving MIPs additional controls of the solution process are provided Priority orders and branching directions can be used to control the branching in a static way These are discussed in Heuristics on page 238 These controls are static in the sense that they allow you to control the solution process based on data that does not change during the solution and can thus be set up before solving the model Dynamic control of the solution process of MIPs is provided through goals or control callbacks They are discussed in Goals in IloCplex on page 319 and in Using Callbacks on page 341 Goals and callbacks allow you to control the solution process based on information that is generated during the solution process Accessing Solution Information Information about e solution feasibility e solution variables e basis information e solution quality can be accessed with the methods described in this section ILOG CPLEX 8 1 USER S MANUAL 41 ACCESSING SOLUTION INFORMATION Accessing Solution Status Calling cplex solve ret
34. The message argument for ourmsgfunc must not be a constant SO copy the mesage to a buffer strcpy errmsg Could not open CPLEX environment Nn ourmsgfunc Our Message errmsg goto TERMINATE Now get the standard channels If an error just call our message function directly status CPXgetchannels env amp cpxresults amp cpxwarning amp cpxerror NULL if status 1 strcpy errmsg Could not get standard channels n ourmsgfunc Our Message errmsg CPXgeterrorstring env status errmsg ourmsgfunc Our Message errmsg goto TERMINATE Now set up the error channel first The label will be cpxerror status CPXaddfuncdest env cpxerror errorlabel ourmsgfunc if status strcpy errmsg Could not set up error message handler in ourmsgfunc Our Message errmsg CPXgeterrorstring env status errmsg ourmsgfunc Our Message errmsg Now that we have the error message handler set up all CPLEX generated errors will go through ourmsgfunc So we don t have to use CPXgeterrorstring to determine the text of the message We can also use CPXmsg to do any other printing status CPXaddfuncdest env cpxwarning warnlabel ourmsgfunc if status ILOG CPLEX 8 1 USER S MANUAL 301 z EN 563 O 2 oS Us a UE fo MANAGING INPUT amp OUTPUT CPXmsg cpxerror Failed to set up handler for cpxwarning n goto TERMINATE stat
35. char probname 16 Problem name is max 16 characters Declare and allocate space for the variables and arrays where we will store the optimization results including the status value variable values dual values row slacks and variable reduced costs int solstat double objval double x NUMCOLS double pi NUMROWS double slack NUMROWS double dj NUMCOLS CPXENVptr env NULL CPXLPptr lp NULL int status int Xp 3s int cur numrows cur numcols char errmsg 1024 CPXCHANNELptr cpxerror NULL CPXCHANNELptr cpxwarning NULL CPXCHANNELptr cpxresults NULL CPXCHANNELptr ourchannel NULL char errorlabel cpxerror ILOG CPLEX 8 1 USER S MANUAL objective MANAGING INPUT amp OUTPUT char warnlabel cpxwarning char reslabel cpxresults char ourlabel Our Channel CPXFILEptr fpout NULL Initialize the CPLEX environment env CPXopenCPLEX amp status If an error occurs the status value indicates the reason for failure A call to CPXgeterrorstring will produce the text of the error message Note that CPXopenCPLEX produces no output so the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines the errors will be seen if the CPX PARAM SCRIND indicator is set to CPX ON Since the message handler is yet to be set up we ll call our messaging function directly to print out any errors if env NULL
36. destroying 87 freeing 87 initializing 86 instantiating 86 network 176 populating 86 181 problem query routine defined 84 problem type changing from network to LP 189 changing to qp 200 changing to zeroed_qp 200 prod 62 pruned node 319 418 ILOG CPLEX 8 1 Q QP example 203 215 problem formulation 195 solution example 215 solving 195 to 221 QP file format 198 291 QP relaxation 202 quadratic coefficient changing 199 200 quadratic objective functions 37 Quadratic Programming QP problem see QP query routine 309 R ranged constraints 63 create 61 ranged row 293 reading advanced basis 130 advanced basis from file 130 MIP problem data 269 MIP problem data from file 225 MIP tree from TRE file 242 network data from file 189 perturbed problem from DPE file 257 problem data from VEC file 160 QP problem data from file 215 start values from MST file 240 redirecting diagnostic routines 94 log file output 296 oputput 120 screen output 296 reduced costs 72 accessing 43 reduced cost pricing 131 reference counting 326 reference row values 246 reflection scaling 180 relative objective difference 252 relative optimality tolerance 252 USER S MANUAL relaxation algorithm applied to 257 of MIP problem 231 QP 202 RelObjDif 232 relocating log file 295 remove member function IloModel class 36 45 renaming log file 295 residual dual 141 maximum dual 142 maximum row 142 row 141 return st
37. getValue cut i getExpr if cut il getLB gt valteps val eps gt cut i getUB add cut i cut i null Instead of receiving expressions and right hand side values we chose to directly pass an array of I1oRange constraints to the callback which are stored in member cut The main method loops over all cuts and evaluates the constraint expressions at the current solution by calling getValue cut i getExpr If this exceeds the constraint bounds by more than eps the cut is added during the search by calling add cut 1 and cut i is set to null to avoid unneccessarily evaluating it again If for the C version the array of cuts passed to the callback is initialized in a separate function makeCut s The callback is then created and used to with the noswot cuts by calling Cplex use new Callback makeCuts cplex 1p We should point out that IloCplex provides an easier way to manage such cuts in a case like this where all cuts can be easily enumerated before starting the optimization Calling the methods cplex addCut and cplex addCuts allows you to copy the cuts to IloCplex before the optimization Thus instead of creating and using the callback we could have written cplex addCuts makeCuts var as shown in example iloadmipex4 cpp in the distribution During branch amp cut ILOG CPLEX will consider adding individual cuts to its representation of the model only if they are violated b
38. int matind_p double matval_p double lb_p double ub p char ctype p char zprobname NULL Problem name lt 16 characters double zobj NULL double zrhs NULL char zsense NU LL int zmatbeg NULL int zmatcnt NULL int zmatind NULL double zmatval NULL double zlb NULL double zub NULL char zctype NULL int status 0 zprobname char malloc 16 sizeof char j zobj double malloc NUMCOLS sizeof double zrhs double malloc NUMROWS sizeof double ILOG CPLEX 8 1 USER S MANUAL 283 EXAMPLE 284 USING SOS AND PRIORITY zsense char malloc NUMROWS sizeof char zmatbeg int malloc NUMCOLS sizeof int zmatcnt int malloc NUMCOLS sizeof int zmatind int malloc NUMNZ sizeof int zmatval double malloc NUMNZ sizeof double zlb double malloc NUMCOLS sizeof double zub double malloc NUMCOLS sizeof double zctype char malloc NUMCOLS sizeof char if zprobname NULL zobj NULL zrhs NULL zsense NULL zmatbeg NULL zmatcnt NULL zmatind NULL zmatval NULL zlb NULL zub NULL zctype NULL status 1 goto TERMINATE strcpy zprobname example The code is formatted to make a visual correspondence between the mathematical linear program and the specific data ite
39. is provided to do so with only one function call double x cplex getValues vars Similarly slack values can be queried for the constraints in the active model using methods IloCplex getSlack or IloCplex getSlacks Printing the Solution to the Diet Model This can now be applied to solving the diet problem we discussed earlier and printing its solution IloCplex cplex new IloCplex IloNumVar Buy new IloNumVar nFoods if byColumn buildModelByColumn cplex data Buy varType else buildModelByRow cplex data Buy varType Solve model if cplex solve System out println System out println Solution status cplex getStatus System out println System out println cost cplex getObjValue for int i 0 i lt nFoods i System out println Buy i cplex getValue Buy i System out println The program extract starts by creating a new I1oCplex object and passing it along with the raw data in another object either to the method buildModelByColumn or buildModelByRow The array of variables returned by it is saved as array Buy Then the method solve is called to optimize the active model and upon success solution information is printed ILOG CPLEX 8 1 USER S MANUAL CHOOSING AN OPTIMIZER Choosing an Optimizer The solution algorithm used in the solve methods can be controlled and if necessary tailored to the particular needs
40. lsseeeeeee RI 259 Complete Program mipex1 C lsssseeeeseeeee n 260 Example Reading a MIP Problem from aFile eee eee eee eee 269 Complete Program ilomipex2 cpp 0 0 cette eee 269 Complete Program mipex2 c 1 6 eee 271 Example Using SOS and Priority llle 275 Complete Program ilomipex3 cpp 0 0 cece IRA 275 Complete Program mipex8 C islssseeeseeeeee n 277 More About Using ILOG CPLEX seeseesseeer n 289 Managing Input amp Output llssseeseseeeeeeee RR I hh nh 290 Understanding File Formats 0 00 cee eee RII 290 Managing Log Files the Log File Parameter 0 cee eee 295 Handling Message Channels the Output Channel Parameter 296 Handling Message Channels Callable Library Routines 20055 297 Example Using the Message Handler 0 00 0 cece tees 298 Using Query Routines in the Callable Library lesen enn 308 Using Surplus Arguments for Array Allocations llle eese 308 Example Using Query Routines nananana aana 309 Complete Program lpex7 C ssslsseseseeee mmn 310 Goals in lloCplex pii e iR e EA edd Ee RE D qaweqir EE da aussi fms 319 The Goal Stack aii osos I bed pA maipiedesTQOTiienrag q e eese 325 Memory Management and Goals 0 000 cece teens 326 GCSE ECD Ie PCR 327 ILOG CPLEX 8 1 USER S MANUAL TABLE OF CONTENTS In
41. lt 20 c add x 0 3 x 1 x 2 lt 30 c add x 1 3 5 x 3 e 0 model add c END populatebyrow Complete Program mipex1 c The example derives from 1pex8 c Here are the differences between that linear program and this mixed integer program The problem to solve is slightly different It appears in Sample Stating a MIP Problem on page 224 The routine setproblemdata has a parameter ctype to set the types of the variables to indicate which ones must assume integer values The routine CPXcopyctype associates this data with the problem that CPXcreateprob creates The example calls CPXmipopt to optimize the problem rather than CPX1popt ILOG CPLEX 8 1 USER S MANUAL EXAMPLE OPTIMIZING A BASIC MIP PROBLEM The example calls the routines CPXgetstat CPXgetmipobjval CPXgetmipx and CPXgetmipslack instead of CPXsolution to get a solution We do not get dual variables this way If we want dual variables we must do the following e Use CPXchgprobtype to change the problem type to CPXPROB_FIXEDMILP e Then call CPXprimopt to optimize that problem e Then use CPXsolution to get a solution to the fixed problem a UU DRM File examples src mipexl c Version 8 1 p o Copyright C 1997 2002 by ILOG All Rights Reserved rd Permission is ex
42. status CPXERR NEGATIVE SURPLUS amp amp status 0 fprintf stderr Could not determine amount of space for column names n goto TERMINATE cur colnamespace surplus if cur colnamespace gt 0 cur colname char malloc sizeof char cur numcols cur colnamestore char malloc cur colnamespace if cur colname NULL cur colnamestore NULL fprintf stderr Failed to get memory for column names Nin status 1 goto TERMINATE status CPXgetcolname env lp cur_colname cur_colnamestore cur colnamespace amp surplus 0 cur numcols 1 if status 4 fprintf stderr CPXgetcolname failed n goto TERMINATE ILOG CPLEX 8 1 USER S MANUAL 315 z EN 563 O 2 oS Us a UE Q USING QUERY ROUTINES IN THE CALLABLE LIBRARY else printf No names associated with problem Using Fake names n Write out the solution for j 0 j lt cur_numcols j if cur_colnamespace gt 0 printf 16s cur_colname j else printf Fake 6 6d so me e printf 17 10g x J if cstat NULL switch cstat j case CPX_AT_LOWER basismsg Nonbasic at lower bound break case CPX_BASIC basismsg Basic break case CPX_AT_UPPER basismsg Nonbasic at upper bound break case CPX_FREE_SUPER basismsg Superbasic or free variable at zero break default basismsg Bad basis stat
43. 2 threads Real time 0 16 Critical time total 0 00 Spin time average 0 02 Il e i HG o 0 Q Total sequential parallel Cover cuts applied 1 Flow cuts applied 45 Gomory fractional cuts applied 6 Integer optimal solution Objective 3 9830000000e 03 Solution time 0 72 sec Iterations 1187 Nodes 41 The summary at the end of the sample tells us that 0 55 seconds were spent in the sequential phase that is all the combined steps preprocessing root relaxation solution cutting planes heuristic that occur at the root before the first branch occurs The parallel part of this sample run took 0 16 seconds of real time that is elapsed time for that phase Other parts of the sample report indicate that the processors spent an average of 0 02 seconds of real time spinning that is waiting for work while there were too few active 378 ILOG CPLEX 8 1 USER S MANUAL USING PARALLEL OPTIMIZERS nodes available The real critical time was a total of 0 00 seconds time spent by individual processors in updating global shared information Since only one processor can access the critical region at any instant in time the amount of time spent in this region really is crucial any other processor that tries to access this region must wait thus sitting idle and this idle time is counted separately from the spin time There is another difference in the way logging occurs in the parallel MIP optimizer When th
44. 291 objective function 138 variable bounds 138 piecewise linear expression 35 piecewise linear functions 61 single LP 69 populating problem object 86 181 portability 95 PPE file format 291 PRE file format 291 PreCompress 135 preprocessing barrier optimizer 167 dense columns removed 171 dependency parameter 167 IIS files and 147 infeasibility detected in 143 infeasibility finder and 148 MIPs 239 network optimizer and 181 starting point heuristics and 168 presolve 71 presolve compression parameter 129 presolver barrier preprocessing 167 file format to save reduced problem 291 pricing algorithms 179 primal feasibility 157 primal simplex algorithm 71 primal simplex optimizer 125 perturbing variable bounds 138 stalling 138 see also simplex primal variables 133 USER S MANUAL 417 INDEX primal degenerate problem 125 primal dual barrier optimizer see barrier optimizer PrimalPricing class 71 priority 241 derived from set members 245 file format for orders 291 order 240 245 special ordered sets SOSs and 245 priority orders 72 probing parameter 238 problem analyzing infeasible 44 solving with Concert Technology Library 31 problem formulation barrier 157 dual 157 159 ill conditioned 140 infeasibility reports 139 linear 22 network 177 network flow 176 primal 157 159 removing dense columns 167 switching from network to LP 188 189 problem modification routines 84 problem object creating 86
45. CPXget cols routine 308 309 CPXgetctype routine 226 CPXgetdblparam routine 92 98 CPXgetdblquality routine 138 143 164 CPXgeterrorstring routine 181 351 CPXgetintparam routine 92 98 CPXgetintquality routine 164 CPXgetmipob jval routine 261 271 CPXgetmipslack routine 261 CPXgetmipx routine 261 271 CPXgetnumcols routine 91 CPXgetrowindex routine 93 CPXgetrowname routine 91 CPXgetsos routine 226 CPXgetstat routine 261 271 350 CPXgetstrparam routine 92 98 CPXget x routine 88 CPXiiswrite routine 144 190 CPXinfodblparam routine 92 98 CPXinfointparam routine 92 98 CPXinfostrparam routine 92 98 cpxlog message channel 297 CPXlpopt 215 CPXlpopt routine 101 352 CPXLPptr data type 89 ILOG CPLEX 8 1 CX C CY Gi Cb Qv Cb OQ QC x Ck CL OQ CX Q x Qr CY QUO Ong XX OE OX OQ Oc C CO QV Q0 CY CX CY Q0 O2 Q O INDEX PXmbasewrite routine 130 PXmemcpy routine 96 PXMIP ABORT FEAS symbolic constant 351 PXMIP ABORT INFEAS symbolic constant 351 PXmipopt routine 260 271 PXmsg routine 85 95 298 299 PXmsgstr routine 96 PXNETaddarcs routine 181 PX addnodes routine 181 PX checkcopynet routine 94 PX chgob jsen routine 182 PX createprob routine 89 181 PX delnodes routine 182 PX freeprob routine 182 PX primopt routine 182 190 PXNETptr data type 89 PX solution routine 182 PXnewcols routine 86 101 114 PXnewrows routine 86 114 PXopenCPLEX routine 85 89 98 101 151
46. Generalized Upper Bound GUB Cover Cuts A GUB constraint for a set of binary variables is a sum of variables less than or equal to one If the variables in a GUB constraint are also members of a knapsack constraint then the minimal cover can be selected with the additional consideration that at most one of the members of the GUB constraint can be one in a solution This additional restriction makes the GUB cover cuts stronger that is more restrictive than ordinary cover cuts Implied Bound Cuts In some models binary variables imply bounds on continuous variables ILOG CPLEX generates potential cuts to reflect these relationships Mixed Integer Rounding MIR Cuts MIR cuts are generated by applying integer rounding on the coefficients of integer variables and the right hand side of a constraint Adding Cuts and Re Optimizing Each time ILOG CPLEX adds a cut the subproblem is re optimized ILOG CPLEX repeats the process of adding cuts at a node until it finds no further effective cuts It then selects the branching variable for the subproblem 236 ILOG CPLEX 8 1 USER S MANUAL USING THE MIXED INTEGER OPTIMIZER Parameters Affecting Cuts Parameters control the way each class of cuts is used Those parameters are listed in Table 8 7 Table 8 7 Parameters for Controlling Cuts Cut Type interactive Command Concert Technology Callable Library Library Parameter Parameter Clique s
47. IloNumExpr x01 model prod 200 model prod x 0 x 1 IloNumExpr Q model prod 0 5 model sum x00 x11 x01 model add model minimize Q i Again the user could choose to simplify the above expression algebraically if that suits the purposes of the program better Finally a Callable Library program in C might construct the quadratic objective function in a way similar to the following zgmatind 0 0 zqmatind 2 0 zqmatval 0O 100 0 zqmatval 2 100 0 zgmatind 1 1 zqmatind 3 1 zqgmatval 1 100 0 zqmatval 3 100 0 To re emphasize the point about the factor of 1 2 in any of these methods if the above objective function is evaluated with a solution of x1 1 000000 and x2 3 000000 the result to be expected is 200 not 400 Saving QP Problems After you enter a QP problem whether interactively or by reading a formatted file you can then save the problem in a formatted file The formats available to you are LP MPS and SAV When you save a QP problem in one of these formats the quadratic information will also be recorded in the formatted file In addition you can save the quadratic part of a problem in a QP file a formatted file with the extension qp as described on page 291 To do so In the Interactive Optimizer use the write command In the Callable Library use the routine CPXqpwrite Writing a QP format file is not supported by IloCplex Changing Problem Type in QPs
48. Messages from multiple channels may be sent to one destination All predefined ILOG CPLEX channels can be directed to a single file by a call to CPXsetlogfile Similarly all predefined ILOG CPLEX channels except cpx1og can be directed to the screen using the CPX PARAM SCRIND parameter For a finer level of control or to define ILOG CPLEX 8 1 USER S MANUAL 297 MANAGING 298 INPUT amp OUTPUT destinations for application specific messages use the following message handling routines all documented in the ILOG CPLEX Reference Manual cPXmsg writes a message to a predefined channel Q PXflushchannel flushes a channel to its associated destination Q CPXdisconnectchannel flushes a channel and clears its destination list Q PXdelchannel flushes a channel clears its destination list frees memory for that channel Q PXaddchannel adds a channel Q PXaddfpdest adds a destination file to the list of destinations associated with a channel Q PXdelfpdest deletes a destination from the destination list of a channel cPXaddfuncdest adds a destination function to a channel CPXdelfuncdest deletes a destination function to a channel Once channel destinations are established messages can be sent to multiple destinations by a single call to a message handling routine User written EO aati PXa est a application ea oe 2 Destin
49. Note The discussion of the details of using goals will be presented mainly in terms of the C library The Java library follows the same design and is thus equivalent In cases where a difference between the C and Java API needs to be observed the point will be raised Where the difference is only in syntax the Java syntax will be mentioned in parentheses following the C syntax In C goals are implemented in objects of type 11oCplex GoalI having handle class IloCplex Goal In Java goals are implemented in objects of type IloCplex Goal and there are no handle classes The method IloCplex GoallI execute IloCplex Goal execute is where all the control is implemented This method is called by 11oCplex after a node relaxation has been solved and all cuts have been added Invoking method execute of a goal is often referred to as executing a goal When method execute is executed the member functions of class I1o0Cplex GoalI ILOG CPLEX 8 1 USER S MANUAL 319 z a D3 qe oS Us a UE Q GOALS 320 IN ILOCPLEX IloCplex Goal can be called to query information about the current node problem and the solution of its relaxation Typically the implementation of method execute will perform the following steps 1 Check feasibility An interesting possibility here is that the feasibility check may include more than verifying integrality of the solution This allows you to enforce constraint
50. That error code can be transformed into a string by the Callable Library routine CPXgeterrorstring After main initializes the ILOG CPLEX environment it uses the Callable Library routine CPXsetintparam to turn on the ILOG CPLEX screen indicator parameter CPX_PARAM_SCRIND so that ILOG CPLEX output appears on screen If this parameter is turned off ILOG CPLEX does not produce viewable output neither on screen nor in a log file We recommend turning this parameter on when you are debugging your application The Callable Library routine CPXNETcreateprob creates an empty problem object that is a minimum cost network flow problem with no arcs and no nodes The function buildNetwork populates the problem object that is it loads the problem data into the problem object Pointer variables in the example are initialized as NULL so that you can check whether they point to valid data a good programming practice The most important calls in this function are to the Callable Library routines CPXNETaddnodes which adds nodes with the specified supply values to the network problem and CPXNETaddarcs which adds the arcs connecting the nodes with the specified objective values and bounds In this example both routines are called with their last argument NULL indicating that no names are assigned to the network nodes and arcs If you want to name arcs and nodes in your problem pass an array of strings instead The function
51. The quadratic coefficient of an off diagonal term must be distributed within the Q matrix and it is always one half the value of the quadratic algebraic term To clarify that terminology consider this example Minimize a b I 2 4ab 7b ILOG CPLEX 8 1 USER S MANUAL 199 CHANGING QUADRATIC TERMS 200 subject to a b 2 10 with these bounds a 2 0 and b 20 The off diagonal quadratic algebraic term in that example is 4 so the quadratic matrix Q is E Ina QP you can change the quadratic matrix coefficients in the Interactive Optimizer by using the command change qpterm From the Callable Library use the routine CPXchgqpcoef to change quadratic matrix coefficients Concert Technology does not support direct editing of expressions other than linear expressions Consequently to change a quadratic objective function you need to create an expression with the modified quadratic objective and use the setExpr method of IloObjective to install Changing an off diagonal element changes the corresponding symmetric element as well In other words if a call to CPXchgapcoef changes Qj to a value it also changes Qj to that same value To continue our example if we want to change the off diagonal quadratic term from 4 to 6 we would use this sequence of commands in the Interactive Optimizer CPLEX gt change qpterm Change which quadratic term variable variable a b Present quadratic term
52. USER S MANUAL EXAMPLE DIETARY OPTIMIZATION void usage const char name cerr lt lt endl cerr lt lt usage name lt lt options lt file gt lt lt endl E cerr lt lt options c build model by column lt lt endl 9 cerr i use integer variables endl cerr lt lt endl oO ey 2 c typedef IloArray lt IloNumArray gt IloNumArray2 e lt void buildModelByRow IloModel mod IloNumVarArray Buy const IloNumArray foodMin const IloNumArray foodMax const IloNumArray foodCost const IloNumArray nutrMin const IloNumArray nutrMax const IloNumArray2 nutrPer IloNumVar Type type IloEnv env mod getEnv Buy clear IloNumVarArray tmp env foodMin foodMax type Buy add tmp tmp end IloInt i j IloInt n foodCost getSize IloInt m nutrMin getSize mod add IloMinimize env IloScalProd Buy foodCost for i 0 i lt m i IloExpr expr env for j 0 j lt n j expr Buy j nutrPer i jl mod add nutrMin i lt expr lt nutrMax i expr end void buildModelByColumn IloModel mod IloNumVarArray Buy const IloNumArray foodMin const IloNumArray foodMax const IloNumArray foodCost ILOG CPLEX 8 1 USER S MANUAL 55 EXAMPLE DIETARY OPTIMIZATION const IloNumArray const IloNumArray const IloNumArray2 IloNumVar Type loEnv env mod getEnv loInt i j loInt n foodCos
53. USER S MANUAL USING CALLBACKS fprintf stderr s errmsg return status END main This function builds by column the linear program Maximize obj xl 2 x2 3 x3 Subject To Cl xl x2 x3 lt 20 C2 xl 3 x2 x3 lt 30 Bounds 0 lt x1 lt 40 End RY static int populatebycolumn CPXENVptr env CPXLPptr lp int status 0 double obj NUMCOLS double lb NUMCOLS double ub NUMCOLS char colname NUMCOLS int matbeg NUMCOLS int matind NUMNZ double matval NUMNZ double rhs NUMROWS char sense NUMROWS char rowname NUMROWS To build the problem by column create the rows and then add the columns CPXchgobjsen env lp CPX MAX Problem is maximization Now create the new rows First populate the arrays z E 563 O 2 oS Us a UE Q rowname 0 c1 sense 0 L rhs 0 20 0 rowname 1 c2 sense 1 L rhs 1 30 0 status CPXnewrows env lp NUMROWS rhs sense NULL rowname if status goto TERMINATE ILOG CPLEX 8 1 USER S MANUAL 357 USING CALLBACKS 358 Now add the new columns First populate the arrays obj 0 1 0 obj 1 matbeg 0 0 matbeg 1 matind 0 0 matind 2 matval 0 1 0 matval 2 matind 1 1 matind 3 matval 1 1 0 matval 3 lb 0 0 0 lb 1 ub 0 40 0 ub 1 colname 0 x1 colname 1 status
54. all default parameters 41 99 callbacks to null 41 99 customized parameters 400 parameter specification file 400 parameters 41 98 400 see also changing setUB 82 simplex dual 125 optimizer 158 primal 125 see also dual simplex optimizer see also primal simplex optimizer simplex optimizer parallel 379 SimThreads 376 singularity 138 slack variable accessing values 43 slack variables 133 solution accessing quality information 45 basic infeasible primal 139 basis 158 binary files for 290 complementary 157 differences between barrier simplex 158 example QP 215 feasible in MIPs 240 file format for nonbasis 292 incumbent 232 infeasible basis 172 midface 158 nonbasis 158 quality 163 164 169 supplying first integer in MIPs 240 text file for 292 verifying 169 solution algorithm 69 solution value accessing 43 solve a single LP 69 solve member function 420 ILOG CPLEX 8 1 IloCplex class 39 42 44 45 46 53 solve subsequent LPs or QPs in a MIP 70 solving model 39 solving the diet problem 68 SOS branching priority 245 file format for 291 type 1 37 type 2 37 using 244 weights in 246 SOS file format 245 291 sparse matrix 74 Special Ordered Set SOS see SOS special ordered sets 61 single LP 69 speed increase 375 square 62 stalling 138 starting algorithm parallel processing 376 static variables 87 status variables using 352 steepest edge pricing 132 254 string 70 StringParam 70 stro
55. char amp ub free and null char amp nutrmin free and null char amp nutrmax free and null char amp x return status END main static int populatebyrow CPXENVptr env CPXLPptr lp int nfoods double cost double lb double ub int nnutr double nutrmin double nutrmax double nutrper int status 0 int zero 0 int ind NULL int i Jy ind int malloc nfoods sizeof int if ind NULL status CPXERR NO MEMORY goto TERMINATE for j 0 j nfoods ind j ji j status if status CPXnewcols env lp goto TERMINATE nfoods cost lb ub NULL NULL for i 0 i lt nnutr itt ILOG CPLEX 8 1 USER S MANUAL the errors will be seen if the CPX_PARAM_SCRIND indicator is set to CPX_ON EXAMPLE DIETARY OPTIMIZATION double rng nutrmax i nutrmin i status CPXaddrows env lp 0 1 nfoods nutrminti R amp zero ind nutrper i NULL NULL if status goto TERMINATE status CPXchgrngval env lp 1 amp i amp rng if status goto TERMINATE TERMINATE free and null char amp ind return status END populatebyrow To populate by column we first create the rows and then add the columns static int populatebycolumn CPXENVptr env CPXLPptr lp int nfoods double cost double lb double ub int nnutr double nutrmin double nutrmax double nutrper int st
56. endl cerr lt lt MPS SAV or LP lower case is allowed lt lt endl cerr lt lt Exiting lt lt endl As this example is an extension of example ilogoalex1 cpp we shall only concentrate on the differences Also we will discuss the example only in terms of the C version the Java version has identical structure and design and differs only in syntax The first is the definition of class DepthEvaluatorlI as a subclass of TloCplex NodeEvaluatorl It implement methods evaluate and duplicateEvaluator Method evaluate simply returns the negative depth value queried for the current node by calling method getDepth Since IloCplex by default chooses nodes with the lowest evaluation value this evaluator will favor nodes deep in the tree Method duplicateEvaluator simply returns a copy of the invoking object by ILOG CPLEX 8 1 USER S MANUAL GOALS IN ILOCPLEX calling the default copy constructor Along with the class we also define function DepthEvaluator which creates an instance of class DepthEvaluatorI and returns a handle to it Similarly we define class 118umEvaluatorI and function IISumEvaluator The evaluate method returns the negation of the sum of integer infeasibilities of the node being evaluated This number is obtained by calling method get InfeasibilitySum Thus this evaluator favors nodes with larger sums of integer infeasibilities This example uses t
57. for int i 0 i lt num i lin addTerm value i variable il It should be noted that the special case of the scalar product of an array of values with an array of variables is directly supported through the method scalProd Thus the above loop can be rewritten as IloLinearNumExpr lin cplex scalProd value variable It is recommended that you build expressions in terms of data that is either integer or double precision 64 bit floating point Single precision 32 bit floating point data should ILOG CPLEX 8 1 USER S MANUAL MODELING WITH CONCERT TECHNOLOGY be avoided as it can result in unnecessarily ill conditioned problems For more information refer to Numerical Difficulties on page 135 Ranged Constraints Ranged constraints are constraints of the form 1b lt expression Sub and are represented in Concert Technology by objects of type IloRange The most general constructor is IloRange rng cplex range lb xpr ub name where 1b and ub are double values expr is of type IloNumExpr and name is a string By choosing the range bounds appropriately ranged constraints can be used to model any of the more commonly found constraints of the form expr rel rhs oon on t 35 where re1 is the relation S or 2 The following table shows how to choose 1b and ub for modeling these relations e re E c8 g lt cs 05 29 o o Q lt put fa Table 2 1 Choosing Lower an
58. if lp NULL fprintf stderr Failed to create LP object Nn goto TERMINATE Copy LP representation of network problem to lp object along with the current basis available in the network object status CPXcopynettolp env lp net if status fprintf stderr Failed to copy network as LP n goto TERMINATE Optimize the LP with primal to create an LP solution This optimization will start from the basis previously generated by CPXNETprimopt as long as the advance indicator is switched on its default status CPXsetintparam env CPX PARAM LPMETHOD CPX ALG PRIMAL if status fprintf stderr Failure to set LP method error d n status goto TERMINATE status CPXlpopt env lp if status fprintf stderr Failed to optimize LP n goto TERMINATE Find IIS and write it to a file status CPXiiswrite env lp netex2 iis if status fprintf stderr Failed to find IIS or write IIS file n goto TERMINATE printf IIS written to file netex2 iis n else printf Network problem not proved to be infeasible n TERMINATE 192 ILOG CPLEX 8 1 USER S MANUAL Lf if Af EXAMPLE NETWORK TO LP TRANSFORMATION Free up the problem as allocated by CPXNETcreateprob if necessary net NULL CPXNETfreeprob env amp net if status fprintf stderr CPXNETfreeprob failed er
59. maximum row residual 142 memory 254 memory allocation 166 memory leaks 34 memory management 134 253 refactoring frequency and 135 message channel 414 ILOG CPLEX 8 1 diagnostic routines and 94 message handler example 298 MILP definition 69 MIN file format 291 minimal covers recorded in MIP node log file 248 minimization convex QPs 196 see also optimization upper cutoff parameter 253 minimize 64 MIP 223 to 287 active model 69 branch amp cut 69 changing variable type 228 memory problems and 253 optimizer 223 problem formulation 224 progress reports 246 relaxation algorithm 257 solution information 243 subproblem algorithm 257 subproblems 256 supplying first integer solution 240 terminating optimization 241 MIP optimizer solution information 243 IPEmphasis 229 ipThreads 376 MIQP definition 69 MIR cuts 236 Mixed Integer Programming MIP problem see MIP model active 64 adding objects 45 adding submodels 36 deleting objects 46 extracting 38 manipulations 61 modifying 82 notifying changes to cplex object 45 USER S MANUAL removing objects 45 solving 32 37 39 solving with IloCplex 53 modeling columnwise 50 100 objects 32 rowwise 49 100 modeling by column 61 75 modeling variable IloNumVar 61 modelling variables create 61 modifying a model 82 MPS file format BAS files and 290 CPLEX extensions 293 defined 291 DUA format 290 proprietary information in 291
60. parallel 379 performance tuning 165 preprocessing 167 primal dual 126 quadratic 195 to 221 row ordering algorithms 167 simplex optimizer and 158 solution quality 163 solving LP problems 156 starting point heuristics 168 unbounded optimal face and 171 unbounded problems 172 uses 158 working storage allocation 166 BarThreads 376 BAS file format 130 138 290 basis 73 accessing information 43 condition number 137 141 crossover algorithms 158 current 85 file formats to save 290 291 previous optimal 87 removing objects from 46 saving best so far 138 unstable optimal 141 see also advanced basis Best Bound 233 Best Estimate 233 bibliography 30 BIN file format 290 Boolean or semi continuous variables single LP 69 boolVar 62 404 ILOG CPLEX 8 1 boolVarArray 62 bound violation 142 Bounded return status 67 branch amp cut 69 algorithm 231 parallel processing 375 parameters 232 solves MIP models 229 tree 231 branch amp cut algorithm memory problems and 253 priority order 240 special ordered sets SOS 244 storing tree nodes 254 tree subproblems 257 branching directions 72 BtTol 233 C C parameter names 385 Calable Library parameter names 385 call by value 88 Callable Library categories of routines 84 core 84 debugging and 118 description 21 parallel optimizers 374 parameters 98 using 83 to 111 see also individual CPXxxx routines callback graphic user interface and 352 resetting to nu
61. reference row values 246 REW 291 saving basis 290 saving dual 290 saving embedded network 290 saving modifications 294 saving QP 198 weights 246 MST file format 291 multithreaded application needs multiple environments 85 N name 63 namespace conflicts 88 naming arcs in network flow 181 conventions 293 log file 295 node file 255 nodes in network flow 181 negative 62 Nested parallel processing 376 NET file format 182 291 NetItLim 179 ILOG CPLEX 8 1 INDEX network converting to LP model 188 embedded 179 infeasibility in 177 modeling variables 176 problem formulation 176 177 network extractor 180 Network Flow problem see network network object 176 network optimizer 126 175 to 181 column growth parameter 182 file format to save extracted network 290 preprocessing and 181 problem formulation 177 row growth parameter 182 turn off preprocessing 181 nexample net 178 node 319 demand 177 from 176 head 176 sink 177 source 177 supply 177 tail 176 to 176 transshipment 177 node file 254 cpx name convention 255 node log 246 node problem 319 node selection strategy best estimate 256 depth first search 256 nondeterminism 373 nonseparable 196 notation 26 notation in this manual 26 notifying changes to cplex object 45 numbering conventions C 121 Fortran 121 row column order 292 USER S MANUAL 415 INDEX numerical difficulties 135 170 barrier growth parameter 171 basis condition number a
62. so no iterations are required to optimize the problem 150 ILOG CPLEX 8 1 USER S MANUAL EXAMPLE USING A STARTING BASIS IN AN LP PROBLEM The application begins with declarations of arrays to store the solution of the problem Then before it calls any other ILOG CPLEX routine the application invokes the Callable Library routine CPXopenCPLEX to initialize the ILOG CPLEX environment Once the environment has been initialized the application calls other ILOG CPLEX Callable Library routines such as CPXsetintparam with the argument CPX PARAM SCRIND to direct output to the screen and most importantly CPXcreateprob to create the problem object The routine populatebycolumn builds the problem object and as we noted earlier CPXcopybase copies the advanced starting basis Before the application ends it calls CPX reeprob to free space allocated to the problem object and CPXcloseCPLEX to free the environment Complete Program The complete program 1pex6 c appears here and online in the standard distribution File examples src lpex6 c Version 8 1 x a Copyright C 1997 2002 by ILOG All Rights Reserved x7 Permission is expressly granted to use this example in the course of developing applications that use ILOG products prr lpex6 c Illustrates that optima
63. status CPXcopylp env lp numcols numrows objsen obj rhs sense matbeg matcnt matind matval lb ub NULL if status fprintf stderr Failed to copy problem data n goto TERMINATE Now copy the ctype array Status CPXcopyctype env lp ctype if status 4 fprintf stderr Failed to copy ctype n goto TERMINATE Write a copy of the problem to a file status CPXwriteprob env lp mipex3 mps NULL if status fprintf stderr Failed to write LP to disk n goto TERMINATE Set up the SOS set and priority order 280 ILOG CPLEX 8 1 USER S MANUAL EXAMPLE USING SOS AND PRIORITY status setsosandorder env lp if status goto TERMINATE Turn off CPLEX presolve aggregate and print every node This is just to make it interesting Turning off CPLEX presolve is NOT recommended practice status CPXsetintparam env CPX PARAM PREIND CPX OFF if status CPXsetintparam env CPX PARAM AGGIND CPX OFF if status CPXsetintparam env CPX PARAM MIPINTERVAL 1 if status fprintf stderr Failed to set some CPLEX parameters Nn goto TERMINATE Optimize the problem and obtain solution status CPXmipopt env lp if status fprintf stderr Failed to optimize MIP n goto TERMINATE solstat CPXgetstat env 1p Write the output to the screen printf nSolution status d n solstat status CPXge
64. still looking Heuristic complete O 0 436 0000 0 436 0000 405 2891 5288 7 04 ILOG CPLEX 8 1 USER S MANUAL PROGRESS REPORTS INTERPRETING THE NODE LOG Periodically if the MIP display parameter is 2 or greater ILOG CPLEX records the cumulative time spent since the beginning of the current MIP optimization and the amount of memory used by branch amp cut By periodically we mean that time and memory information appears either every 20 nodes or ten times the MIP display parameter whichever is greater The following example shows you one line from a node log file indicating elapsed time and memory use Elapsed b amp c time 120 01 sec tree size 0 09 MB The Interactive Optimizer prints an additional summary line in the log if optimization stops before it is complete This summary line shows the best MIP bound that is the best objective value among all the remaining node subproblems The following example shows you lines from a node log file where an integer solution has not yet been found and the best remaining objective value is 2973 9912281 Node limit no integer solution Current MIP best bound 2 9739912281e 03 gap is infinite Solution time 0 01 sec Iterations 68 Nodes 7 7 Sample Stating a MIP Problem on page 224 presents a typical MIP problem Here is the node log file for that problem with the default setting of the MIP display parameter Tried aggregator 1 time Aggregator did 1 substitutions
65. w34 w35 loNumVar w41 w42 w43 w44 w45 loNumVar w51 w52 w53 w54 w55 loInt num vars getSize for IloInt i 0 i lt num i 4t stremp vars i getName X11 0 x11 vars il else if strcmp vars i getName X12 0 x12 vars i z else if strcemp vars i getName X13 0 x13 vars i Q else if strcmp vars i getName X14 0 x14 vars i o D else if strcmp vars i getName X15 0 x15 vars i Q E else if strcomp vars i getName X21 0 x21 vars i O 0 else if strcmp vars i getName X22 0 x22 vars i m S else if strcmp vars i getName X23 0 x23 vars i mc else if strcmp vars i getName X24 0 x24 vars i x Y else if strcomp vars i getName X25 0 x25 vars i a else if strcmp vars i getName X31 0 x31 vars i else if strcmp vars i getName X32 0 x32 vars i else if strcmp vars i getName X33 0 x33 vars i else if strcomp vars i getName X34 0 x34 vars i else if strcemp vars i getName X35 0 x35 vars i else if strcomp vars i getName X41 0 x41 vars i else if strcmp vars i getName X42 0 x42 vars i else if strcmp vars i getName X43 0 x43 vars i else if strcmp vars i getName X44 0 x44 vars i ILOG CPLEX 8 1 USER S MA
66. 0 zsense 0 L zmatval 0 1 0 zmatval 2 1 0 zmatval 4 1 0 zrhs 0 20 0 zmatind 1 1 zmatind 3 1 zmatind 5 1 zsense 1 L zmatval 1 1 0 zmatval 3 3 0 zmatval 5 1 0 zrhs 1 30 0 zlb 0 0 0 zlb 1 0 0 zlb 2 0 0 zub 0 40 0 zub 1 CPX INFBOUND zub 2 CPX INFBOUND Now set up the Q matrix Note that we set the values knowing that we re doing a maximization problem so negative values go on the diagonal Also the off diagonal terms are each repeated by taking the algebraic term and dividing by 2 Il I I zqmatbeg 0 zqmatcnt 0 0 zqmatbeg 1 2 zqmatbeg 2 5 23 zqmatcnt 1 E zqmatcnt 2 2 ll II Il Matrix is set up visually Note that the x1 x3 term is 0 and is left out of the matrix zqmatind 0 0 zqmatind 2 0 zqgmatval 0 33 0 zqmatval 2 6 0 zqmatind 1 1 zqmatind 3 1 zqmatind 5 1 ILOG CPLEX 8 1 USER S MANUAL 213 EXAMPLE 214 CREATING A QP OPTIMIZING FINDING A SOLUTION zqmatval 1 6 0 zqmatval 3 22 0 zgmatval 5 11 5 zqmatind 4 2 zgmatind 6 2 zqmatval 4 11 5 zqmatval 6 11 0 TERMINATE if status free and null char amp zprobname free and null char amp zobj free and null char amp zrhs free and null char amp zsense free and null char amp zmatbeg free and null char amp zmatcnt free and null c
67. 4 Symbolic Constant o9 bey bea Mae eX ead tae ie is edad eder EE 91 Parameter Routines 0 2 0 sawna ita E a ee eee rn 91 NUILATQUMeNISi nes ce xia dds inca ORDRE EUR Poe RR eho i ee eae ea oes 92 Row and Column References 0 000 eee e eect eee ee 92 Character Strings seiri iiaa aara a eet ns 93 Checking Problem Data 2 4 222 n mre ache Reg ERRARE ER RRRRE ds bad AG 93 Callbacks 4am EHE 94 Portability 2 eae Gad be Pee eae iE AEN OE eet eee eile Se eed Gates 95 FORTRAN Interface cote een ged OR eves aes et eee eee 96 CHa Interface isi hace ee ee dae Re ERU A E EEA I Deana Wawa Ee Rae Eee 97 Managing Parameters from the Callable Library 00 cece eee eee eee 98 Example Dietary Optimization cece eee RII 99 Program Descriptiori x 2 eke ed ke DR er aci qux dre Ros eta oe dae mes 101 Complete Program oss ss eso aadis cc mn 102 Further Programming Considerations leslie 113 Tips for Successful Application Development eseseeeeeeeeeeeene 113 Prototype the Model er ec ee doc Ege xe ee eno Od a ae 113 Identify Routines to Use 0 2 eee nh 114 Testlriteractively i22 un Pea tend E E od Pa GES ele SEE eis 114 Assemble Data Efficiently sls 114 TESDA RP ETM 115 Choose an Optimizer 0 0 0 s 115 Program with a View toward Maintenance and Modifications cles 116 Using the Interactive Optimizer for Debugging leeseeeeen
68. 4 CPX_VARSEL_PSEUDOREDUCED Use pseudo reduced costs which is a computationally less intensive version of pseudo costs Once a variable has been selected for branching the BrDir parameter influences the direction up or down of the branch on that variable to be explored first Table 8 6 BrDir Parameter Values for Branching Direction Choice Pre Symbolic Value Branching Direction Choice Value 0 CPX BRANCH GLOBAL ILOG CPLEX makes the determination of Default each branch direction 1 CPX BRANCH DOWN Branch downward 1 CPX BRANCH UP Branch upward Note that Priority Orders on page 240 complement the behavior of these parameters as a mechanism by which you supply problem specific directives about the order in which to branch on variables In a Priority Order you can also provide preferred branching directions for specific variables ILOG CPLEX 8 1 USER S MANUAL USING THE MIXED INTEGER OPTIMIZER Cuts Cuts are constraints added to a model to restrict cut away noninteger solutions that would otherwise be solutions of the continuous relaxation The addition of cuts usually reduces the number of branches needed to solve a MIP In the following descriptions of cuts the term subproblem includes the root node that is the root relaxation Cuts are most frequently seen at the root node but they may be added by ILOG CPLEX at other nodes as conditions warrant ILOG CPLEX generates i
69. Buy3 0 Buy4 0 BuyS 6 14754 Buy6 0 Buy7 3 42213 Buy8 0 x 58 ILOG CPLEX 8 1 USER S MANUAL ILOG Concert Technology for Java Users In this chapter we explore the features ILOG CPLEX offers Java users to solve mathematical programming problems An overview of the architecture is given then techniques for creating models with ranged constraints and for creating objective functions are explained These elements are then used to build and solve the Dietary Optimization example model introduced in the last chapter A user written application first creates an IloCplex object It then uses the Concert Technology modeling interface implemented by 11oCplex to create the variables the constraints and the objective function of the model to be solved For example every variable in a model is represented by an object that implements the Concert Technology variable interface IloNumVar The user code only accesses the variable through its Concert Technology interface Similarly all other modeling objects are only accessed through their respective Concert Technology interfaces from the user written application while the actual objects are maintained in the ILOG CPLEX database Figure 2 1 illustrates how an application uses Concert Technology IloCplex and the ILOG CPLEX database The Java interfaces represented by the dashed outline do not actually consume memory The ILOG CPLEX database includes the computing environment its co
70. C library or setting the RootAlg parameter to Network in the C and Java library When doing so ILOG CPLEX performs a sequence of steps It first searches for a part of the LP that conforms to network structure Such a part is known as an embedded network It then uses the network optimizer to solve that embedded network Next it uses the resulting basis to construct a starting basis for the full LP problem Finally it solves the LP problem with a simplex optimizer You can also use the network optimizer when solving QPs To do so using the C library you set the CPX_PARAM_QPMETHOD parameter to CPX ALG NET For C and Java the RootAlg parameter must be set to Network When ILOG CPLEX uses the network ILOG CPLEX 8 1 USER S MANUAL 179 SOLVING PROBLEMS WITH THE NETWORK OPTIMIZER 180 optimizer to solve a QP it first ignores the quadratic term and uses the network optimizer to solve the resulting LP as described above ILOG CPLEX then uses the resulting basis to start a simplex algorithm on the QP model with the original quadratic objective Network Extraction The ILOG CPLEX network extractor searches an LP constraint matrix for a submatrix with the following characteristics the coefficients of the submatrix are all 0 zero 7 one or minus one each variable appears in at most two rows with at most one coefficient of and at most one coefficient of ILOG CPLEX can perform different levels
71. CPLEX the Callable Library and the Interactive Optimizer require an explicit notion of a Problem Type to distinguish continuous LPs and ILOG CPLEX 8 1 USER S MANUAL CHANGING PROBLEM TYPE IN MIPS QPs from MIPs Techniques to determine the Problem Type with the Callable Library and the Interactive Optimizer are discussed in this topic When you enter a problem ILOG CPLEX determines the Problem Type from the available information If the problem is read from a file LP MPS or SAV format for example or entered interactively the Problem Type is determined as follows Table 8 2 Problem Type Definitions No Quadratic Has Quadratic Problem No Integer Has Integer Terms in the Terms in the Type Variables Variables Objective Objective Function Function lp X X qp X X milp X X miqp X X However if you enter a problem with no integer variables so that its Problem Type is initially 1p or qp and you then wish to modify the problem to contain integer variables this is accomplished by first changing the Problem Type to milp or miqp Conversely if you have entered an MILP or MIQP model and wish to remove all the integer declarations and thus convert the model to a continuous formulation you can change the Problem Type to 1p or qp Note that deleting each of the integer variable declarations individually still leaves the Problem Type as milp or miqp although in most instances the distinction betwee
72. CPXaddcols env lp 2 0 obj 2 3 0 2 matbeg 2 4 0 matind 4 0 1 0 matval 4 1 0 1 matind 5 1 3 0 matval 5 1 0 0 0 lb 2 0 0 CPX INFBOUND ub 2 CPX INFBOUND x2 colname 2 x3 NUMCOLS NUMNZ obj matbeg matind matval lb ub colname if status goto TERMINATE TERMINATE return status END populatebycolumn The callback function will print out the Phase of the simplex method the sum of infeasibilities if If any of our requests fails y static int CPXPUBLIC mycallback CPXCENVptr env void in Phase 1 or the objective if in Phase 2 we ll return an indication to abort cbdata int wherefrom void cbhandle int status 0 int phase 1 double suminf or objective int itcnt 1 if wherefrom CPX CALLBACK PRIMAL status CPXgetcallbackinfo env cbdata wherefrom CPX CALLBACK INFO ITCOUNT amp itcnt if status goto TERMINATE status CPXgetcallbackinfo env cbdata wherefrom CPX CALLBACK INFO PRIMAL FEAS amp phase if status goto TERMINATE if phase 0 status CPXgetcallbackinfo env cbdata wherefrom ILOG CPLEX 8 1 USER S MANUAL USING CALLBACKS CPX_CALLBACK_INFO_PRIMAL_INFMEAS amp suminf or objective if status goto TERMINATE printf Iteration d Infeasibility measure f n itcnt suminf or objective else
73. Concert Technology class for example IloNumArray the one dimensional array class for numerical data ILOG CPLEX 8 1 USER S MANUAL EXAMPLE DIETARY OPTIMIZATION Program Description The main program starts by declaring the environment and terminates by calling method end for the environment The code in between is encapsulated in a try block that catches all Concert Technology exceptions and prints them to the C error stream cerr All other exceptions are caught as well and a simple error message is issued The first action of the program is to evaluate command line parameters and call function usage in cases of misuse the program is terminated Q e O D e m ES O ey ES Q lt pee In such cases an exception is thrown This ensures that env end is called before Using Arrays for Input Output If all goes well the input file is opened in the file ifst ream After that the arrays for storing the problem data are created by declaring the appropriate variables Then the arrays are filled by using the input operator with the data file The data is checked for consistency and if it fails the program is aborted again by throwing an exception After the problem data has been read and verified we are ready to build the model To do so we construct the model object with the declaration IloModel mod env The array Buy is created to store the modeling variables Since the environment is not
74. End Uu amp Ld m m c x 9 static int I Q populatebycolumn CPXENVptr env CPXLPptr lp int status 0 double obj NUMCOLS double lb NUMCOLS double ub NUMCOLS char colname NUMCOLS int matbeg NUMCOLS int matind NUMNZ double matval NUMNZ double rhs NUMROWS ILOG CPLEX 8 1 USER S MANUAL 305 MANAGING INPUT amp OUTPUT char sense NUMROWS char rowname NUMROWS To build the problem by column create the rows and then add the columns CPXchgobjsen env lp CPX MAX Problem is maximization Now create the new rows First populate the arrays rowname 0 c1 sense 0 L rhs 0 20 0 rowname 1 c2 sense 1 L rhs 1 30 0 status CPXnewrows env lp NUMROWS rhs sense NULL rowname if status goto TERMINATE Now add the new columns First populate the arrays obj 0 1 0 obj 1 2 0 obj 2 3 0 matbeg 0 0 matbeg 1 2 matbeg 2 4 matind 0 0 matind 2 0 matind 4 0 matval 0 1 0 matval 2 1 0 matval 4 1 0 matind 1 1 matind 3 1 matind 5 1 matval 1 1 0 matval 3 3 0 matval 5 1 0 lb 0 0 0 lb 1 0 0 lb 2 0 0 ub 0 40 0 ub 1 CPX INFBOUND ub 2 CPX INFBOUND colname 0 x1 colname 1 x2 colname 2 x3 status CPXaddcols env lp NUMCOLS NUMNZ obj matbeg matind matval lb ub colname if status
75. H H H H H H H see ILOG License Manager ILM loAdd template class 52 loAddable 60 64 loAlgorithm Exception class 48 loAlgorithm Status enumeration 42 loAnd class 37 loArray template class 37 loColumnArray 76 loConversion 82 loConversion class 34 37 47 loCplex 60 implements I1o0MPModeler 61 objects in user application 32 loCplex class exportModel member function 138 getBasisStatuses member function 43 getBoundSA member function 44 getCplexStatus member function 43 44 getDefault member function 40 getDual member function 43 getDuals member function 43 getIIS member function 44 getMax member function 40 getMin member function 40 getObjSA member function 44 getObjValue member function 43 getParam member function 40 getQuality member function 45 137 164 getReducedCost member function 43 getReducedCosts member function 43 getRHSSA member function 44 getSlack member function 43 getSlacks member function 43 getStatus member function 42 getStatuses member function 148 getValue member function 43 UsER S MANUAL 411 INDEX getValues member function 43 importModel member function 130 isDualFeasible member function 43 isPrimalFeasible member function 43 setDefaults member function 41 setParam member function 41 solve member function 39 42 44 45 46 53 IloCplex AdvInd parameter 130 IloCplex Algorithm enumeration 39 IloCplex BarStartAlg 169 IloCplex BasisStatus enumeration 44 IloCplex B
76. ILOG CPLEX works between refactorization the greater the amount of memory it needs for each iteration Consequently one way of conserving memory is to decrease the interval between refactorizations In fact if little memory is available to it ILOG CPLEX ILOG CPLEX 8 1 USER S MANUAL DIAGNOSING PERFORMANCE PROBLEMS will automatically decrease the refactorization interval in order to use less memory at each iteration Since refactorization is an expensive operation decreasing the refactorization interval will generally slow performance You can tell whether performance is being degraded in this way by checking the iteration log file In an extreme case lack of memory may force ILOG CPLEX to refactorize at every iteration and the impact on performance will be dramatic If you provide more memory in such a situation the benefit will be tremendous Preprocessing and Memory Requirements By default ILOG CPLEX automatically preprocesses your problem before optimizing and this preprocessing requires memory If memory is extremely tight consider turning off preprocessing by setting the PreInd parameter to 0 But doing this foregoes the potential performance benefit of preprocessing and should be considered only as a last resort Alternatively consider turning on presolve compression using the PreCompress parameter Numerical Difficulties ILOG CPLEX is designed to handle the numerical difficulties of linear programming auto
77. If the latter parameter is set to zero then optimization proceeds with the tree stored in memory until ILOG CPLEX reaches the tree memory limit TreLim If the NodeFileInd parameter is set to 1 the default then a fast ILOG CPLEX 8 1 USER S MANUAL TROUBLESHOOTING MIP PERFORMANCE PROBLEMS compression algorithm is used on the nodes to try to conserve memory without resorting to writing the node files to disk If the parameter is set to 2 then node files are written to disk If the parameter is set to 3 then nodes are both compressed as in option 1 and written to disk as in option 2 Thus regardless of the setting of NodeFileInd ILOG CPLEX will stop the optimization when the total memory used to store the tree exceeds the tree memory limit Table 8 12 summarizes these different options Table 8 12 Values for the Node File Storage Parameter Value Meaning Comments 0 no node files optimization continues 1 node file in memory and compressed optimization continues default 2 node file on disk files created in temporary directory 3 node file on disk and compressed files created in temporary directory In cases where node files are written to disk ILOG CPLEX will create a temporary subdirectory under the directory specified by the WorkDir parameter The directory named by this parameter must exist before ILOG CPLEX attempts to create node files By default TEL the value of this parameter is
78. Ind to 1 instead of its default value of 0 The perturbation constant EpPer is usually appropriate at its default value of 7 e 6 but can be set to any value 7 e or larger If you observe that your problem has been perturbed more than once then consider whether the simplex perturbation limit parameter is too large The perturbation limit parameter PerLim determines the number of iterations ILOG CPLEX tries before it assumes the problem has stalled At its default value 0 zero ILOG CPLEX determines internally how many iterations to perform before declaring a stall If you set this parameter to some other nonnegative integer then ILOG CPLEX uses that limit to determine when a problem has stalled If you reduce the perturbation limit parameter ILOG CPLEX may be able to solve the problem more smoothly by perturbing sooner Inability to Stay Feasible If a problem repeatedly becomes infeasible in Phase II that is after ILOG CPLEX has achieved a feasible solution then numerical difficulties may be occurring It may help to increase the Markowitz tolerance in such a case By default the value of the parameter EpMrk is 0 01 and suitable values range from 0 0001 to 0 99999 Sometimes slow progress in Phase I the period when ILOG CPLEX calculates the first feasible solution is due to similar numerical difficulties less obvious because feasibility is not gained and lost In the progress reported in the log file an increase in the pri
79. LP netex2 c Complete Program netex2 c on page 190 quadratic programming maximizing a QP iloqpexl cpp QPexl java qpexl c Example iloqpex1 cpp on page 203 Complete Program QPex1 java on page 206 Complete Program qpex1 c on page 207 quadratic programming reading a QP from a formatted file qpex2 c Complete Program qpex2 c on page 215 mixed integer programming optimizing a basic MIP ilomipexl cpp mipexl c Complete Program ilomipex1 cpp on page 259 Complete Program mipex1 c on page 260 mixed integer programming reading a MIP from a formatted file ilomipex2 cpp mipex2 c Complete Program ilomipex2 cpp on page 269 Complete Program mipex2 c on page 271 mixed integer programming using special ordered sets SOS and priority orders ilomipex3 cpp mipex3 c Complete Program ilomipex3 cpp on page 275 Complete Program mipex3 c on page 277 input and output using the message handler 1pex5 c Complete Program lpex5 c on page 299 using query routines lpex7 c Complete Program lpex7 c on page 310 using callbacks ilolpex4 c Complete Program ilolpex4 cpp on page 347 lpex4 c Complete Program lpex4 c on page 352 iloadmipex5 cpp Complete Program iloadmipex5 cpp on page 365 Notation in This Manual Like the reference manual this manual uses the following conventions Important ideas are italicized the first time they appear The names of C routines a
80. MANUAL EXAMPLE READING A QP FROM A FILE If an error occurs the status value indicates the reason for failure A call to CPXgeterrorstring will produce the text of the error message Note that CPXopenCPLEX produces no output so the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines the errors will be seen if the CPX PARAM SCRIND indicator is set to CPX ON if env NULL char errmsg 1024 fprintf stderr Could not open CPLEX environment Mn CPXgeterrorstring env status errmsg fprintf stderr s errmsg goto TERMINATE goto TERMINATE ep Turn on output to the screen status CPXsetintparam env CPX PARAM SCRIND CPX ON amp if status o fprintf stderr U Failure to turn on screen indicator error d n status y O c 3 Create the problem using the filename as the problem name lp CPXoreateprob env amp status argv l A returned pointer of NULL may mean that not enough memory was available or there was some other problem In the case of failure an error message will have been written to the error channel from inside CPLEX In this example the setting of the parameter CPX PARAM SCRIND causes the error message to appear on stdout Note that most CPLEX routines return an error code to indicate the reason for failure if lp NULL fprintf stderr Failed to create LP n goto TERMINATE
81. MipThreads than of the LP or QP optimizer SimThreads or Barthreads this is in keeping with the general observation that MIP speed increases are on average closer to linear in the number of threads than the speed increases for the continuous optimizers Note Nested parallelism is not supported by most OpenMP compilers and runtime libraries so it is not available with the OpenMP version of ILOG CPLEX On the OpenMP version you may set MipThreads to a value greater than 1 or either of SimThreads or BarThreads fo a value greater than 1 but not both in a single call to the MIP optimizer Memory Considerations and the Parallel MIP Optimizer Before the parallel MIP optimizer invokes parallel processing it makes separate internal copies of the initial problem The individual processors use these copies during computation so each of them requires an amount of memory roughly equal to the size of the original model after it is presolved Output from the Parallel MIP Optimizer The parallel MIP optimizer generates slightly different output in the node log see Progress Reports Interpreting the Node Log on page 246 from the serial MIP optimizer The following paragraphs explain those differences If the MIP optimizer is running in parallel it will display elapsed time for the MIP optimizer in wall clock time independent of the setting of the clock type parameter assuming MIP logging has not been turned off ILOG CPLEX prints a summary of
82. NULL fprintf stderr Failed to create problem n goto TERMINATE Now copy the LP part of the problem data into the lp status CPXcopylp env lp numcols numrows objsen obj rhs sense matbeg matcnt matind matval lb ub NULL if status fprintf stderr Failed to copy problem data n goto TERMINATE status CPXcopyquad env lp qmatbeg qmatcnt qmatind qmatval if status fprintf stderr Failed to copy quadratic matrix Mn goto TERMINATE Optimize the problem and obtain solution status CPXqpopt env lp if status fprintf stderr Failed to optimize QP n goto TERMINATE status CPXsolution env lp amp solstat amp objval x pi slack dj if status fprintf stderr Failed to obtain solution n goto TERMINATE Write the output to the screen printf nSolution status d n solstat printf Solution value f n n objval The size of the problem should be obtained by asking CPLEX what the actual size is rather than using what was passed to CPXcopylp 210 ILOG CPLEX 8 1 USER S MANUAL EXAMPLE CREATING A QP OPTIMIZING FINDING A SOLUTION cur_numrows and cur_numcols store the current number of rows and columns respectively cur numrows CPXgetnumrows env 1p cur numcols CPXgetnumcols env 1p for i 0 i lt cur numrows i printf Row d Slack 10f Pi 10f n i slack i
83. NULL zrhs NULL zsense NULL zmatbeg NULL zmatcnt NULL zmatind NULL zmatval NULL zlb NULL zub NULL zctype NULL status 1 goto TERMINATE strcpy zprobname example The code is formatted to make a visual correspondence between the mathematical linear program and the specific data items 2 zobj 0 1 0 zobj 1 2 0 zobj 2 3 0 zobj 3 1 0 ep zmatbeg 0 0 zmatbeg 1 2 zmatbeg 2 5 zmatbeg 3 7 y o zmatcnt 0 2 zmatcnt 1 3 zmatcnt 2 2 zmatcnt 3 2 o Q zmatind 0 0 zmatind 2 0 zmatind 5 0 zmatind 7 0 32 zmatval 0 1 0 zmatval 2 1 0 zmatval 5 1 0 zmatval 7 10 0 o UU zmatind 1 1 zmatind 3 1 zmatind 6 1 zmatval 1 1 0 zmatval 3 3 0 zmatval 6 1 0 zmatind 4 2 zmatind 8 2 zmatval 4 1 0 zmatval 8 3 5 zlb 0 0 0 zlb 1 0 0 zlb 2 0 0 zlb 3 2 0 zub 0 40 0 zub 1 CPX INFBOUND zub 2 CPX INFBOUND zub 3 3 0 zctype 0 C zctype 1 C zctype 2 C zctype 3 I The right hand side values don t fit nicely on a line above So put them here zsense 0 L zrhs 0 20 0 zsense 1 L zrhs 1 30 0 ILOG CPLEX 8 1 UsER s MANUAL 267 EXAMPLE OPTIMIZING A BASIC MIP PROBLEM zsense 2 E zrhs 2 0 0 TERMINATE if status free and null char amp zprobname free and null char
84. NUMCOLS sizeof double zrhs double malloc NUMROWS sizeof double ILOG CPLEX 8 1 USER S MANUAL EXAMPLE CREATING A QP OPTIMIZING FINDING A SOLUTION zsense char malloc NUMROWS sizeof char zmatbeg int malloc NUMCOLS sizeof int zmatcnt int malloc NUMCOLS sizeof int zmatind int malloc NUMNZ sizeof int zmatval double malloc NUMNZ sizeof double zlb double malloc NUMCOLS sizeof double zub double malloc NUMCOLS sizeof double zqmatbeg int malloc NUMCOLS sizeof int zqmatcnt int malloc NUMCOLS sizeof int zqmatind int malloc NUMQNZ sizeof int zqmatval double malloc NUMQNZ sizeof double if zprobname NULL zobj NULL zrhs NULL zsense NULL zmatbeg NULL zmatcnt NULL zmatind NULL zmatval NULL zlb NULL zub NULL zqmatbeg NULL zqmatcnt NULL zqmatind NULL zqmatval NULL status 1 goto TERMINATE strcpy zprobname example o 5 Q 9 U Ru E e D 3 2 The code is formatted to make a visual correspondence between the mathematical linear program and the specific data items y zobj 0 1 0 zobj 1 2 0 zobj 2 3 0 zmatbeg 0 0 zmatbeg 1 2 zmatbeg 2 4 zmatcnt 0 2 zmatcnt 1 2 zmatcnt 2 2 zmatind 0 0 zmatind 2 0 zmatind 4
85. Primal IloCplex Dual and so on Table 1 2 displays the meaning of the optimizer options defined by IloCplex Algorithm Table 1 2 Optimizer Options IloCplex Primal use the primal simplex algorithm IloCplex Dual use the dual simplex algorithm IloCplex Barrier use the barrier algorithm The type of crossover performed after the barrier algorithm is determined by parameter IloCplex BarCrossAlg IloCplex Network use the primal network simplex algorithm on an embedded network followed by the dual simplex algorithm for LPs and the primal simplex algorithm for QPs on the entire problem IloCplex Sifting use the sifting algorithm IloCplex Concurrent use multiple algorithms concurrently on a multiprocessor system If the extracted model requires the solution of more than one LP or QP the algorithm for solving all but the first is controlled by the NodeA1g parameter cplex setParam IloCplex NodeAlg alg Controlling ILOG CPLEX Optimizers Though ILOG CPLEX defaults will prove sufficient to solve most of the problems ILOG CPLEX offers a variety of parameters to control various algorithmic choices ILOG CPLEX parameters can assume values of type bool num int and string IloCplex provides four categories of parameters that are listed in the nested enumeration types IloCplex BoolParam IloCplex IntParam IloCplex NumParam IloCplex StringParam To access the current value of a parameter that interests you from the Conce
86. Problem Representation The problem contains a set of foods which are the modeling variables a set of nutritional requirements to be satisfied which are the constraints and an objective of minimizing the total cost of the food There are two ways to look at this problem ILOG CPLEX 8 1 USER S MANUAL 99 EXAMPLE 100 DIETARY OPTIMIZATION The problem can be modeled in a row wise fashion by entering the variables first and then adding the constraints on the variables and the objective function The problem can be modeled in a column wise fashion by constructing a series of empty constraints and then inserting the variables into the constraints and the objective function The diet problem is equally suited for both kinds of modeling In fact you can even mix both approaches in the same program If a new food product you can create a new variable for it regardless of how the model was originally built Similarly is a new nutrient is discovered you can add a new constraint for it Creating a Model Row by Row You walk into the store and compile a list of foods that are offered For each food you store the price per unit and the amount they have in stock For some foods that you particularly like you also set a minimum amount you would like to use in your diet Then for each of the foods you create a modeling variable to represent the quantity to be purchased for your diet Now you get a medical book and look up which
87. QF At the end of a MIP optimization the optimal values for the variables are directly available However you may wish to obtain information about the LP or QP associated with this optimal solution for instance to know the reduced costs for the continuous variables of the problem at this solution To do this you will want to change the problem to be of type Fixed either ixed milp or fixed miqgp for the MILP or MIQP case respectively The fixed MIP is the continuous problem in which the integer variables are fixed at the values they attained in the best integer solution After changing the problem type you can then call any of the continuous optimizers to re optimize and then display solution information for the continuous version of the problem If you then wish to change the problem type back to the associated milp or miqp you can do so without loss of information in the model Changing Variable Type The command change type adds or removes the restriction on a variable that it must be an integer In the Interactive Optimizer when you enter the command change type the system prompts you to enter the variable that you want to change and then it prompts you to enter the type c for continuous b for binary i for general integer s for semi continuous n for semi integer You can change a variable to binary even if its bounds are not 0 zero and one However in such a case the system issues a warning message at optimization and
88. SS SS SS Sa SSS SS A dietary model Input data foodMin j minimum amount of food j to use foodMax j maximum amount of food j to use foodCost j cost for one unit of food j nutrMin i minimum amount of nutrient i nutrMax i maximum amount of nutrient i nutrPerFood i jl nutrition amount of nutrient i in food j Modeling variables Buy j amount of food j to purchase Objective minimize sum j Buy j foodCost j Constraints forall foods i nutrMin i lt sum j Buy j nutrPer i j lt nutrMax j import ilog concert import ilog cplex public class Diet static class Data int nFoods int nNutrs double foodCost double foodMin double foodMax double nutrMin double nutrMax double nutrPerFood Data String filename throws IloException java io IOException InputDataReader InputDataReaderException 78 ILOG CPLEX 8 1 USER S MANUAL SOLVING THE DIET MODEL WITH THE JAVA API InputDataReader reader new InputDataReader filename foodCost reader readDoubleArray foodMin reader readDoubleArray foodMax reader readDoubleArray nutrMin reader readDoubleArray nutrMax reader readDoubleArray nutrPerFood reader readDoubleArrayArray nFoods foodMax length nNutrs nutrMax length if nFoods foodMin length throw new IloException inconsistent data in file filename
89. Table 2 5 Classes with Parameters Defined by Integers 0 0 e cece eee eee eee 71 Table 3 1 Special data types in the ILOG CPLEX Callable Library 89 Table 3 2 Default values of ILOG CPLEX Growth Parameters 0002 e eee eee eee 90 Table 3 3 Callable Library Routines for Parameters in the ILOG CPLEX Environment 92 Table 5 1 LPMethod Parameter Values for Optimizer Choice 0 000 e eee eee 124 Table 5 2 Symbolic Names for LP Solution Methods 0 020 cece eee eee 125 Table 5 3 DPrilnd Parameter Values for Dual Simplex Pricing Algorithm 131 Table 5 4 PPrilnd Parameter Values for Primal Simplex Pricing Algorithm 131 Table 5 5 ScalndParameter Values for Scaling Methods 0 0 0 cece eee eee eee 132 Table 5 6 Cralnd Parameter Values for the Dual Simplex Optimizer sss 133 Table 5 7 Cralnd Parameter Values for the Primal Simplex Optimizer 133 Table 5 8 BarCrossAlg Parameter Values 0 000 c cece eee ee eese 160 Table 5 9 BarDisplay Parameter Values 0000 0c eect eee eee 161 Table 5 10 Infeasibilities and Norms in the Log File of a Barrier Optimization 163 Table 5 11 Barrier Solution Quality Display 0 0 0 0 cee eee 164 ILOG CPLEX 8 1 USER S MANUAL 17 LIST OF TABLES 18 Table 5 12 BarStartAlg Parameter Values for Starting Point Heuristics
90. That is the default 0 or CPX DPRIIND AUTO automatically selects 2 or CPX DPRIIND STEEP For the primal simplex pricing parameter reduced cost pricing 1 is less computationally expensive so you may prefer it for small or relatively easy problems Try reduced cost ILOG CPLEX 8 1 USER S MANUAL 131 o Q T U v al e D 3 7 TUNING LP PERFORMANCE 132 pricing and watch for faster solution times Also if your problem is dense say 20 30 nonzeros per column reduced cost pricing may be advantageous In contrast if you have a more difficult problem taking many iterations to complete Phase I and arrive at an initial solution then you should consider devex pricing 1 Devex pricing benefits more from ILOG CPLEX linear algebra enhancements than does partial pricing so it may be an attractive alternative to partial pricing in some problems Do not use devex pricing however if your problem has many columns and relatively few rows In such a case the number of calculations required per iteration will usually be disadvantageous If you observe that devex pricing helps then you might also consider steepest edge pricing 2 Steepest edge pricing is computationally more expensive than reduced cost pricing but it may produce the best results on difficult problems One way of reducing the computational intensity of steepest edge pricing is to choose steepest edge pricing with initial slack nor
91. a cutoff or an infeasible combination of branches or the discovery of a new incumbent integer feasible solution See the ILOG CPLEX Reference Manual Appendix A for more details on how this parameter affects the computation that determines the decision to backtrack When ILOG CPLEX backtracks there usually remain large numbers of unexplored nodes from which to begin a new dive The node selection parameter NodeSe1 determines this choice Table 8 4 NodeSel Parameter Values for Node Search Type NodeSel Value Symbolic Value Node Search Type 1 CPX NODESEL BESTBOUND Best Bound search which means that the node Default with the best objective function will be selected generally near the top of the tree 2 CPX NODESEL BESTEST Best Estimate search whereby ILOG CPLEX will estimate a given node s progress toward integer feasibility relative to its degradation of the objective function This setting can be useful in cases where there is difficulty in finding feasible solutions or in cases where a proof of optimality is not crucial i A fej ES D 7 di Buinjos 2 CPX_NODESEL_BESTEST_ALT A variation on the Best Estimate search 0 CPX NODESEL DFS Depth First search will be conducted In many cases this amounts to a brute force strategy for solving the combinatorial problem gaining a small amount of tactical efficiency due to a variety of reasons a
92. adjustments of all these parameters While preprocessing ILOG CPLEX also attempts to strengthen bounds on variables This bound strengthening may take a long time In such cases you may want to turn off bound strengthening ILOG CPLEX also attempts to reduce coefficients during preprocessing Coefficient reduction usually strengthens the continuous relaxation and reduces the number of nodes in the branch amp cut tree but not always Sometimes it increases the amount of time needed to solve the linear relaxations at each node enough time to offset the benefit of fewer nodes Two levels of coefficient reduction are available so it is worthwhile to experiment with these preprocessing options to see whether they are beneficial to your problem In addition you may also set the relaxation parameter to tell ILOG CPLEX to apply preprocessing to the initial relaxation of the problem Sometimes this preprocessing will result in additional beneficial presolve transformations in the LP or QP relaxation transformations that are not possible in the original MIP model In general MIP preprocessing reductions and continuous LP or QP reductions are not the same as some ILOG CPLEX 8 1 USER S MANUAL 239 USING THE MIXED INTEGER OPTIMIZER 240 MIP reductions are not applicable to the continuous case and some continuous reductions do not apply in the MIP case Thus the RelaxPreInd parameter allows you to get the benefit of both styles of p
93. an optimization you may improve solution speed by a factor of 20 In such a case you should set the parameters simplex limit threads and mip limit threads to different values in order to use your computing resources efficiently Another key consideration in setting optimizer and global thread limits is your management of overall system load Nondeterminism Among the ILOG CPLEX parallel optimizers only parallel simplex follows a deterministic algorithm producing the same number of iterations and the same solution path when you apply it to the same problem more than once In contrast the parallel barrier and parallel MIP optimizers are nondeterministic repeated solutions of a model using exactly the same settings can produce different solution paths and in the case of the parallel MIP optimizer very different solution times and results The basic algorithm in the ILOG CPLEX Parallel MIP Optimizer is branch amp cut The primary source of parallelism in branch amp cut is the solution of the LP or QP subproblems at the individual nodes of the search tree These subproblems can be distributed over available processors to be carried out in parallel The individual solution paths for these subproblems will in fact be deterministic but the speed at which their solutions occur can vary slightly These variations lead to nodes being taken from and replaced in the branch amp cut tree in different order and this reordering leads to nondete
94. and sets ptr to NULL z EN 563 O 2 oS US a UE Q static void free_and_null char ptr if ptr NULL free ptr ptr NULL END free_and_null ILOG CPLEX 8 1 USER S MANUAL 317 USING QUERY ROUTINES 318 static void usage char progname fprintf fprintf fprintf fprintf fprintf fprintf fprintf fprintf fprintf fprintf fprintf fprintf fprintf stderr Usage where filename is a file with extension n stderr stderr stderr stderr stderr stderr stderr stderr stderr stderr stderr stderr END usage ILOG CPLEX 8 1 MPS IN THE CALLABLE LIBRARY s filename algorithm n progname SAV or LP lower case is allowed Nin and algorithm is one of the letters n 025 o0oo250 00 c default n primal simplex n dual simplex n network simplex n barrier n barrier with crossover n sifting n concurrent n Exiting n USER S MANUAL Goals in lloCplex GOALS IN ILOCPLEX Goals allow you to take control of the branch amp cut search procedure used by IloCplex to solve MIP problems To help you understand how to use goals with IloCplex we review how this procedure works The 11oCplex branch amp cut search procedure manages a search tree consisting of nodes Every node represents a subproblem to be solved and the root node of the tree represents
95. appears to be advantageous You can still direct the preprocessor to form the dual with other optimizers by setting the PreDual parameter to 1 Conversely to entirely inhibit the dual formulation for the barrier optimizer you can set the PreDual parameter to 1 The default automatic setting is 0 It is worth emphasizing to those familiar with linear programming theory that the decision to solve the dual formulation of your model via this preprocessing parameter is entirely separate from the choice between using the dual simplex method or the primal simplex method to perform the optimization Although these features have theoretical foundations in common it is valid to consider for example solving the dual formulation of your model with the dual simplex method this would not simply result in the same computational path as solving the primal formulation with the primal simplex method In the case already mentioned of a model with many more rows than columns either simplex variant may perform much better when solving the dual formulation due to the smaller basis matrix that is maintained ILOG CPLEX 8 1 USER S MANUAL TUNING LP PERFORMANCE The ILOG CPLEX preprocessor offers a dependency checker which strengthens problem reduction by detecting redundant constraints Such reductions are usually most effective with the barrier optimizer To turn on the dependency checker to strengthen reduction set the parameter DepiInd to 1 instead
96. are dual degenerate in the Interactive Optimizer write out the perturbed problem as a DPE file with the command write filename dpe substituting an appropriate file name A dpe file is saved as a binary SAV format file Then you can read the saved file back in and solve it The subproblem should then solve more cleanly and quickly In the case of DPE files solved by the dual simplex optimizer any integer solution is also guaranteed to be an integer feasible solution to the original problem In most cases the solution will be optimal or near optimal as well Subproblem Optimization In some problems you can improve performance by evaluating how the LP or QP subproblems are solved at the nodes in the branch amp cut tree and then possibly modifying the choice of algorithm to solve them You can control which algorithm ILOG CPLEX applies to the initial relaxation of your problem separately from your control of which algorithm ILOG CPLEX applies to other subproblems The following sections explain those parameters more fully RootAlg Parameter Uv e ES D The RootA1g algorithm parameter indicates the algorithm for ILOG CPLEX to use on the initial subproblem In a typical MIP that initial subproblem is usually the linear relaxation of the original MIP By default ILOG CPLEX starts the initial subproblem with the dual simplex optimizer You may have information about your problem that indicates another optimizer cou
97. as the cutoff Again it is not typical that users set these parameters but they are available if you find them useful Use care in changing these tolerances if either of them is nonzero you may miss the optimal solution by as much as that amount For example in a model where the true minimum is 100 and the absolute cutoff is set to 5 if a feasible solution of say 103 is found at some point the cutoff will discard all nodes with a solution worse than 98 and thus the solution of 100 would be overlooked Periodically during the branch amp cut algorithm ILOG CPLEX may apply a heuristic process that attempts to compute an integer solution from available information such as the solution to the relaxation at the current node This activity does not replace the branching steps but sometimes is able to inexpensively locate a new feasible solution sooner than by branching and a solution found in this way is treated in the same way as any other feasible solution At intervals in the tree new cuts beyond those computed at the root node may also be added to the problem Once ILOG CPLEX finds an integer solution it does the following it makes that integer solution the incumbent solution and that node the incumbent node it makes the value of the objective function at that node modified by the objective difference parameter the new cutoff value itprunes from the tree all subproblems for which the value of the objective function is n
98. been found Running Out of Memory A very common difficulty with MIPs is running out of memory This problem occurs when the branch amp cut tree becomes so large that insufficient memory remains to solve an LP or QP subproblem As memory gets tight you may observe warning messages from ILOG CPLEX as it attempts various operations in spite of limited memory In such a situation if ILOG CPLEX does not find a solution shortly it terminates the process with an error message The information about a tree that ILOG CPLEX accumulates in memory can be substantial In particular ILOG CPLEX saves a basis for every unexplored node Furthermore when ILOG CPLEX uses the best bound or best estimate strategies of node selection the list of unexplored nodes itself can become very long for large or difficult problems How large the unexplored node list can be depends on the actual amount of memory available the size of the problem and algorithm selected A less frequent cause of memory consumption is the generation of cutting planes Gomory fractional cuts and in rare instances Mixed Integer Rounding cuts are the ones most likely to be dense and thus use significant memory under default automatic settings You can try turning off these cuts or any of the cuts you see listed as being generated for your model in the cuts summary at the end of the node log or simply all cuts through the use of parameter settings discussed in the section on cuts i
99. buildNetwork also includes a few routines that are not strictly necessary to this example but illustrate concepts you may find useful in other applications To delete a ILOG CPLEX 8 1 USER S MANUAL 181 EXAMPLE USING THE NETWORK OPTIMIZER WITH THE CALLABLE LIBRARY node and all arcs dependent on that node it uses the Callable Library routine CPXNETdelnodes To change the objective sense to minimization it uses the Callable Library routine CPXNETchgobjsen Also buildNetwork sets the row growth and column growth parameters CPX PARAM ROWGROWTH and CPX PARAM COLGROWTH These parameters specify the amount that internal arrays are extended if more nodes or arcs are added than currently fit in allocated memory If you build up a problem by adding nodes and arcs one by one and if these parameters are set to a low value then internal arrays will be frequently reallocated frequent reallocation may negatively impact performance Ideally these parameters are set to the maximum number of nodes and arcs that the problem will ever have This setting will avoid all reallocation and therefore provide best performance The parameter CPX PARAM ROWGROWTH pertains to adding nodes to a network problem and rows to an LP QP or MIP problem whereas CPX PARAM COLGROWTH pertains to adding arcs to a network problem or columns to an LP QP or MIP problem Let s return to main where it actually calls the network optimizer with the Call
100. by calling 11oModel delete This will cause the specified variables to be deleted from the model and thus from all modeling objects in the model that are using these variables In other words deleting variables from a model may implicitly modify other modeling objects in that model The API of specific modeling objects may provide modification methods For example variable bounds can be changed using methods 11oNumVar setLB and IloNumVar setUB Similarly the bounds of ranged constraints can be changed using IloRange setLB and IloRange setUB Because not all the optimizers that implement the 11oModeler interface support the ability to modify a model modification methods are implemented in 11o0MPModeler These methods are for manipulating the linear expressions in ranged constraints and objective functions used with IloCplex The methods IloMPModeler setLinearCoef IloMPModeler setLinearCoefs and IloMPModeler addToExpr apply in this situation The type of a variable cannot be changed However it can be overwritten for a particular model by adding an 11oConversion object which allows you to specify new types for variables within that model When ILOG CPLEX finds a conversion object in the active model it uses the variable types specified in the conversion object instead of the original type specified for the optimization For example in a model containing IloNumVar x cplex numVar 0 0 1 0 cplex add cplex conversion
101. by the user and the preprocessor will only perform primal reductions If the preprocessor still finds inconsistency in the model it will be declared by the preprocessor to be infeasible instead of infeasible or unbounded Similarly setting the parameter to 2 means that if the preprocessor detects unboundedness in the model it will be declared unambiguously to be unbounded These parameters are intended for diagnostic use as turning off reductions will usually have a negative impact on performance of the optimization algorithms in the normal feasible and bounded case Coping with an Ill Conditioned Problem or Handling Unscaled Infeasibilities By default ILOG CPLEX scales a problem before attempting to solve it After it finds an optimal solution it then checks for any violations of optimality or feasibility in the original unscaled problem If there is a violation of reduced cost indicating nonoptimality or of a bound indicating infeasibility ILOG CPLEX reports both the maximum scaled and unscaled feasibility violations Unscaled infeasibilities are rare but they may occur when a problem is ill conditioned For example a problem containing a row in which the coefficients have vastly different magnitude is ill conditioned in this sense and may result in unscaled infeasibilities ILOG CPLEX 8 1 USER S MANUAL DIAGNOSING LP INFEASIBILITY It may be possible to produce a better solution anyway in spite of unscaled infeasib
102. callback with an IloCplex object cplex simply call IloCplex Callback mycallback cplex use MyCallback env 10 The callback that is added to cplex is returned by the method use and stored in variable mycallback This allows you to call mycallback end to remove the callback from cplex If you do not intend accessing your callback for example in order to delete it before ending the environment you may safely leave out the declaration and initialization of variable mycallback Callback Interface Two callback classes in the hierarchy need extra attention The first is the base class IloCplex CallbackI IloCplex CallbackI Since there is no corresponding callback in the Callable Library this class cannot be used for implementing user callbacks Instead its purpose is to provide an interface common to all callback functions This consists of the methods getModel1 which returns the model that is extracted to the T1oCplex object that is calling the callback get Env which returns the corresponding environment C only and abort which aborts the current optimization Further methods getNrows and getNcols allow you to query the number of rows and columns of the current cplex LP matrix These methods can be called from all callbacks Note For C users no manipulation of the model or more precisely any extracted modeling object is allowed during the execution of a callback No modification is allowed of any array or e
103. ch status 1 goto TERMINATE ILOG CPL EX 8 1 USER S MANUAL 109 2 D ie D D D o A 5 lt EXAMPLE 110 DIETARY OPTIMIZATION num p num TERMINATE return status END readarray static int readdata char file int nfoods p double cost p int nnutr p double nutrmin p double nutrper p int status 0 int ncost nlb nub int nmin nmax int i nj char ch FILE in NULL in fopen file r if in NULL status 1 goto TERMINATE double lb p double ub p double nutrmax p if status readarray in amp ncost cost p goto TERMINATE if status readarray in amp nlb lb p goto TERMINATE if status readarray in amp nub ub p goto TERMINATE if ncost nlb ncost nub status 1 goto TERMINATE nfoods_p ncost if status readarray in if status readarray in if nmax nmin status 1 goto TERMINATE amp nmax nnutr_p nmin nutrper_p if nutrper_p NULL status CPXERR_NO_MEMORY goto TERMINATE for fscanf in te amp ch if ch Nt gh see INe qu ch ILOG CPLEX 8 1 USER amp nmin nutrmin p nutrmax p goto TERMINATE goto TERMINATE double malloc nmin sizeof double S MANUAL EXAMPLE DIETARY OPTIMIZATION ch An continue if ch
104. char amp matbeg free and null char amp matcnt free and null char amp matind free and null char amp matval free and null char amp 1b free and null char amp ub free and null char amp qmatbeg free and null char amp qmatcnt free and null char amp qmatind free and null char amp qmatval return status END main This function fills in the data structures for the quadratic program Maximize obj xl 2 x2 4 3 x3 0 5 33x1l x1l 22 x2 x2 Il x3 x3 dLZ xl x2 235x2 x3 Subject To Cl xl x2 x3 lt 20 c2 x1 3 x2 x3 lt 30 Bounds 0 lt x1 lt 40 End static int set problemdata char probname_p int numcols_p int numrows_p int objsen_p double obj_p double rhs_p char sense_p int matbeg_p int matcnt_p int matind p double matval p double lb p double ub p int qmatbeg p int qmatcnt p int qgmatind p double qgmatval p char zprobname NULL Problem name 16 characters double zobj NULL double zrhs NULL char zsense NULL int zmatbeg NULL int zmatcnt NULL int zmatind NULL double zmatval NULL double zlb NULL double zub NULL int zqmatbeg NULL int zqmatcnt NULL int zqmatind NULL double zqmatval NULL int status 0 zprobname char malloc 16 sizeof char zobj double malloc
105. conducting presolution problem analysis and reductions appropriate for a QP Note that unlike the LP case the Barrier optimizer for QP does not provide the capability of a crossover step that provides an optimal basic solution The QP Simplex optimizers by contrast do return basic solutions and these bases can be used for purposes of restarting sequences of optimizations for instance As a result application writers who wish to allow ILOG CPLEX 8 1 USER S MANUAL 201 OPTIMIZING QPS 202 end users control over the choice of QP optimizer need to be aware of this fundamental difference and to program carefully For most purposes the nonbasic Barrier solution is entirely satisfactory in that all such solutions fully satisfy the standard optimality and feasibility conditions of optimization theory Diagnosing QP Infeasibility Diagnosis of an infeasible QP problem is best done by relaxing it to its associated LP problem that is where the Q matrix has been set to 0 To change the Problem Type in the Interactive Optimizer use the command change problem 1p from the Callable Library use the routine CPXchgprobtype Since 11oCplex handles Problem Types transparently the way to diagnose an infeasible model is slightly different Since infeasibility does not depend on the objective function you start by removing the objective extractable from the extracted model This way the model seen by the cplex object is an LP wi
106. conversions frequently lead to strange application behavior Tell Us Finally if your problem remains unsolved by ILOG CPLEX or if you believe you have discovered a bug in ILOG CPLEX we would appreciate hearing from you about it e e 2 D Q p P A e 2 7 Buiwwesbodg 1ou1inJ ILOG CPLEX 8 1 USER S MANUAL 121 TELL US 122 ILOG CPLEX 8 1 USER S MANUAL Solving Linear Programming Problems The preceding chapters have focused on the details of writing applications that model optimization problems and access the solutions to those problems with minimal attention to the optimizer that solves them This is because most models are solved well by the default optimizers provided by ILOG CPLEX For instances where a user wishes to exert more direct influence over the solution process ILOG CPLEX provides a number of features that may be of interest This chapter tells you more about solving linear programs with ILOG CPLEX using the LP optimizers It contains sections on Choosing an Optimizer for Your LP Problem Tuning LP Performance Diagnosing Performance Problems Diagnosing LP Infeasibility Example Using a Starting Basis in an LP Problem Solving LP Problems with the Barrier Optimizer Interpreting the Barrier Log File Understanding Solution Quality from the Barrier LP Optimizer Overcoming Numerical Difficulties 999999 9 FF 3 Diagnosing Barrier Optimizer Infeasibility ILOG CPLEX
107. crossover at a later time After you read a VEC file into ILOG CPLEX all three optimizers primal simplex dual simplex and barrier simplex automatically invoke crossover Even if you have set the advanced basis indicator to no meaning that you do not intend to start from an advanced basis ILOG CPLEX automatically resets the indicator to yes when it reads a VEC file If you turn off the advanced basis indicator after reading a VEC file then the simplex optimizers will honor this setting and will not initiate crossover Interpreting the Barrier Log File Like the ILOG CPLEX simplex optimizers the barrier optimizer records information about its progress in a log file as it works Some users find it helpful to keep a new log file for each session By default ILOG CPLEX records information in a file named cplex 10g In the Interactive Optimizer use the command set logfile filename to change the name of the log file Callable Library use the routine CPXsetlogfile with arguments to indicate the log file ILOG CPLEX 8 1 USER S MANUAL SOLVING LP PROBLEMS WITH THE BARRIER OPTIMIZER You can control the level of information that ILOG CPLEX records about barrier optimization by setting the BarDisplay parameter Its allowed values and their meanings are as follows Table 5 9 BarDisplay Parameter Values oe Meaning 0 no display 1 display normal information default 2 display detailed diagnostic output
108. data nutrPerFood i j1 Buy j model numVar col data foodMin j data foodMax j type public static void main String args try String filename examples data diet dat boolean byColumn false IloNumVarType varType IloNumVarType Float for inti 0 i lt args length i if args i charAt 0 switch args i charAt 1 case c byColumn true break case i varType IloNumVarType Int break default usage return else filename args i break Data data new Data filename int nFoods data nFoods int nNutrs data nNutrs Build model IloCplex cplex IloNumVar Buy new IloCplex new IloNumVar nFoods Il if byColumn buildModelByColumn cplex data Buy varType else buildModelByRow cplex data Buy varType 80 ILOG CPLEX 8 1 USER S MANUAL SOLVING THE DIET MODEL WITH THE JAVA API Solve model if cplex solve System out println System out println Solution status cplex getStatus System out println System out println cost cplex getObjValue for int i 0 i lt nFoods i System out println Buy i cplex getValue Buy il System out println e cplex end catch IloException ex ET hi System out println Concert Error ex E D cs catch InputDataReader InputDataReaderException ex a System out println Data Er
109. default ILOG CPLEX channels Therefore calls to ourmsg unc print directly any messages that occur before the program gets the address of cpxerror a channel After a call to CPXgetchannels gets the address of cpxerror and after a call to CPXaddfuncdest associates the message function ourmsgfunc with cpxerror then error messages are generated by calls to CPXmsg After the TERMINATE label any error must be generated with care in case the error message function has not been set up properly Thus ourmsgfunc is also called directly to generate any error messages there Acallto the ILOG CPLEX Callable Library routine CPXaddchannel initializes the channel ourchannel The Callable Library routine open opens the file 1pex5 out to accept solution information A call the ILOG CPLEX Callable Library routine CPXaddfpdest associates that file with that channel Solution information is also displayed on screen since ourmsg unc is associated with that new channel too Thus in the loops near the end of main when the solution is printed only one call to CPXmsg suffices to put the output both on screen and into the file A call to CPXdelchannel deletes ourchannel Although CPXcloseCPLEX will automatically delete file and function destinations for channels we recommend that you call CPXdelfpdest and CPXdelfuncdest as the end of your programs Complete Program Ipex5 c The comp
110. developed to exploit the characteristics of models with large aspect ratios that is a large ratio of the number of columns to the number or rows In particular the method is well suited to large aspect ratio models where an optimal solution can be expected to place most variables at their lower bounds The sifting algorithm can be thought of as an extension to the familiar simplex method It starts by solving a subproblem called the working problem consisting of all rows but only a small subset of the full set of columns by assuming an arbitrary value such as its lower bound for the solution value of each of the remaining columns This solution is then used to re evaluate the reduced costs of the remaining columns Any columns whose reduced costs violate the optimality criterion become candidates to be added to the working problem for the next major sifting iteration When no candidates are present the solution of the working problem is optimal to the full problem and sifting terminates The choice of optimizer to solve the working problem is governed by the SiftAlg parameter You can set this parameter to any of the values accepted by the LPMethod parameter except for Concurrent and of course Sifting itself Under the default ILOG CPLEX 8 1 USER S MANUAL TUNING LP PERFORMANCE SiftAlg setting ILOG CPLEX chooses the optimizer automatically typically switching between primal simplex and barrier as the optimization proceeds C
111. e From the Callable Library use the routine CPXqpopt e In Concert programs use the solve method of 11oCplex Under default settings this will result in the Barrier optimizer being called when solving a continuous QP For users who wish to do some performance tuning of their applications there are two Simplex optimizers that can be tried for solving QPs They are Dual Simplex and Primal Simplex You can also use the Network Simplex optimizer this solves the model as an LP network temporarily ignoring the quadratic term in the objective function and takes this solution as a starting point for the Primal Simplex QP optimizer This choice of QP optimizer is controlled by the Root A1g parameter QPMETHOD in the Interactive Optimizer and in the Callable Library Permitted values are o gt Q 2 U Uv a io D 3 Table 7 1 RootAlg Parameter Values RootAlg Value Optimizer 0 Automatic default 1 Primal Simplex 2 Dual Simplex 3 Network Simplex 4 Barrier Many of the optimizer tuning decisions for LP apply in the QP case and parameters that control Barrier and Simplex optimizers in the LP case can be set for the QP case although in some instances to differing effect Most models are solved fastest under default parameter settings See the LP chapter for tuning advice Just as for the LP case each of the available QP optimizers automatically preprocesses your model
112. endl The 0 in the macro indicates that 0 parameters are passed to the constructor of the callback For callbacks requiring up to 7 parameters similar macros are defined where the 0 is replaced by the number of parameters ranging from 1 through 7 For an example of this using the cut callback see Example Controlling Cuts on page 360 If you need more than 7 parameters you will need to derive your callback class yourself without the help of a macro After the callback MyCallback is defined it can be used with the line cplex use MyCallback env in C or cplex use new MyCallback in Java In the case of C function MyCallback creates an instance of the implementation class MyCallbackI A handle to this implementation object is passed to cplex method use If your application defines more than one primal simplex callback object possibly with different subclasses only the last one passed to ILOG CPLEX with the use method is actually used during primal simplex On the other hand 11oCpl1ex can handle one callback for each callback class at the same time For example a simplex callback and a MIP callback can be used at the same time z E D3 qe oS Us a UE Q Complete Program ilolpex4 cpp The complete program ilolpex4 cpp appears here and online in the standard distribution fo moe ett tt eee C File examples src ilolpex4 cpp Version 8 1 ff Ee BE lu eae a Sa aa ae aa a a S
113. foodMin j upper bound foodMax 3j and type type and adds it to the existing objective and ranges with the coefficients specified in column col After creating the variable for this column the 11o0Column object is deleted by calling col end Q e O D e m ES O ey gt e Q lt Solving the Model with lloCplex After the model has been populated we are ready to create the cplex object and extract the model to it by calling IloCplex cplex mod It is then ready to solve the model but for demonstration purposes we first write the extracted model to file diet 1p Doing so can help you debug your model as the file contains exactly what ILOG CPLEX sees If it does not match what you expected it will probably help you locate the code that generated the wrong part The model is then solved by calling method solve Finally the solution status and solution vector are output to the output channel cplex out By default this channel is initialized to cout All logging during optimization is also output to this channel To turn off logging you would set the out stream of cplex to a null stream by calling cplex setOut env getNullStream ILOG CPLEX 8 1 USER S MANUAL 53 EXAMPLE DIETARY OPTIMIZATION Complete Program The complete program ilodiet cpp shown here is also provided online in the standard distribution Notes All the definitions needed for an ILOG CPLEX Concert T
114. for early and then improved feasible solutions It is likely on most models that an eventual proof of optimality would take longer by setting MIPEmphasis to 1 but since the user has given ILOG CPLEX the additional information that this proof is of less importance than usual the user s needs will actually be met more effectively Another choice for MIPEmphasisis 2 MIPEmphasisOptimality Or CPX MIPEMPHASIS OPTIMALITY which results in a greater emphasis on optimality than on feasibility The search for feasible solutions is not ignored completely but the balance is shifted toward moving the Best Bound described in the following paragraph more rapidly at the likely expense of feasible solutions being found less rapidly and improved feasible solutions less frequently than under the default emphasis This setting also provides a general though not precise compatibility mode to prior versions of ILOG CPLEX The fourth choice for MIPEmphasis 3 MIPEmphasisBestBound Or CPX MIPEMPHASIS BESTBOUND works exclusively at moving the Best Bound The Best Bound represents the objective function value at which an integer feasible solution could still potentially exist As possibilities are eliminated this Best Bound value will move in the opposite direction to that of any improving series of integer feasible solutions The process of moving the Best Bound will eventually result in the optimal feasible solution being discovered a
115. for this parameter means that a priority order will be used if one has been read in Problems that use integer variables to represent different types of decisions should assign higher priority to those that must be decided first For example if some variables in a model activate processes and others use those activated processes then the first group of variables should be assigned higher priority than the second group In that way you can use priority to achieve better solutions Setting priority based on the magnitude of objective coefficients is also sometimes helpful Termination ILOG CPLEX terminates MIP optimization under a variety of circumstances First ILOG CPLEX declares integer optimality and terminates when it finds an integer solution and all nodes have been processed Optimality in this case is relative to whatever tolerances and optimality criteria you have set For example ILOG CPLEX considers the cutoff value and the objective difference parameter in this context ILOG CPLEX 8 1 USER S MANUAL 241 i e ES o diN Bulnjos USING THE MIXED 242 INTEGER OPTIMIZER In addition ILOG CPLEX terminates optimization when it reaches a limit that you have set You can set limits on time number of nodes size of tree memory and number of integer solutions Table 8 10 summarizes those parameters and their purpose Table 8 10 Parameters to limit MIP optimization To set a limit on Use
116. function makeCuts ILOG CPLEX 8 1 USER S MANUAL 331 GOALS 332 IN ILOCPLEX The goal Cut Goal checks if any of the constraints passed to it are violated by more than the tolerance value It adds violated constraints as global cuts Other than that it follows the branching strategy IloCplex would use on its own The goal starts out by checking if the solution of the continuous relaxation of the current node subproblem is integer feasible This is done by calling method isIntegerFeasible If the current solution is integer feasible a candidate for a new incumbent has been found and the goal returns the empty goal to instruct 110Cplex to continue on its own Otherwise the goal checks if any of the constraints passed to it are violated It computes the value of every 1hs expression for current solution by calling getvalue 1hs i The result is compared against the corresponding rhs value rhs i If a violation of more than eps is detected the constraint is added as a global cut and the rhs value will be set to IloInfinity to avoid checking it again unnecessarily The global cut goal for 1hs i Srhs i is created by calling method GlobalCutGoal It is then combined with goal goal using method AndGoal so that the new global cut goal will be executed first The resulting goal is stored again in variable goa1 Before adding any global cut goals variable goa1 is initialized as IloCplex Goal goal AndGoal BranchAsCplexGoal
117. goto TERMINATE TERMINATE return status END populatebycolumn For our message functions we will interpret the handle as a pointer to a string which will be the label for the channel We ll put angle brackets around the message so its clear what the function is sending to us We ll place the newlines that appear at the end of a message after the bracket The message argument must not be a constant since it is changed by this function ee dp XR RO e amp static void CPXPUBLIC 306 ILOG CPLEX 8 1 USER S MANUAL MANAGING INPUT amp OUTPUT ourmsgfunc void handle const char msg char label int lenstr int flag 0 char message char msg lenstr strlen message if message lenstr 1 n message lenstr 1 0 flag 1 label char handle printf 15s lt s gt label message if flag putchar n If we clobbered the n we need to put it back if flag message lenstr 1 n END ourmsgfunc TENE o rg o gt os Us i ms Q ILOG CPLEX 8 1 USER S MANUAL 307 USING QUERY ROUTINES IN THE CALLABLE LIBRARY Using Query Routines in the Callable Library 308 This section tells you how to use the Callable Library query routines In Concert Technology for C and Java users query methods such as getName use objects that can be referenced directly Thus this section concentrates on the Call
118. goto TERMINATE status readdata argv 2 amp nfoods amp cost amp lb amp ub amp nnutr amp nutrmin amp nutrmax amp nutrper if status goto TERMINATE Initialize the CPLEX environment env CPXopenCPLEX amp status If an error occurs the status value indicates the reason for failure A call to CPXgeterrorstring will produce the text of the error message Note that CPXopenCPLEX produces no output so the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines the errors will be seen if the CPX PARAM SCRIND indicator is set to CPX ON if env NULL ILOG CPLEX 8 1 USER S MANUAL 103 EXAMPLE 104 DIETARY OPTIMIZATION char errmsg 1024 fprintf stderr Could not open CPLEX environment n CPXgeterrorstring env status errmsg fprintf stderr s errmsg goto TERMINATE Turn on output to the screen status CPXsetintparam env CPX PARAM SCRIND CPX ON IT status fprintf stderr Failure to turn on screen indicator error d n status goto TERMINATE Turn on data checking status CPXsetintparam env CPX PARAM DATACHECK CPX ON IE lp if status fprintf stderr Failure to turn on data checking error d n status goto TERMINATE Create the problem CPXcreateprob env amp status diet A returned pointer of NULL may mean
119. including linear programming formulations How you formulate your model is at least as important as what ILOG CPLEX does with it It also offers a description of the branch amp bound algorithm Nemhauser George L and Laurence A Wolsey Integer and Combinatorial Optimization New York John Wiley amp Sons 1999 A reprint of the 1988 edition A widely cited reference about integer programming this book explains the branch amp bound algorithm in detail Gill Philip E Walter Murray and Margaret H Wright Practical Optimization New York Academic Press 1982 reprint edition This book covers among other topics quadratic programming ILOG CPLEX 8 1 USER S MANUAL Q e Ss 7 I La m ES o 7 zz i ES e Q lt ILOG Concert Technology for C Users This chapter describes how to write C programs using the ILOG CPLEX Concert Technology library for C users It includes sections on The Design of the ILOG CPLEX Concert Technology Library including information on licensing and on compiling and linking your programs Creating an Application with the Concert Technology Library Modeling an Optimization Problem with Concert Technology Solving Concert Technology Models with 11oCplex Accessing Solution Information Modifying a Model Handling Errors 9 9 9 9 Example Dietary Optimization The Design of the ILOG CPLEX Concert Technology Library Figure 1 1 A View of Concert Technolog
120. integer programming problems require noticeably more computation than the methods for similarly sized continuous problems Many relatively small integer programming models still take enormous amounts of computing time to solve Indeed some such models have never yet been solved In the face of these practical obstacles to a solution proper formulation of the model is crucial to successful solution of pure integer or mixed integer programs For help in formulating a model of your own integer or mixed integer problem you may want to consult H P Williams s textbook about practical model building referenced in Further Reading on page 30 in this manual Also you may want to develop a better understanding of the branch amp cut algorithm For that purpose Williams s book offers a good introduction and Nemhauser and Wolsey s book also referenced in Further Reading on page 30 in this manual goes into greater depth about branch amp cut as well as other techniques implemented in the ILOG CPLEX MIP Optimizer The section Performance Features of the Mixed Integer Optimizer in this chapter has already discussed several specific features that are important for performance tuning of difficult models Here we turn attention to specific performance symptoms and the remedies that can be tried Too Much Time at Node 0 If you observe that a very long time passes before the branch amp cut algorithm begins processing nodes it may be that the root r
121. it is actually unnecessary but if more function calls are used finding the right settings may improve performance v BS fej ES 3 TEXT Bley NET NB UIAJOS status CPXsetintparam env CPX_PARAM_ROWGROWTH NNODES if status goto TERMINATE status CPXsetintparam env CPX PARAM COLGROWTH NARCS if status goto TERMINATE Set optimization sense status CPXNETchgobjsen env net CPX MIN if status goto TERMINATE Add nodes to network along with their supply values but without any names status CPXNETaddnodes env net NNODES supply NULL if status goto TERMINATE Add arcs to network along with their objective values and bounds but without any names status CPXNETaddarcs env net NARCS tail head lb ub obj NULL if status goto TERMINATE TERMINATE return status END buildnetwork static void free and null char ptr if ptr NULL free ptr ptr NULL END free_and_null ILOG CPLEX 8 1 USER S MANUAL 187 SOLVING NETWORK FLOW PROBLEMS AS LP PROBLEMS Solving Network Flow Problems as LP Problems Minimize 3ay 3a 4a3 3a bag 6ag 78 4ag subject to 84 ay a2 a2 a3 a3 with these bounds 18 0 188 lt lt lA IA IA IA ay a2 a3 a4 a5 ag a7 ag lt lt IA IA 24 25 12 10 9 free
122. its evaluation value is smaller than that of the candidate This behavior can be altered by overwriting the method IloBool IloCplex NodeEvaluatorI subsume IloNum candVal IloNum nodeVal or in the case of Java boolean IloCplex NodeEvaluator subsume double candVal double nodeVal IloCplex calls this method of an evaluator attached to the current candidate if the node being compared also has the same evaluator attached The first parameter candVal is the evaluation value the evaluator has previously computed for the current candidate and nodeVal is the evaluation value the evaluator has previously computed for the node being tested If this method returns IloTrue true the candidate is replaced Otherwise the method is called again with reversed parameters If it still returns IloFalse false both nodes are tied with respect to that evaluator and the next evaluator they share is consulted Otherwise the current candidate is kept and tested against the next node There are two more virtual methods defined for node evaluators that should be considered when implementing your own node evaluator Method void init is called right before evaluate is called for the first time thus allowing you to initialize internal data of the evaluator When this happens the evaluator has been initialized to the first node to be evaluated thus information about this node can be queried by calling the methods of class IloCplex NodeEvaluatorI IloC
123. j 0 j lt cur_numcols j CPXmsg ourchannel Column d Value 10f Reduced cost 10f n j x j 833l31 Finally write a copy of the problem to a file status CPXwriteprob env lp lpex5 1lp NULL if status 3 CPXmsg cpxerror Failed to write LP to disk n goto TERMINATE ILOG CPLEX 8 1 USER S MANUAL 303 MANAGING 304 INPUT amp OUTPUT TERMINATE Lf if E if First check if ourchannel is open ourchannel NULL int chanstat chanstat CPXdelfuncdest env ourchannel ourlabel ourmsgfunc if chanstat strcpy errmsg CPXdelfuncdest failed Wn ourmsgfunc Our Message errmsg if status status chanstat if fpout NULL chanstat CPXdelfpdest env ourchannel fpout if chanstat strcpy errmsg CPXdelfpdest failed Wn ourmsgfunc Our Message errmsg if status status chanstat CPXfclose fpout CPXdelchannel env amp ourchannel Free up the problem as allocated by CPXcreateprob if necessary lp NULL status CPXfreeprob env amp lp if f status strcpy errmsg CPXfreeprob failed n ourmsgfunc Our Message errmsg Now delete our function destinations from the 3 CPLEX channels cpxresults NULL int chanstat chanstat CPXdelfuncdest env cpxresults reslabel ourmsgfunc if chanstat amp amp status status chanstat
124. lp NULL status CPXfreeprob env amp lp if status fprintf stderr CPXfreeprob failed error code d n status Free up the CPLEX environment if necessary if env NULL status CPXcloseCPLEX amp env Note that CPXcloseCPLEX produces no output so the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines the errors will be seen if the CPX_PARAM_SCRIND indicator is set to CPX_ON ILOG CPLEX 8 1 USER S MANUAL EXAMPLE READING A QP FROM A FILE if status char errmsg 1024 fprintf stderr Could not close CPLEX environment Nn CPXgeterrorstring env status errmsg fprintf stderr s errmsg return status END main This simple routine frees up the pointer ptr and sets ptr to NULL static void free and null char ptr if ptr NULL free ptr ptr NULL END free_and_null o gt Q 2 U v E O D 3 2 static void usage char progname fprintf stderr Usage s filename algorithm n progname fprintf stderr where filename is a file with extension Mn fprintf stderr MPS SAV or LP lower case is allowed Nin fprintf stderr and algorithm is one of the letters Win fprintf stderr fprintf stderr fprintf stderr fprintf stderr fprintf stderr fprintf stderr Exiting n END usage
125. modification of lpexl c where we use a callback function to print the iteration info rather than have CPLEX ILOG CPLEX 8 1 USER S MANUAL USING CALLBACKS do it Bring in the CPLEX function declarations and the C library header file stdio h with the following single include include lt ilcplex cplex h gt Bring in the declarations for the string functions include lt string h gt Include declaration for function at end of program static int populatebycolumn CPXENVptr env CPXLPptr 1p static int CPXPUBLIC mycallback CPXCENVptr env void cbdata int wherefrom void cbhandle The problem we are optimizing will have 2 rows 3 columns and 6 nonzeros define NUMROWS 2 define NUMCOLS 3 define NUMNZ 6 int main void char probname 16 Problem name is max 16 characters Declare and allocate space for the variables and arrays where we will store the optimization results including the status objective value variable values dual values row slacks and variable reduced costs int solstat double objval double x NUMCOLS double pi NUMROWS double slack NUMROWS double dj NUMCOLS CPXENVptr env NULL CPXLPptr lp NULL int status int Lg int cur numrows cur numcols ILOG CPLEX 8 1 USER S MANUAL 353 z E 563 O 2 oS Us a UE Q USING CALLBACKS 354 Initialize the CPLEX environment env CPXop
126. needs to be observed when dealing with goals In particular goals don t have end methods like other handle classes in ILOG Concert Technology Instead 11oCplex goal objects are automatically deleted when no more references to them exist Local cut goals contain 11oRange objects Since the 11oRange object is only applied when the goal is executed method end must not be called for a range constraint from which a local cut goal is built The goal will take over memory management for the constraints and call method end when the goal itself is destroyed Also an 11oRange object can only be used in exactly one local cut goal Similarly method end must not be called for IloRangeArray objects that are passed to local cut goals Also such arrays must not contain duplicate elements Going back to example ilogoalex1 cpp we see that method end is called for the temporary arrays x obj and eas at the end of the execute method Though a bit hidden two IloRange constraints are constructed for the goal corresponding to the parameters of the Or goal IloCplex takes over memory management for these two constraints as soon as they are enclosed in a goal This happens via the implicit constructor IloCplex Goal Goal IloRange rng thatis called when the range constraints are passed as parameters to the Or goal In summary the user is responsible for calling end on all ILOG Concert technology object created in a goal except if they have
127. of extraction The level it performs depends on the NetFind parameter When the NetFind parameter is set to 1 one ILOG CPLEX extracts only the obvious network it uses no scaling it scans rows in their natural order it stops extraction as soon as no more rows can be added to the network found so far When the NetFind parameter is set to 2 the default setting ILOG CPLEX also uses reflection scaling that is it multiplies rows by 1 in an attempt to extract a larger network When the NetFind parameter is set to 3 ILOG CPLEX uses general scaling rescaling both rows and columns in an attempt to extract a larger network In terms of total solution time expended it may or may not be advantageous to extract the largest possible network Characteristics of your problem will determine the tradeoff between network size and the number of simplex iterations required to finish solving the model after solving the embedded network Even if your problem does not conform precisely to network conventions the network optimizer may still be advantageous to use When it is possible to transform the original statement of a linear program into network conventions by these algebraic operations changing the signs of coefficients multiplying constraints by constants rescaling columns adding or eliminating redundant relations then ILOG CPLEX will carry out such transformations automatically if you set the NetFind parameter appropr
128. of memory management Likewise parameters controlling row growth CPX PARAM ROWGROWTH column growth CPX PARAM COLGROWTH and nonzero growth CPX PARAM NZGROWTH can also influence how efficiently ILOG CPLEX allocates memory to accommodate the problem object These growth parameters determine how much extra space ILOG CPLEX allocates in its internal structures when additions to a problem object increase the size of the problem object so that it exceeds currently allocated space Table 3 2 Default values of ILOG CPLEX Growth Parameters Parameter Default value CPX PARAM ROWGROWTH 100 CPX PARAM COLGROWTH 100 CPX PARAM NZGROWTH 500 Table 3 2 shows you the default values of these growth parameters At these default values if an application populates the problem object one row at a time then ILOG CPLEX will cache the row additions until an updated problem is needed for example when a query or optimization function is called Similarly it will cache column based additions after 100 columns and nonzero based arrays when the additions of coefficients produces another 500 ILOG CPLEX 8 1 USER S MANUAL ILOG CPLEX PROGRAMMING PRACTICES nonzeros to add to the matrix Memory Management and Problem Growth on page 133 offers guidelines about performance tuning with these parameters Status and Return Values The Callable Library routine CPXopenCPLEX returns a pointer to a ILOG CPLEX environment In case of
129. of the model The most important control is that of selecting the optimizer For solving the active model ILOG CPLEX solves one LP one QP or a series of LPs or QPs Asingle LP is solved if 110Cplex isMIP and IloCplex isQuadratic return false This is the case if the active model does not include e integer variables Boolean or semi continuous variables e special ordered sets e piecewise linear functions or e quadratic terms in the objective function e re E c8 g lt cs 29 o o Q lt pst fa IloCplex provides several optimizing algorithms to solve LPs Asingle QP is solved if 11o0Cplex isMIP returns false and IloCplex isQuadratic returns t rue This is the case if the active model contains a quadratic and positive semi definite objective but does not contain e integer variables Boolean or semi continuous variables e special ordered sets or e piecewise linear functions As in the case of LPs 11oCplex provides several optimizing algorithms to solve QPs A series of LPs or QPs is solved if the active model is a MIP which can be recognized by IloCplex isMIP returning t rue This is the case if the model contains any of the objects excluded for single QPs above If a MIP contains a purely linear objective function that is I1oCplex isQuadratic returns false the problem is more precisely called an MILP Otherwise it is called an MIQP MIPs are solved using branch amp cut
130. of the routine that it calls before it proceeds 2 D ie E D D E ey A 5 lt Symbolic Constants Most ILOG CPLEX routines return or require values that are defined as symbolic constants in the header file that is the include file cplex h We highly recommend this practice of using symbolic constants rather than hard coded numeric values Symbolic names improve the readability of calling applications Moreover if numeric values happen to change in subsequent releases of the product the symbolic names will remain the same thus making applications easier to maintain Parameter Routines You can set many parameters in the ILOG CPLEX environment to control ILOG CPLEX operation The values of these parameters may be integer double or character strings so ILOG CPLEX 8 1 USER S MANUAL 91 ILOG CPLEX PROGRAMMING PRACTICES 92 there are sets of routines for accessing and setting them Table 3 3 shows you the names and Table 3 3 Callable Library Routines for Parameters in the ILOG CPLEX Environment Type X Change value Access current value Access default max min integer CPXsetintparam CPXgetintparam CPXinfointparam double CPXsetdblparam CPXgetdblparam CPXinfodblparam string CPXsetstrparam CPXgetstrparam CPXinfostrparam purpose of these routines Each of these routines accepts the same first argument a pointer to the ILOG CPLEX environment that
131. of variable a variable b is 4 000000 Change quadratic term of variable a variable b to what 6 0 Quadratic term of variable a variable b changed to 6 000000 From the Callable Library the CcPXchgqpcoef call to change the off diagonal term from 4 to 6 would change both of the off diagonal matrix coefficients from 2 to 3 Thus the indices would be 0 and 1 and the new matrix coefficient value would be 3 If you have entered a linear problem without any quadratic terms and you want to create quadratic terms you must first change the Problem Type to QP To do so use the command change problem qp This command will create an empty quadratic matrix with Q 0 When you change quadratic terms there are still restrictions on the properties of the Q matrix In a minimization problem it must be convex positive semi definite In a maximization problem it must be concave negative semi definite For example if you change the sense of an objective function in a convex Q matrix from minimization to maximization you will thus make the problem unsolvable Likewise in a convex Q matrix if you make a diagonal term negative you will thus make the problem unsolvable ILOG CPLEX 8 1 USER S MANUAL Optimizing QPs OPTIMIZING QPS ILOG CPLEX allows you to solve your QP models through a simple interface by calling the default optimizer as follows e In the Interactive Optimizer use the command optimize
132. off selectively set mip cuts covers 1 orallatonce set mip cuts all 1 Inthe Component Libraries set the parameters that control classes of cuts The parameters are described in Table 8 7 on page 237 Lack of Movement in the Best Node For some models the Best Node value in the node log changes very slowly or not at all Runtimes for such models can sometimes be reduced by the variable selection strategy ILOG CPLEX 8 1 USER S MANUAL 251 TROUBLESHOOTING MIP PERFORMANCE PROBLEMS 252 known as strong branching Strong branching explores a set of candidate branching variables in depth performing a limited number of simplex iterations to estimate the effect of branching up or down on each Important Strong branching consumes significantly more computation time per node than the default variable selection strategy To activate strong branching set the Varsel parameter to a value of 3 On rare occasions it can be helpful to modify strong branching limits If you modify the limit on the size of the candidate list then strong branching will explore a larger or smaller set of candidates If you modify the limit on strong branching iteration then strong branching will perform more or fewer simplex iterations per candidate These limits are controlled by the parameters St rongCandLim and StrongItLin respectively Other parameters to consider trying in the case of slow movement of the Best Node value are non defaul
133. or upgrade ILOG CPLEX Contact your local ILOG support department if this information has not been communicated to you or if you find that you need help in establishing your ILOG CPLEX license Compiling and Linking Compilation and linking instructions are provided with the files that come in the standard distribution of ILOG CPLEX for your computer platform Check the readme htm1 file for details ILOG CPLEX 8 1 USER S MANUAL CREATING AN APPLICATION WITH THE CONCERT TECHNOLOGY LIBRARY Creating an Application with the Concert Technology Library The remainder of this chapter is organized by the steps most applications are likely to follow First the model to be solved must be created With Concert Technology this is done independently of ILOG CPLEX A short introduction to model creation is provided in Modeling an Optimization Problem with Concert Technology on page 33 A more comprehensive discussion can be found in the ZLOG Concert Technology User s Manual When the model is ready to be solved it is handed over to ILOG CPLEX for solving The process for doing this is shown in Solving Concert Technology Models with IloCplex on page 37 which includes a survey of the IloCp1lex interface for controlling the optimization Individual controls are discussed in the chapters explaining the individual optimizers Q e 3 iv e m E o ig zz i e Q lt Accessing Solution Information on page 41 shows
134. passed to the constructor of Buy an empty handle is constructed So at this point the variable Buy cannot be used Depending on the command line function either bui ldMethodByRow or buildMethodByColumn is called Both create the dietary model from the input data and return an array of modeling variables as an instance of the class IloNumVarArray At that point Buy is assigned to an initialized handle containing all the modeling variables and can be used afterwards Building the Model by Row The model is created by rows using the function buildModelByRow It first gets the environment from the model object passed to it Then the modeling variables Buy are created Instead of calling the constructor for the variables individually for each variable we create the full array of variables with the array of lower and upper bounds and the variable type as parameter In this array variable Buy i is created such that it has lower bound foodMin i upper bound foodMax i and type type The statement mod add IloMinimize env IloScalProd Buy foodCost creates the objective function and adds it to the model The IloScalProd function creates the expression L Buy j foodCost j which is then passed to the function ILOG CPLEX 8 1 USER S MANUAL 51 EXAMPLE 52 DIETARY OPTIMIZATION IloMinimize That function creates and returns the actual TloOb jective object which is added to the model with the call mod add The follow
135. progname Branch on var with largest objective coefficient among those with largest infeasibility ILOCPLEXGOAL1 MyBranchGoal IloNumVarArray vars IloNumArray x IloNumArray obj IntegerFeasibilityArray feas x IloNumArray getEnv obj IloNumArray getEnv feas IntegerFeasibilityArray getEnv getValues x vars getObjCoefs obj vars getFeasibilities feas vars IloInt bestj 1 IloNum maxinf 0 0 IloNum maxobj 0 0 IloInt cols vars getSize for IloInt j 0 J lt cols j3 if feas j Infeasible IloNum xj inf x j IloFloor x j if xj inf 0 5 xj inf 1 0 xj inf if xj inf gt maxinf amp amp xj inf gt maxinf IloAbs obj j gt maxobj bestj j maxinf xj inf maxobj IloAbs 0obj jl IloCplex Goal res if bestj gt 0 res AndGoal OrGoal vars bestj gt IloFloor x bestj 41 vars bestj lt IloFloor x bestj this 336 ILOG CPLEX 8 1 USER S MANUAL GOALS IN ILOCPLEX x end obj end feas end return res Depth first search node evaluator class DepthEvaluatorl public IloCplex NodeEvaluatorI public IloNum evaluate const return getDepth IloCplex NodeEvaluatorl duplicateEvaluator return new DepthEvaluatorI IloCplex NodeEvaluator DepthEvaluator return new DepthEvaluatorI integer infeasibility sum node evaluator class IISumEvaluatorl
136. re solves the relaxation Next this will be popped from the goal stack and executed This means that the same search strategy as implemented in the original goal is applied at that node Memory Management and Goals Java uses garbage collection to handle all memory management issues Thus the following only applies to the C library Java users may safely skip ahead to Cuts and Goals To conserve memory 11oCplex only stores active nodes of the tree and deletes nodes as soon as they become inactive When deleting nodes 11oCplex also deletes the goal stacks associated with them including all goals they may still contain In other words IloCplex takes over memory management for goals It does so by keeping track of how many references to every goal are in use As soon as this number drops to zero 0 the goal is automatically deleted This technique is known as reference counting IloCplex implements reference counting in the handle class 110Cplex Goal Every IloCplex GoalI object maintains a count of how many I1oCplex Goal handle ILOG CPLEX 8 1 USER S MANUAL GOALS IN ILOCPLEX objects refer to it The assignment operator the constructors and the destructor of class IloCplex Goal are implemented in such a way as to keep the reference count up to date This means that users should always access goals through handle objects rather than keeping their own pointers to implementation objects Other than that nothing special
137. services such as training maintenance technical support and outlines special programs In addition it links you to an ftp site where you can pick up examples The technical support pages contain FAQ Frequently Asked Answered Questions and the latest patches for some of our products Access to these pages is restricted to owners of an ongoing maintenance contract The maintenance contract number and the name of the person this contract is sent to in your company will be needed for access as explained on the login page ILOG CPLEX 8 1 USER S MANUAL 29 FOR MORE 30 INFORMATION All three of the following sites contain the same information but access is localized so we recommend that you connect to the site corresponding to your location and select the support page from the home page The Americas http www ilog com Asia amp Pacific nations http www ilog com sg Europe Africa and Middle East http www ilog fr On those Web pages you will find additional information about ILOG CPLEX in technical papers that have also appeared at industrial and academic conferences Further Reading In case you want to know more about optimization and mathematical or linear programming here is a brief selection of printed resources Williams H P Model Building in Mathematical Programming 4th ed New York John Wiley amp Sons 1999 This textbook includes many examples of how to design mathematical models
138. sets SOS priority orders and MIP start information z a E O 2 oS Us a UE Q Example Using Query Routines This example uses the ILOG CPLEX Callable Library query routine CPXgetcolname to get the column names from a problem object To do so it applies the programming pattern we just described in Using Surplus Arguments for Array Allocations on page 308 It derives ILOG CPLEX 8 1 USER S MANUAL 309 USING QUERY ROUTINES IN THE CALLABLE LIBRARY from the example 1pex2 c explained in the manual ILOG CPLEX Getting Started manual This query routine example differs from that simpler example in several ways Theexample calls CPXgetcolname twice after optimization the first call determines how much space to allocate to hold the names the second call gets the names and stores them in the arrays cur colname and cur colnamestore When the example prints its answer it uses the names as stored in cur colname If no names exist there the example creates generic names This example assumes that the current problem has been read from a file by CPXreadcopyprob You can adapt the example to use other ILOG CPLEX query routines to get information about any problem read from a file Complete Program Ipex7 c The complete program 1pex7 c appears here and online in the standard distribution p ol File examples src lpex7 c y Version 8 1 y e E ESE E E
139. size and removing extraneous constraints that do not directly cause the infeasibility but still appear in the IIS Similarly running ILOG CPLEX 8 1 USER S MANUAL 147 o J Q T ge ge E e D 3 7 EXAMPLE USING A STARTING BASIS IN AN LP PROBLEM the infeasibility finder on an aggregated problem may help because the aggregator performs substitutions that may remove extraneous variables that clutter the IIS output More generally if you perform substitutions you may simplify the output so that it can be interpreted more easily Other simplifications of the constraints in the IIS such as combining variables multiplying constraints by constants and rearranging sums may make it easier to interpret the IIS Example Using a Starting Basis in an LP Problem We now return to an approach mentioned in the section Tuning LP Performance which is to start with an advanced basis The following small example demonstrates an approach to setting a starting basis by hand Example ilolpex6 cpp The example ilolpex6 cpp resembles one you may have studied in the ILOG CPLEX Getting Started manual ilolpex1 cpp This example differs from that one in these ways Arrays are constructed using the populatebycolumn method and thus no command line arguments are needed to select a construction method Inthe main routine the arrays cstat and rstat set the status of the initial basis After the problem data has be
140. so then a call to CPXgetcallbackinfo gets the following information e iteration count e feasibility indicator e sum of infeasibilities if infeasible e Objective value if feasible The function then prints these values to indicate progress Before the program calls CPX1popt the default optimizer from the ILOG CPLEX Callable Library it sets the callback function by calling CPXsetl1pcallbackfunc It unsets the callback immediately after optimization This callback function offers a model for graphic user interfaces that display optimization progress as well as those GUIs that allow a user to interrupt and stop optimization If you want to provide your end user a facility like that to interrupt and stop optimization then you should make mycallback return a nonzero value to indicate the end user interrupt Complete Program Ipex4 c The complete program 1pex4 c appears here and online in the standard distribution mc ON File examples src lpex4 c aA Version 8 1 p o Copyright C 1997 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products lpex4 c Illustrating the CPLEX callback functionality This is a
141. solving it modifying the model and solving it again under default settings the advanced basis will be used for the last of these steps automatically In other cases you can communicate the final basis from one run to the start of the next by first saving the basis to a file before the end of the first run To save the basis of the optimized problem to a file When using the Component Libraries to optimize your problem save by means of the method cplex exportModel or the routine CPXwriteprob In the Interactive Optimizer use the write command with the file type bas To read an advanced basis from a saved file into the Interactive Optimizer follow these steps 1 Assure that the advanced start parameter is set to its default value of yes set advance y 2 Read the file with the read command and specify the file type as bas Similarly when using the Component Libraries set the parameter 110Cplex AdvInd or CPX PARAM ADVIND to 1 and call the method IloCplex importModel or the routine CPXreadcopybase Simplex Parameters After you have chosen the right optimizer and if appropriate you have started from an advanced basis you may want to experiment with different parameter settings to improve performance This section describes parameters that are most likely to affect performance of the simplex linear optimizers The barrier optimizer is different enough from the simplex optimizers that it is discussed elsewh
142. source code of this example can be found in the examples src directory of the ILOG CPLEX distribution The equivalent Java version can be found as GoalEx2 java in the same location Palio lrl1il ce C File examples src ilogoalex2 cpp Version 8 1 Ju ee ae a a a eS eee ee Copyright C 1999 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products ilogoalex2 cpp Solve noswot by adding cuts through the goal API finclude ilcplex ilocplex h ILOSTLBEGIN ILOG CPLEX 8 1 USER S MANUAL GOALS IN ILOCPLEX ILOCPLEXGOAL3 CutGoal IloExprArray lhs IloNumArray rhs IloNum eps if isIntegerFeasible return 0 IloCplex Goal goal AndGoal BranchAsCplexGoal getEnv this IloInt n lhs getSize for IloInt i 0 i lt n i IloNum xrhs rhs i if xrhs lt IloInfinity amp amp getValue lhs i gt xrhs eps goal AndGoal GlobalCutGoal lhs i lt xrhs goal rhs i IloInfinity return goal void makeCuts const IloNumVarArray vars IloExprArray lhs IloNumArray rhs loNumVar x11 x12 x13 x14 x15 loNumVar x21 x22 x23 x24 x25 loNumVar x31 x32 x33 x34 x35 loNumVar x41 x42 x43 x44 x45 loNumVar x51 x52 x53 x54 x55 loNumVar wll w12 w13 w14 w15 loNumVar w21 w22 w23 w24 w25 loNumVar w31 w32 w33
143. specify the type of the variables being created The function starts by creating the modeling variables one by one and storing them in array Buy Each variable j is initialized to have bounds data foodMin 4 and data foodMax 4 and to be of type type The variables are first used to construct the objective function expression with method model scalProd foodCost Buy This expression is immediately used to create the minimization objective which is directly added to the active model by addMinimize In the loop that follows the nutritional constraints are added For each nutrient i the expression representing the amount of nutrient in a diet with food levels Buy is computed using model scalProd nutrPerFood i Buy This amount of nutrient must be within the ranged constraint bounds nut rMin i and nutrMax i This constraint is created and added to the active model with addRange Note that function buildModelByRow uses interface IloModeler rather than IloCplex This allows the function to be called without change in another implementation of IloModeler such as I1oSolver Once you have created an optimization problem in your active model the 11oCplex object is ready to solve it This is done for a model represented by cplex by calling cplex solve The solve method returns a Boolean indicating whether or not a feasible solution was found and can be queried However when t rue is returned the solution that was found may
144. strcpy errmsg Failed to delete cpxresults function n ourmsgfunc Our Message errmsg cpxwarning NULL int chanstat chanstat CPXdelfuncdest env cpxwarning warnlabel ourmsgfunc if chanstat amp amp status status chanstat strcpy errmsg Failed to delete cpxwarning function n ourmsgfunc Our Message errmsg ILOG CPLEX 8 1 USER S MANUAL MANAGING INPUT amp OUTPUT if cpxerror NULL int chanstat chanstat CPXdelfuncdest env cpxerror errorlabel ourmsgfunc if chanstat amp amp status status chanstat strcpy errmsg Failed to delete cpxerror function n ourmsgfunc Our Message errmsg Free up the CPLEX environment if necessary if env NULL status CPXcloseCPLEX amp env Note that CPXcloseCPLEX produces no output so the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines the errors will be seen if the CPX_PARAM_SCRIND indicator is set to CPX_ON if status strcpy errmsg Could not close CPLEX environment Mn ourmsgfunc Our Message errmsg CPXgeterrorstring env status errmsg ourmsgfunc Our Message errmsg return status END main This function builds by column the linear program Maximize obj xl 2 x2 3 x3 Subject To 4 Cl xl x2 x3 lt 20 _ 9 rc be i c2 xl 3 x2 x3 lt 30 e D Bounds or 0 xl 40 oS
145. text of the error message Note that CPXopenCPLEX produces no output so the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines the errors will be seen if the CPX PARAM SCRIND indicator is set to CPX ON if env NULL char errmsg 1024 fprintf stderr Could not open CPLEX environment Mn CPXgeterrorstring env status errmsg fprintf stderr s errmsg goto TERMINATE Turn on output to the screen status CPXsetintparam env CPX PARAM SCRIND CPX ON if status fprintf stderr Failure to turn on screen indicator error d n status goto TERMINATE ILOG CPLEX 8 1 USER S MANUAL EXAMPLE USING A STARTING BASIS IN AN LP PROBLEM Create the problem strcpy probname example lp CPXcreateprob env amp status probname A returned pointer of NULL may mean that not enough memory was available or there was some other problem In the case of failure an error message will have been written to the error channel from inside CPLEX In this example the setting of the parameter CPX PARAM SCRIND causes the error message to appear on stdout if lp NULL fprintf stderr Failed to create LP n goto TERMINATE Now populate the problem with the data status populatebycolumn env 1p if status fprintf stderr Failed to populate problem data n goto TERMINATE We assume we know the optimal b
146. the Callable Library use the routine CPXchgprobtype ILOG CPLEX 8 1 USER S MANUAL 243 USING SPECIAL ORDERED SETS ILOG CPLEX then sets the variable bounds so that upper and lower bounds are those in the current integer solution You can then optimize the resulting continuous program and display its post solution statistics Using Special Ordered Sets 244 A special ordered set SOS is an additional way to specify integrality conditions in a model There are various types of SOS SOS Type is a set of variables whether all integer all continuous or mixed integer and continuous where at most one variable may be nonzero SOS Type 2 is a set or integer or continuous variables where at most two variables may be nonzero If two variables are nonzero they must be adjacent in the set ILOG CPLEX uses special branching strategies to take advantage of SOSs The special branching strategies depend upon the order among the variables in the set The order is specified by assigning weights to each variable The order of the variables in the model such as in the MPS or LP format data file or the column index in a Callable Library application is not used in SOS branching If there is no order relationship among the variables such that weights cannot be specified or would not be meaningful SOS branching should not be used For many classes of problems these branching strategies can significantly improve performance E
147. the environment all memory of arrays belonging to the same environment is returned to the system as well Thus in practice you do not need to call end on an array or any other Concert Technology object just before calling env end The constructor for arrays specifies that an array of size 3 with elements 1 0 2 0 and 3 0 is constructed This output format can be read back in with for example cin data ILOG CPLEX 8 1 USER S MANUAL SOLVING CONCERT TECHNOLOGY MODELS WITH ILOCPLEX The example at the end of this chapter takes advantage of this function and reads the problem data from a file Finally we want to point out that Concert Technology provides the template class IloArray X to create array classes for your own type X This can be used to generate multidimensional arrays All the functions described above are supported for IloArray classes except for input output which depends on the input and output operator being defined for type X Q e iv m ES o 7 ey i ES e Q lt Solving Concert Technology Models with lloCplex ILOG CPLEX generally does not need to be involved while you create your model However once the model is set up it is time to create your cplex object that is an instance of the class IloCplex to be used to solve the model IloCplex is a class derived from IloAlgorithm There are other Concert Technology algorithm classes also derived from IloAlgorithm So
148. the include file cplex h a pointer to a variable to hold the default value of the parameter a pointer to a variable to hold the minimum value of the parameter apointer to a variable to hold the maximum value of the parameter The routine CPXinfostrparam differs slightly in that it does not expect pointers to variables to hold the minimum and maximum values as those concepts do not apply to a string parameter To access the current value of a parameter that interests you from the Callable Library use the routine CPXgetintparam for parameters of type int CPXgetdblparam for parameters of type double and CPXgetstrparam for string parameters These routines also expect arguments to indicate the environment the parameter you want to check and a pointer to a variable to hold that current value No doubt you have noticed in other chapters of this manual that you can set parameters from the Callable Library There are of course routines in the Callable Library to set such parameters one sets parameters of type int another sets parameters of type double another sets string parameters CPXsetintparam accepts arguments to indicate e the environment that is a pointer of type CPXENVptr returned by CPXopenCPLEX ILOG CPLEX 8 1 USER S MANUAL EXAMPLE DIETARY OPTIMIZATION e the parameter to set this routine sets parameters of type int e the value you want the parameter to assume cCPXsetd
149. the memory used for the cut could not be reclaimed For convenience method add returns the cut that has been added and thus we can call end directly on the returned IloRange object It is important that all resources that have been allocated during a callback are freed again before leaving the callback even in the case of an exception Here exceptions could be thrown when creating the cut itself or when trying to add it for example due to memory exhaustion Thus we enclose these operations in a try block and catch all exceptions that may occur In the case of an exception we delete the cut by calling cut end and re throw whatever exception was caught Re throwing the exception can be omitted if you want to continue the optimization without the cut After the cut has been added we set the rhs value to IloInfinity to avoid checking this cut for violation at the next invocation of the callback Note that we did not simply remove the ith element of arrays rhs and 1hs because this is not supported if the cut callback is invoked from a parallel optimizer However changing array elements is allowed Also for the potential use of the callback in parallel the variable xrhs ensures that we are using the same value when checking for violation of the cut as when adding the cut Otherwise another thread may have set the rhs value to 1101nfinity just between the two actions and a useless cut would be added ILOG CPLEX would actually handle th
150. the modeling variables will be stored by buildModelByRow or buildModelByColumn ILOG CPLEX 8 1 USER S MANUAL SOLVING THE DIET MODEL WITH THE JAVA API We have already discussed a method very similar to bui 1dModelByRow This function is called when byColumn is false which is the case when the example is executed without the c command line option otherwise buildModelByColumn is called Note that unlike buildModelByRow this method requires 110MPModeler rather than IloModeler as parameter since modeling by column is not available with IloModeler First the function creates an empty minimization objective and empty ranged constraints and adds them to the active model IloObjective cost model addMinimize IloRange constraint new IloRange nNutrs for int i 0 i lt nNutrs i i constraint i model addRange data nutrMin i data nutrMax i Empty means that they use a 0 expression After that the variables are created one by one and installed in the objective and constraints modeling by column For each variable a column object is created We start by creating a column object for the objective by calling e E c8 g lt cs 05 5 o o Q lt z IloColumn col model column cost data foodCost j The column is then expanded to include the coefficients for all the constraints using col and with the column objects that are created for each constraint This
151. the network display parameter at its default value 2 If you have changed the default value you can reset it with the command set network display 2 v AS fa 7 Tuning Performance of the Network Optimizer MO 4 X10M N UIAJOS The default values of parameters controlling the network optimizer are generally the best choices for effective performance However the following sections indicate parameters that you may want to experiment with in your particular problem Controlling Tolerance You control the feasibility tolerance for the network optimizer through the parameter NetEpRHS Likewise you control the optimality tolerance for the network optimizer through the parameter Net EpOpt Selecting a Pricing Algorithm for the Network Optimizer On the rare occasions when the network optimizer seems to take too long to find a solution you may want to change the pricing algorithm to try to speed up computation The pricing algorithm for the network optimizer is controlled by parameter Net PPriInd All the choices use variations of partial reduced cost pricing Limiting Iterations in the Network Optimizer Use the parameter Net 1t Limif you want to limit the number of iterations that the network optimizer performs Solving Problems with the Network Optimizer You instruct ILOG CPLEX to apply the network optimizer for solving the LP at hand by setting the CPX PARAM LPMETHOD parameter to CPX ALG NET in the
152. the optimization may terminate with a bound violation Consequently in the example that we mentioned see Sample Stating a MIP Problem on page 224 if we want to make x a binary variable we should first change the bounds on x4 to 0 and 7 then we can safely change its type to binary If you change a variable s type to be semi continuous or semi integer be sure to create both a lower bound and an upper bound for it These variable types specify that at an optimal solution the value for the variable must be either exactly zero or else be between the lower and upper bounds and further subject to the restriction that the value be an integer in the case of semi integer variables By the way a problem may be changed to a mixed integer problem even if all its variables are continuous ILOG CPLEX 8 1 USER S MANUAL USING THE MIXED INTEGER OPTIMIZER Using the Mixed Integer Optimizer The ILOG CPLEX Mixed Integer Optimizer solves MIP models using a very general and robust branch amp cut algorithm While MIP models have the potential to be much more difficult than their continuous LP and QP counterparts it is also the case that large MIP models are routinely solved in many production applications A great deal of algorithmic development effort has been devoted to establishing default ILOG CPLEX parameter settings that achieve good performance on a wide variety of MIP models Therefore it is recommended to try solving your model by f
153. the screen if you are working in the Interactive Optimizer or if the message to screen indicator CPX_PARAM_SCRIND is set to 1 one Once it finds an optimal solution under these conditions ILOG CPLEX will then re include the discarded column to be sure that no better solution is available If no better objective value can be obtained then the problem has been solved Otherwise ILOG CPLEX continues its work until it reaches optimality Occasionally new singularities occur or the same singularities recur ILOG CPLEX observes a limit on the number of singularities it tolerates The parameter SingLim specifies this limit By default the limit is ten After encountering this many singularities ILOG CPLEX will save in memory the best factorizable basis found so far and stop its solution process You may want to save this basis to a file for later use To save the best factorizable basis found so far in the Interactive Optimizer use the write command with the file type bas When using the Component Libraries use the method cplex exportModel or the routine CPXwriteprob If ILOG CPLEX encounters repeated singularities in your problem you may want to try alternative scaling on the problem rather than simply increasing ILOG CPLEX tolerance for singularities Scaling on page 132 explains how to try alternative scaling If alternate scaling does not help another tactic to try is to increase the Markowitz tolerance The Markowitz tolerance
154. their internal data structures Not only does ILOG CPLEX track all modifications of the model it has extracted but also it tries to maintain as much solution information from a previous invocation of solve as is possible and reasonable We already encountered what is perhaps the most important modification method that is the method IloModel add for adding modeling objects to a model Conversely you may call 11oModel remove to remove a modeling object from a model Objective functions ILOG CPLEX 8 1 USER S MANUAL 45 MODIFYING A MODEL 46 can be modified by changing their sense and by editing their expression or by changing their expression completely Similarly the bounds of constraints and their expressions can be modified For a complete list of supported modifications see the documentation of the individual modeling objects in the LOG Concert Reference Manual Deleting and Removing Modeling Objects A special type of modification is that of deleting a modeling object by calling its end method Consider for example the deletion of a variable What happens if the variable you delete has been used in constraints or the objective or has been extracted to ILOG CPLEX Concert Technology carefully removes the deleted variable from all other modeling objects and algorithms that may keep a reference to the variable in question This applies to any modeling object to be removed However user defined handles to the
155. this parameter Concert Technology Callable Library Interactive Optimizer elapsed time TiLim CPX PARAM TILIM timelimit number of nodes NodeLim CPX PARAM NODELIM mip limits nodes size of tree TreLim CPX PARAM TRELIM mip limits treememory size of node file WorkMem CPX PARAM WORKMEM workmem number of integer solutions IntSolLim CPX PARAM INTSOLLIM mip limits solutions ILOG CPLEX also terminates when an error occurs such as when ILOG CPLEX runs out of memory or when a subproblem cannot be solved If an error is due to failure to solve a subproblem an additional line appears in the node log file to indicate the reason for that failure Writing a Tree File When ILOG CPLEX terminates a MIP optimization before it achieves optimality for example because it has reached a limit you set it still has significant information about the current branch amp cut tree You can save this information by writing it to a file of type TRE a binary proprietary ILOG CPLEX format Later you can then read the saved TRE file and restart the optimization from where ILOG CPLEX left off To save a MIP in a TRE file In the Interactive Optimizer use the command write filename tre or write filename tre From the Callable Library use the routine CPXtreewrite Note that resuming a branch amp cut optimization by reading a tree file back in may not result in precisely the same solution path being t
156. this phenomenon commonly occurs In such a situation the equality constraints transfer the infeasibility from one part of the model to another until eventually no more transfers can occur Consequently such an IIS file will also contain a cumulative constraint consisting of the sum of all the equality rows This cumulative constraint can direct you toward the cause of infeasibility as the following sample IIS illustrates Minimize subject to Rows in the iis 2 x24 x97 x98 x99 x104 7758 33 x97 x99 x100 x114 x115 0 4 x98 x104 0 10 x105 x107 x108 x109 151 11 x108 x109 x110 x111 642 12 x101 x102 x110 x111 x112 x113 x117 2517 13 x112 x117 x118 x119 186 14 x118 x119 x120 x121 x122 x123 271 15 x120 x122 130 16 x121 x123 x124 x125 716 17 x124 x125 x126 x127 2627 18 x126 x127 x128 x129 1077 19 x128 x129 x130 x131 593 249 x100 x101 x103 0 251 x113 x114 x116 0 Sum of equality rows in iis X24 x102 x103 x105 x107 x115 x116 x130 x131 16668 Columns in the iis Bounds x24 lt 14434 x102 0 x103 0 x105 0 x107 0 x115 0 x116 0 x130 0 x131 0 Non iis columns intersecting iis rows x97 Free x98 Free x99 Free End Since there are 15 rows in this IIS file the cause of infeasibility is not immediately obvious However if
157. this requires calling the CPXputenv routine from the ILOG CPLEX 8 1 USER S MANUAL 381 CPLEX RUNTIME DEVELOPMENT AND LICENSING PROCEDURES Callable Library and C Concert or the IloCplex putenv static method from Java to specify the location of the key through the ILOG_LICENSE_FILE environment variable For memory based RUNTIME keys this requires calling the CPXRegisterLicense routine for Callable Library and C users or the static method IloCplex registerLicense for Java users to pass the RUNTIME key to ILM Descriptions of the CPXputenv and CPXRegisterLicense routines are in the ILOG CPLEX Reference Manual descriptions of IloCplex putenv and IloCplex registerLicense are in the ILOG CPLEX Java Reference Manual Examples Here are some code samples that illustrate the usage of the above runtime license routines The first example illustrates usage of the CPXputenv routine when opening the CPLEX environment Notes This example assumes a Microsoft Windows file directory structure that requires an additional backslash when specifying the path of the file containing the key It also assumes that the application uses an environment variable called MYAPP_HOME to identify the directory in which it was installed The string argument to CPXputenv must remain active throughout the time ILOG CPLEX is active the best way to do this is to malloc the strin
158. timing statistics specific to the parallel MIP optimizer at the end of optimization You can see typical timing statistics in the following sample run z EN E O 2 oS Us a UE Q ILOG CPLEX 8 1 USER S MANUAL 377 USING PARALLEL OPTIMIZERS Problem fixnet6 mps gz read Read time 0 08 sec CPLEX gt o Tried aggregator 1 time MIP Presolve modified 308 coefficients Aggregator did 1 substitutions Reduced MIP has 477 rows 877 columns and 1754 nonzeros Presolve time 0 02 sec Clique table members 2 MIP emphasis balance optimality and feasibility Root relaxation solution time 0 03 sec Nodes Cuts Node Left Objective IInf Best Integer Best Node ItCnt Gap 0 0 3192 0420 2 3192 0420 308 5 0 0 0 4505 0000 3192 0420 308 29 14 3263 9220 9 4505 0000 Cuts 36 344 27 55 3393 0917 7 4505 0000 Cuts 24 404 24 68 O 0 0 4419 0000 3393 0917 404 23 2254 3439 4758 9 4419 0000 Flowcuts 7 446 22 17 3472 6583 20 4419 0000 Flowcuts 6 462 21 42 3489 9293 9 4419 0000 Flowcuts 5 488 21 02 3498 4754 26 4419 0000 Flowcuts 5 506 20 83 3499 7388 26 4419 0000 Flowcuts 5 521 20 80 3500 8733 26 4419 0000 Flowcuts 3 531 20 78 3526 2044 9 4419 0000 Flowcuts 4 547 20 20 3526 3698 21 4419 0000 Flowcuts 1 548 20 20 d 0 0 0 4310 0000 3526 3698 548 18 18 0 0 0 3985 0000 3526 3698 548 11 51 33 2 0 3983 0000 3791 7448 1130 4 80 Sequential before b amp c Real time 0 55 Parallel b amp c
159. to any positive integer value A line is recorded in the node log for every node with an integer solution if the MIPDisplay parameter is set to 1 or higher and also for any node whose number is a multiple of the MIPInterval value if the MIPDisplay is set to 2 or higher Here is an example of a log file from the Interactive Optimizer where the MIPInterval parameter has been set to 10 Tried aggregator 1 time No MIP presolve or aggregator reductions Presolve time 0 00 sec Root relaxation solution time 0 00 sec Objective is integral Nodes Cuts Node Left Objective IInf Best Integer Best Node ItCnt Gap ep 0 0 4 0000 6 4 0000 12 y o X 4 2 5 0000 0 5 0000 4 0000 17 20 00 10 1 cutoff 5 0000 4 0000 31 20 00 oe cH 3 z Integer optimal solution Objective 5 0000000000e 000 0 Solution time 0 02 sec Iterations 41 Nodes 13 v In that example ILOG CPLEX found the optimal objective function value of 5 0 after exploring 13 nodes and performing 41 dual simplex iterations and ILOG CPLEX found an optimal integer solution at node 4 The MIP interval parameter was set at 10 so every tenth node was logged in addition to the node where an integer solution was found As you can see in that example ILOG CPLEX logs an asterisk in the left most column for any node where it finds an integer feasible solution In the next column it logs the node number It next logs the number of nodes left to explore In the next colu
160. translate applications created in previous versions of ILOG products to Concert Technology Online Documentation The online information files are distributed with the ILOG CPLEX library files and can be found in doc and its sub directories ILOG CPLEX 8 1 USER S MANUAL FOR MORE INFORMATION For More Information ILOG offers technical support and comprehensive Web sites for its products Customer Support For technical support of ILOG CPLEX you should contact your local distributor or if you are a direct ILOG customer contact the nearest regional office Region E mail Telephone Fax France cplex support ilog fr 0 800 09 27 91 33 0 1 49 08 35 10 num ro vert 33 0 1 49 08 35 62 Germany cplex support ilog de 49 6172 406033 49 6172 40 60 10 Spain cplex support ilog es 34 91 710 2480 34 91 372 9976 United Kingdom cplex support ilog co uk 44 0 1344 661600 44 0 1344 661601 Other European cplex support ilog fr 33 0 1 49 08 35 62 33 0 1 49 08 35 10 countries Japan cplex support ilog co jp 81 3 5211 5770 481 3 5211 5771 Singapore cplex support ilog com sg 65 773 06 26 65 773 04 39 USA cplex support ilog com 1 877 ILOG TECH 1 650 567 8001 1 877 456 4832 toll free or 1 650 567 8080 We encourage you to use e mail for faster better service Web Site The ILOG CPLEX Web site at http www ilog com products cplex offers product descriptions press releases and contact information It lists
161. up the pointer ptr and sets ptr to NULL static void free and null char ptr if ptr NULL free ptr ptr NULL END free_and_null static void usage char progname fprintf stderr Usage s X lt datafile gt n progname fprintf stderr where X is one of the following options Mn fprintf stderr is generate problem by row n ILOG CPLEX 8 1 USER S MANUAL fprintf stderr EXAMPLE DIETARY OPTIMIZATION c generate problem by column in fprintf stderr Exiting Mn END usage static int readarray FILE in int status 0 int max num char ch num 0 max 10 data_p double int num_p double data_p malloc max sizeof double if data p NULL status CPXERR NO MEMORY goto TERMINATE for fscanf in c if ch Nt ch Nr ch ch An if ch status 1 goto TERMINATE for int read continue break read fscanf in 1g data_p num if read status 1 goto TERMINATE numt if num gt max max 2 data p double realloc data p max sizeof double if data p NULL status CPXERR NO MEMORY goto TERMINATE do fscanf in c amp ch while ch ch W ch Nt ch Nr if ch break else if
162. we look at the sum of the bounds on the columns we see that x24 x102 x103 x105 x107 x115 x116 x130 x181 2 1443 so it is impossible ILOG CPLEX 8 1 USER S MANUAL DIAGNOSING LP INFEASIBILITY to satisfy the sum of equality rows Therefore to correct the infeasibility we must alter one or more of the bounds or we must increase one or more of the right hand side values Example Setting a Time Limit on the Infeasibility Finder The ILOG CPLEX infeasibility finder will stop when its total runtime exceeds the limit set by the command set timelimit The infeasibility finder works by removing constraints and bounds that cannot be involved in the IIS so it can provide partial information about an IIS when it reaches its time limit The collection of constraints and bounds it offers then do not strictly satisfy the definition of an IIS However the collection does contain a true IIS within it and frequently it provides enough information for you to diagnose the cause of infeasibility in your problem When it reaches the time limit ILOG CPLEX output indicates that it has found only a partial IIS The following example illustrates this idea In it we set a time limit and then invoke the feasibility finder CPLEX set timelimit 2 CPLEX display iis Starting Infeasibility Finder Algorithm Performing row sensitivity filter Infeasibility Finder Algorithm exceeded time limit Partial infeasibility output available Numbe
163. which affects only the aggregator is AggFill Occasionally the substitutions made by the aggregator will increase matrix density and thus make each iteration too expensive to be advantageous In such cases try lowering AggFi11 from its default value of 10 ILOG CPLEX may make fewer substitutions as a consequence and the resulting problem will be less dense Finally if for some reason you wish to turn ILOG CPLEX preprocessing entirely off set the parameter PreInd to O Starting from an Advanced Basis As another performance improvement consider starting from an advanced basis The primal simplex dual simplex and network optimizers can start optimizing from an advanced basis if one is available the barrier optimizer does not start from an advanced basis If you can start from an advanced basis then ILOG CPLEX may iterate significantly fewer times particularly if your current problem is similar to a problem that you have solved previously Even when problems are different starting from an advanced basis may still help performance For example if your current problem is composed of several smaller problems an optimal basis from one of the component problems may significantly speed up solution of the larger problem ILOG CPLEX 8 1 USER S MANUAL 129 o 2 vo T ge Uv al D 3 7 TUNING LP PERFORMANCE 130 Note that if you are solving a sequence of LP models all within one run by entering a model
164. you how to access and interpret results from the optimization after solving the model After analyzing the results you may make changes to the model and study their effect The way to perform such changes and how ILOG CPLEX deals with them is explained in Modifying a Model on page 45 Handling Errors on page 47 discusses the error handling and debugging support provided by Concert Technology and ILOG CPLEX In Example Dietary Optimization on page 49 an example program is presented Not covered in this chapter are advanced functions such as the use of goals or callbacks for querying data about an ongoing optimization and for controlling the optimization itself Goals callbacks and other advanced functions are discussed in Chapter 9 More About Using ILOG CPLEX Modeling an Optimization Problem with Concert Technology In this section we will only give a brief introduction to using Concert Technology for modeling optimization problems to be solved by 11oCplex For a more complete overview see the ILOG Concert Technology User s Manual Modeling Classes A Concert Technology model consists of a set of C objects Each variable each constraint each SOS set and the objective function in a model are represented by an object of the appropriate Concert Technology class We refer to these objects as modeling objects ILOG CPLEX 8 1 USER S MANUAL 33 MODELING AN OPTIMIZATION PROBLEM WITH CONCERT TECHNOLOGY 34 Creatin
165. your application Read Your Messages ILOG CPLEX detects many different kinds of errors and generates exception warnings or error messages about them To query exceptions in the Concert Technology Library use the methods IloInt IloCplex Exception getStatus const const char IloException getMessage const To view warnings and error messages in the Callable Library you must direct them either to your screen or to a log file To direct all messages to your screen use the routine CPXsetintparam to set the parameter CPX PARAM SCRIND To direct all messages to a log file use the routine CPXsetlogfile Check Return Values Most methods and routines of the Component Libraries return a value that indicates whether the routine failed where it failed and why it failed This return value can help you isolate the point in your application where an error occurs If a return value indicates failure always check whether sufficient memory is available Beware of Numbering Conventions If you delete a portion of a problem ILOG CPLEX changes not only the dimensions but also the indices of the problem If your application continues to use the former dimensions and indices errors will occur Therefore in parts of your application that delete portions of the problem look carefully at how dimensions and indices are represented Make Local Variables Temporarily Global If you are having difficulty tracking dow
166. 0 0 0 0 15 0 5 0 0 0 0 0 10 0 Define list of tail or from node indices as well as head or to node indices for the arcs Notice that according to C standard the first node has index 0 int tail NARCS 0 1 2 3 6 5 4 4 2 3 3 5 5 1 int head NARCS 1 2 3 6 5 i T 1 1 4 5 3 4 5 Define list of objective values and lower and upper bound values for the arcs double obj NARCS 3 0 3 0 4 0 3 0 5 0 6 0 7 0 4 0 2 0 6 0 5 0 4 0 3 0 6 0 double ub NARCS 24 0 25 0 12 0 10 0 9 0 inf 20 0 P0 0 5 0 15 0 20 0 2130 6 0 int double lb NARCS 18 0 0 0 12 0 0 0 0 0 inf 0 0 0 0 0 0 OO 0 0 20 0 0 0 20 0 T Delete existing network This is not necessary in this context since we know we have an empty network object Notice that CPXNETdelnodes deletes all arcs incident to 186 ILOG CPLEX 8 1 USER S MANUAL EXAMPLE USING THE NETWORK OPTIMIZER WITH THE CALLABLE LIBRARY the deleted nodes as well Therefore this one function call effectively deletes an existing network problem if CPXNETgetnumnodes env net gt 0 status CPXNETdelnodes env net 0 CPXNETgetnumnodes env net 1 if status goto TERMINATE Set growth rates for rows nodes and columns arcs This is to avoid internal memory reallocations while adding nodes and arcs Since we are adding all nodes and all arcs using only one function call for each
167. 00 0 eee eee nnn 199 Optimizing QPS 1 2 cetien oxen ei asec cae eee ee Bae a 201 Diagnosing QP Infeasibility liliis 202 Example Creating a QP Optimizing Finding a Solution 203 Example llogpexl opp soe were rx deed Ern OX WAP TES ena eene 203 ILOG CPLEX 8 1 USER S MANUAL Chapter 8 TABLE OF CONTENTS Example QPex1 ava vi voire Haw ce Pr had vig Heed eta ed ees 205 Example Reading a QP froma File 00 c eee eee eee eee eens 215 Complete Program qpex2 c 1 cette ents 215 Solving Mixed Integer Programming Problems see 223 Sample Stating a MIP Problem sseseseeeeee RII nnn 224 Considering Preliminary Issues eseeeeeee RII 225 Entering MIP ProblemS ins perre pene ee kc dne ick tete tcp o et lene ee are 225 Displaying MIP Problems sseeeeeeee IIIA 226 Changing Problem Type in MIPS 0 0 e eee eee B BB 226 Using the Mixed Integer Optimizer 0 00 cece eee II 229 Feasibility and Optimality 2 2 2 ete eee 229 Performance Features of the Mixed Integer Optimizer llle cee aca 231 ur Em 235 Parameters Affecting Cuts l l 237 FleuriStiCS x e Magen dh gee ex ian E NX RUE RO wate wees RE 238 PIODING 4 935 S Hed chek eo Rr etate tired tobtsc bone a i epis e dd e 238 Preprocessing Presolver and Aggregator 0 cece tes 239 Starting from a Solution 2 2 nananana 240 P
168. 181 215 297 299 PXordwrite routine 277 PXprimopt routine 97 261 PXPROB FIXEDMILP symbolic constant 261 PXPUBLIC symbolic constant 95 PXPUBVARARGS symbolic constant 95 PXqpopt 215 PXqpopt routine 207 PXqpwrite routine 198 PXreadcopybase routine 130 PXreadcopyprob routine 86 310 pxresults message channel 297 PXsavwrite routine 118 PXsetdblparam routine 92 99 PXsetdefaults routine 99 PXsetintparam routine 92 98 120 151 181 257 374 tlogfile routine 94 95 120 160 295 296 297 tlpcallbackfunc routine 95 350 352 PXsetmipcallbackfunc routine 95 350 PXsetstrparam routine 92 99 PXsolution routine 102 261 350 PXsoswrite routine 277 PXstrcpy routine 96 PXstrlen routine 96 Hj Hj AE E E E E E Di pm PXse PXse USER S MANUAL 407 INDEX CPXtreewrite routine 242 CPXVOIDptr data type 95 cpxwarning message channel 297 CPXwriteprob routine 102 118 138 277 CPXwritesol routine 93 create modeling variables 61 new rows 75 objective function 61 ranged constraints 61 creating application with Concert Technology 33 CPLEX environment 181 log file 295 network flow problem object 181 parameter specification file 401 problem object 86 crossover file format 160 irreducibly inconsistent set IIS and 173 verifying barrier solutions 169 cumulative constraint 146 147 cuts 235 319 adding 2
169. 2X2 A2nXn bz X b Og X Am2X2 Xy with these bounds h K Sys iu Un where the relation may be greater than or equal to less than or equal to or simply equal to and the upper bounds u and lower bounds may be positive infinity negative infinity or any real number When a linear optimization problem is stated in that conventional form we customarily refer to its coefficients and values by these terms objective function coefficients Cp Ch constraint coefficients App gn right hand side bj 3 Dy upper bounds uy Up lower bounds lj d variables or unknowns Xp x AR ILOG CPLEX 8 1 USER S MANUAL WHAT YOU NEED TO KNOW In the most basic linear optimization problem the variables of the objective function are continuous in the mathematical sense with no gaps between real values To solve such linear programming problems ILOG CPLEX implements optimizers based on the simplex algorithms both primal and dual simplex as well as primal dual logarithmic barrier algorithms and a sifting algorithm These alternatives are explained more fully in Chapter 5 Solving Linear Programming Problems ILOG CPLEX can also handle certain problems in which the objective function is not linear but quadratic The constraints in such a problem are still linear Such problems are known as quadratic programs or QPs Chapter 7 Solving Quadratic Programming Problems covers those kinds of problems ILOG CPLEX
170. 3 1 The types starting with CPXC represent the corresponding pointers to constant const objects Table 3 1 Special data types in the ILOG CPLEX Callable Library Data type Is a pointer to Declaration Set by calling CPXENVptr ILOG CPLEX CPXENVptr env CPXopenCPLEX CPXCENVptr environment m CPXLPptr problem object CPXLPptr lp CPXcreateprob z CPXCLPptr 9 CPXNETptr problem object CPXNETptr net CPXNETcreateprob D CPXCNETptr feg D CPXCHANNELptr message channel CPXCHANNELptr channel CPXgetchannels 5 CPXaddchannel D lt When any of these special variables are set to a value returned by an appropriate routine that value can be passed directly to other ILOG CPLEX routines that require such parameters The actual internal type of these variables is a memory address that is a pointer this address uniquely identifies the corresponding object If you are programming in a language other than C you should choose an appropriate integer type or pointer type to hold the values of these variables Ownership of Problem Data The ILOG CPLEX Callable Library does not take ownership of user memory All arguments are copied from your user defined arrays into ILOG CPLEX allocated memory ILOG CPLEX manages all problem related memory After you call a ILOG CPLEX routine that copies data into a ILOG CPLEX problem object you can free the memory you used as arguments to the copying routine IL
171. 36 clique 235 cover 235 disjunctive 235 flow cover 235 flow path 236 Gomory fractional 236 GUB cover 236 implied bound 236 local or global 320 MIR 236 recorded in MIP node log file 248 re optimizing 236 what are 235 D data entering 86 data types special 89 debugging 408 ILOG CPLEX 8 1 Callable Library and 118 diagnostic routines and 94 heap 120 Interactive Optimizer and 118 return values and 120 defined 84 degeneracy 138 dual 257 delete goal stacks 326 deleting model objects 46 deleting nodes 326 deleting variables 82 dense column 167 Depth First 233 destroying CPLEX environment 87 nodes 182 problem object 87 devex pricing 132 diagnosing infeasibility in QPs 202 network infeasibility 190 diagnostic routine 94 log file and 94 message channels and 94 redirecting output from 94 diet model 64 diff 62 DIMACS 291 dimensions checking 121 disjunctive cuts 235 displaying barrier information 160 barrier solution quality 163 basis condition 137 bound infeasibilities 141 column nonzeros parameter 171 infeasibilities on screen 141 143 144 messages 298 MIP information periodically 249 MIP solution information 243 network objective values 178 network solution information 181 network solution on screen 182 USER S MANUAL optimization progress 352 parameter settings 400 401 problem dimensions 121 problem statistics 121 reduced cost infeasibilities 141 simplex so
172. 393 Managing Parameters in the Interactive Optimizer 0 eee eee eee eee 400 Saving a Parameter Specification File 0 0 c cece eee eee eee eee eee 400 2 EEE CEP 403 ILOG CPLEX 8 1 USER S MANUAL 13 TABLE OF CONTENTS 14 ILOG CPLEX 8 1 USER S MANUAL List of Figures Figure 1 1 A View of Concert Technology for C Users 0 0 0 0 cece eee eee 32 Figure 2 1 A View of Concert Technology for Java Users 0 0 0 cece eee eee 60 Figure 3 1 A View of the ILOG CPLEX Callable Library 0 0 00 e eee 84 Figure 6 1 A Directed Network with Arc Capacity Flow Cost Sinks and Sources 178 Figure 7 1 Maximize a Concave Objective Function Minimize a Convex Objective Function 196 Figure 9 1 ILOG CPLEX Message Handling Routines llle eese 298 ILOG CPLEX 8 1 USER S MANUAL 15 LIST OF FIGURES 16 ILOG CPLEX 8 1 USER S MANUAL List of Tables Table 1 1 Concert Technology Modeling Objects 0 0 cece eee ee 37 Table 1 2 Optimizer Options ccecce ecset ett 40 Table 1 3 Algorithm Status and Information About the Model lesus 42 Table 2 1 Choosing Lower and Upper Bound Values 0 000 cece eee esee 63 Tabl 2 2 Solution Status secsi ceri Ru EE 4E Paid ER wae de ute edere 67 Table 2 3 Algorithm Types 2 0 were criari em repete ERES pidis Ree EE ada 70 Table 2 4 Constants in lloCplex PrimalPricing 00 6 e eee ee eee 71
173. 4 2 98 x24 3 47 x34 0 25 w14 0 25 w24 0 25 w34 rhs add 20 25 lhs add 2 08 x15 2 98 x25 3 47 x35 2 24 x45 2 08 x55 0 25 w15 0 25 w25 0 25 w35 0 25 w45 0 25 w55 rhs add 16 25 int main int argc char argv IloEnv env try IloModel m IloCplex cplex env IloObjective obj IloNumVarArray var env IloRangeArray con env env out reading examples data noswot mps endl cplex importModel m examples data noswot mps obj var con env out lt lt extracting model lt lt endl cplex extract m cplex setParam IloCplex MIPInterval 1000 env out lt lt initializing cuts lt lt endl IloExprArray lhs env IloNumArray rhs env makeCuts var lhs rhs env out lt lt solving model n S cplex solve CutGoal env lhs rhs cplex getParam IloCplex EpRHS o env out lt lt solution status is lt lt cplex getStatus lt lt endl Q E env out solution value is cplex getObjValue endl O 0 a amp catch IloException amp ex m Cc cerr lt lt Error lt lt ex lt lt endl x Y vo env end return 0 The goal Cut Goal in this example receives a list of less than constraints to use as global cuts and a tolerance value eps The constraints are passed to the goal as an array of 1hs expressions and an array of corresponding rhs values Both are initialized in
174. 4 x25 loNumVar x31 x32 x33 x34 x35 loNumVar x41 x42 x43 x44 x45 loNumVar x51 x52 x53 x54 x55 3 3 3 Eq 2 o O 2 oS nom R mo Q loNumVar w11 w12 w13 w14 w15 W24 w25 loNumVar w31 w32 w33 w34 w35 loNumVar w41 w42 w43 w44 w45 loNumVar w51 w52 w53 w54 w55 loInt num vars getSize loNumVar w21 w22 w2 ILOG CPLEX 8 1 USER S MANUAL 365 USING CALLBACKS 366 for IloInt i i el el ILOG CPLEX 8 1 LSG LSe LSe LSe LSe LSe LSe LSG LSe LSG LSe LSe LSe LSe LSG LSe LSe LSe LSe LSe se LSG LSe LSe LSe LSE LSG LSe LSe LSe LSe LSG LSe LSG LSe LSe LSe LSe LSG LSe LSe LSe LSe LSe LSe LSe LSe LSe LSe if TE TE IF if if if af ce TE if if If xa TE LT if if if TE AT AF Af if if IF E TE if if if IF if if if if IF TE if TE if IF if if if TE IF if af 0 strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars st
175. 40 and so on Probing While most of the suggestions in this section are oriented toward overcoming specific obstacles the probing feature can help in many different ways on difficult models Probing is a technique that looks at the logical implications of fixing each binary variable to 0 or 1 It is performed after preprocessing and before the solution of the root relaxation Probing can be expensive so this parameter should be used selectively On models that are in some sense easy the extra time spent probing may not reduce the overall time enough to be worthwhile On difficult models probing may incur very large runtime costs at the beginning and yet pay off with shorter overall runtime When you are tuning performance it is usually because the model is difficult and then probing is worth trying At the Probe parameter s default setting of 0 ILOG CPLEX will automatically determine the appropriate level of probing Setting the Probe parameter to 1 2 or 3 results in increasing levels of probing to be performed beyond the default level of probing A setting of 1 results in no probing being performed To activate probing In the Interactive Optimizer use the command set mip strategy probe i Inthe Concert Technology Library set the integer parameter Probe In the Callable Library set the integer parameter CPX PARAM PROBE ILOG CPLEX 8 1 USER S MANUAL USING THE MIXED INTEGER OPTIMIZER Preprocessing Preso
176. 51 getName W52 getName W53 getName W54 getName W55 USER S MANUAL 1 xj 8 Y y in 5 M y 8 j 3j 3 Y i 9 8 1 5 0 y i 2j 8 y n 5 L j 8 1 C O S OO D O S OOO OO CO 0 QUO C CO OU 0 0 O UO OO O XO CO 0 0 0 0 O CO OC 00 0 O0 0 0 O0 O D uu x11 x12 x13 x14 x15 x21 x22 x23 x24 x25 x31 x32 x33 x34 x35 x41 x42 x43 x44 x45 x51 x52 x53 x54 x55 wil w12 w13 w14 w15 w21 w22 w23 w24 w25 w31 w32 w33 w34 w35 w41 w42 w43 w44 w45 w51 w52 w53 w54 w55 vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars vars H H H He He H He H H He H H H H H He H H H H H H H Bop H He H H He pe peo He H He He H He He He He He He He pRope He H H H USING CALLBACKS lhs add x21 x22 rhs add 0 0 lhs add x22 x23 rhs add 0 0 lhs add x23 x24 rhs add 0 0 lhs add 2 08 x11 2 98 x21 3 47 x31 2 24 x41 2 08 x51 0 25 w11 0 25 w21 0 25 w31 0 25 w41 0 25 w51 rhs add 20 25 lhs add 2 08 x12 2 98 x22 3 47 x32 2 24 x42 2 08 x52 0 25 w12 0 25 w22 0 25 w32 0 25 w42 0 25 w
177. 52 rhs add 20 25 lhs add 2 08 x13 2 98 x23 3 47 x33 2 24 x43 2 08 x53 0 25 w13 0 25 w23 0 25 w33 0 25 w43 0 25 w53 rhs add 20 25 lhs add 2 08 x14 2 98 x24 3 47 x34 2 24 x44 2 08 x54 0 25 w14 0 25 w24 0 25 w34 0 25 w44 0 25 w54 rhs add 20 25 lhs add 2 08 x15 2 98 x25 3 47 x35 2 24 x45 2 08 x55 0 25 w15 0 25 w25 0 25 w35 0 25 w45 0 25 w55 rhs add 16 25 int main int argc char argv IloEnv env try IloModel m IloCplex cplex env IloObjective obj a o O 2 oS nom R mo Q IloNumVarArray var env IloRangeArray con env env out lt lt reading examples data noswot mps lt lt endl cplex importModel m examples data noswot mps obj var con env out lt lt constructing cut callback lt lt endl IloExprArray lhs env IloNumArray rhs env makeCuts var lhs rhs ILOG CPLEX 8 1 USER S MANUAL 367 USING CALLBACKS 368 cplex use CtCallback env lhs rhs cplex getParam IloCplex EpRHS env out lt lt extracting model lt lt endl cplex extract m cplex setParam IloCplex MIPInterval 1000 env out lt lt solving model n cplex solve env out lt lt solution status is lt lt cplex getStatus lt lt endl env out lt lt solution value is lt lt cplex getObjValue lt lt endl catch IloException amp ex
178. 7 CPX PA CPX PA M FLOWPATHS parameter 237 CPX PA CPX PA AM FRACCUTS parameter 237 GUBCOVERS parameter 237 IMPLBD parameter 237 INTSOLLIM parameter 242 CPX PA MIPTHREADS parameter 372 CPX PA MIRCUTS parameter 237 CPX PARAM NODELIM parameter 242 CPX PARAM NODESEL parameter 232 CPX PA CPX PA CPX PA CPX PA CPX PA BSS BB d D BREESE SS BS d Di Ud UJ Ud pP p p pp H I M NZGROWTH parameter 90 M PREIND parameter 239 M PROBE parameter 238 M RELAXPREIND parameter 239 ROWGROWTH parameter 90 182 BSS S amp S d D CPX PARAM SCRIND parameter 94 120 138 151 181 297 351 CPX PARAM SIMTHREADS parameter 372 CPX PARAM STARTALG parameter 257 406 ILOG CPLEX 8 1 CX CX Y QeQQ C CQ COR CX CX X OQ OQ Q OQ QC CO O0 CX OQ CO Q Q GO CY CX CY YO CX Qo Gt OQ G A PX PARAM STRONGTHREADLIM parameter 372 PX PARAM THREADS parameter 371 PX PARAM TILIM parameter 242 PX PARAM TRE parameter 242 PX PARAM VARSEL parameter 232 PX PARAM WORKMEM parameter 242 PX SEMICONT 246 PX SEMIINT 246 PXaddchannel routine 89 298 PXaddcols routine 86 90 114 PXaddfpdest routine 95 298 299 PXaddfuncdest routine 95 298 299 PXaddrows routine 86 90 101 114 PXALG BARRIER symbolic constant 258 PXCENVptr 89 PXCHANNELptr data type 89 PXCHARptr data type 95 PXcheckadd
179. 8 1 USER S MANUAL o 2 Q T U Uv al e D 3 7 CHOOSING AN OPTIMIZER FOR YOUR LP PROBLEM Choosing an Optimizer for Your LP Problem 124 ILOG CPLEX offers several different optimizers for linear programming problems Each of these optimizers is available whether you call ILOG CPLEX from within your own application using Concert or the Callable Library or you use the Interactive Optimizer The choice of LP optimizer in ILOG CPLEX can be specified through a parameter named CPX_PARAM_LPMETHOD in the Callable Library and named LPMETHOD in the Interactive Optimizer In both the C and Java versions of Concert the LP method is controlled by the RootAlg parameter which also controls related aspects of QP and MIP solutions as explained in the corresponding chapters of this manual In this chapter this parameter will be referred to uniformly as LPMethod When you solve a model via cplex solve Concert cPXlpopt Callable Library optimize Interactive Optimizer the LPMethod parameter determines which optimizer will be used The choices for LPMethod which are explained in the next subsections are Table 5 1 LPMethod Parameter Values for Optimizer Choice LPMethod Meaning Values 0 Automatic default setting 1 Primal Simplex 2 Dual Simplex 3 Network Simplex Barrier 5 Sifting 6 Concurrent Dual Barrier and Primal ILOG CPLEX 8 1 USER S MA
180. 9 8 Parallel Optimizer Methods and Routines Optimizer lloCplex Method Callable Library Parallel MIP Optimizer solve CPXmipopt Parallel Barrier Optimizer setParam RootAlg Barrier CPXbaropt Or CPXhybbaropt Parallel Simplex Optimizer setParam RootAlg Primal or CPXprimopt or setParam RootAlg Dual CPXdualopt Parallel MIP Optimizer The ILOG CPLEX Parallel MIP Optimizer delivers significant increases in speed on a wide variety of models particularly on difficult ones that solve a large number of nodes in the branch amp cut search tree There are several different opportunities for applying multiple processors to the solution of a MIP problem Increase the Global Thread Parameter The most straightforward way to invoke parallelism is by setting the global thread parameter Threads to a value greater than 1 to indicate the desired degree of parallelism If the other parameters remain set to their default values the result is that nodes in the branch amp cut tree will be processed in parallel that is each node is solved in its entirety on one of the available processors independently of the work being performed on other processors In typical cases the number of nodes waiting for solution quickly becomes greater than the number of threads creating enough work which can be done in parallel to make speed increases possible ILOG CPLEX automatically manages the pool of nodes so tha
181. A flow that satisfies the constraints and bounds is feasible Example Network Optimizer in the Interactive Optimizer This example is based on a network where the aim is to minimize cost and where the flow through the network has both cost and capacity Figure 6 1 shows you the nodes and arcs of this network The nodes are labeled by their identifying node number from 1 through 8 The number inside a node indicates its supply value 0 zero is assumed where no number is given The arcs are labeled 1 through 14 The lower bound 1 upper bound u and objective value c of each arc are displayed in parentheses 1 u c beside each arc In this example node 1 and node 5 are sources representing a positive net flow whereas node 4 and node 8 are sinks representing negative net flow ILOG CPLEX 8 1 USER S MANUAL 177 EXAMPLE 178 NETWORK OPTIMIZER IN THE INTERACTIVE OPTIMIZER N SD oe UJ wm gt oo A14 0 inf 6 A2 0 25 3 py c S 0 6V A10 0 15 6 3 AS 0 9 5 A3 12 12 4 A4 0 10 3 Figure 6 1 A Directed Network with Arc Capacity Flow Cost Sinks and Sources In the standard distribution of ILOG CPLEX the file nexample net contains the formatted problem formulation for this example You can read it into the Interactive Optimizer with the command read nexample net After you read the problem into the Interactive Optimizer you can solve it w
182. AM SIFTALG SIFTING ALGORITHM SiftDisplay Int CPX PARAM SIFTDISPLAY SIFTING DISPLAY SiftItLim Int CPX PARAM SIFTITLIM SIFTING ITERATIONS SimDisplay Int CPX PARAM SIMDISPLAY SIMPLEX DISPLAY SimThreads Int CPX PARAM SIMTHREADS SIMPLEX LIMITS THREADS SingLim Int CPX PARAM SINGLI SIMPLEX LIMITS SINGULARITY StrongCandLim In CPX PARAM STRONGCANDLIM MIP LIMITS STRONGCAND StrongItLim Int CPX PARAM STRONGITLIM MIP LIMITS STRONGIT StrongThreadLim Int CPX PARAM STRONGTHREADLIM MIP LIMITS STRONGTHREADS Symmetry Bool CPX PARAM SYMMETRY PREPROCESSING SYMMETRY Threads Int CPX PARAM THREADS THREADS 390 ILOG CPLEX 8 1 USER S MANUAL ILOG CPLEX Parameter Names Table A 1 Parameter Name Equivalents Concert Type Callable Library Interactive Optimizer TiLim Num CPX PARAM TILI TIMELIMI TreLim Num CPX PARAM TRELIM MIP LIMITS TREEMEMORY VarSel Int CPX PARAM VARSEL MIP STRATEGY VARIABLESELECT WorkDir Str CPX PARAM WORKDIR WORKDIR WorkMem Num CPX PARAM WORKMEM WORKME XXXInd Bool CPX PARAM XXXIND SIMPLEX XXXSTART ILOG CPLEX 8 1 USER S MANUAL 391 ILOG CPLEX Parameter Names 392 ILOG CPLEX 8 1 USER S MANUAL Interactive Optimizer Commands The following table lists Interactive Optimizer commands their primary options and pages in this manual on which usage examples can be found
183. CPLEX 8 1 USER S MANUAL EXAMPLE USING SOS AND PRIORITY x add IloNumVar env 0 0 IloInfinity ILOINT x add IloNumVar env 0 0 IloInfinity ILOINT x add IloNumVar env 2 0 3 0 ILOINT model add IloMaximize env x 0 2 x 1 3 x 2 x 3 e add x 0 x 1 x 2 10 x 3 lt 20 c add x 0 3 x 1 x 2 lt 30 c add x 1 3 5 x 3 0 model add c model add IloSOS1 model getEnv IloNumVarArray model getEnv 2 x 2 x 3 IloNumArray env 2 25 0 18 0 JER END populatebyrow Complete Program mipex3 c This example derives from mipex1 c The differences between that simpler MIP example and this one are The problem solved is slightly different so the output is interesting The actual SOS and priority order that the example implements are arbitrary they do not necessarily represent good data for this problem The routine CPXwriteprob writes the problem to disk before the example copies the SOS and priority order to verify that the base problem was copied correctly v AS fej ES D di Buinjos The ILOG CPLEX preprocessing parameters for the presolver and aggregator are turned off to make the output interesting Generally we do not require nor recommend doing this The routine setsosandorder sets the SOS and priority order e Itcalls CPXcopysos to copy the SOS into the problem object e Itcalls CPXcopyorder to copy the pr
184. CPLEX 8 1 USER S MANUAL 47 HANDLING ERRORS All exceptions thrown by Concert Technology classes including 11oCplex are derived from IloExcept ion Exceptions thrown by algorithm classes such as 11o0Cplex are derived from its child class IloAlgorithm Exception The most common exceptions thrown by ILOG CPLEX are derived from 11oCplex Exception a child class of IloAlgorithm Exception Objects of the exception class IloCplex Exception correspond to the error codes generated by the ILOG CPLEX Callable Library The error code can be queried from a caught exception by calling method IloInt IloCplex Exception getStatus const The error message can be queried by calling method const char IloException getMessage const which is a virtual method inherited from the base class IloException If you want to access only the message for printing to a channel or output stream it is more convenient to use the overloaded output operator operator lt lt provided by Concert Technology for IloException In addition to exceptions corresponding to error codes from the C Callable Library a cplex object may throw exceptions pertaining only to 11oCplex For example the exception IloCplex MultipleObjException is thrown if a model is extracted containing more than one objective function Such additional exception classes are derived from class IloCplex Exception objects can be recognized by a negative status code retur
185. CPLEX calls the MIP callback periodically during the probing phase of MIP preprocessing periodically during cut generation and once before each subproblem is solved in the branch and cut process Every user defined callback must have these arguments env a pointer to the ILOG CPLEX environment cbdata a pointer to ILOG CPLEX internal data structures needed by CPXgetcallbackinfo wherefrom indicates which optimizer is calling the callback cbhandle a pointer supplied when your application calls CPXsetlpcallbackfunc Or CPXsetmipcallbackfunc so that the callback has access to private user data The arguments wherefrom and cbdata should be used only in calls to CPXgetcallbackinfo Return Values for Callbacks A user written callback should return a nonzero value if the user wishes to stop the optimization and a value of zero otherwise For LP or QP problems if the callback returns a nonzero value the solution process will terminate If the process was not terminated during the presolve process the status returned by the function TloCplex getStatus or the routines CPXsolution or CPXgetstat will be CPX STAT ABORT USER value 13 For both LP and MIP problems if the LP callback returns a nonzero value during presolve preprocessing the optimizer will return the value CPXERR PRESLV ABORT and no solution information will be available ILOG CPLEX 8 1 USER S MANUAL USING CALLBACKS
186. CPXsetmipcallbackfunc it must declare the user written callback functions with the CPXPUBLIC designation For UNIX systems this has no effect For Win32 systems this will cause the callback functions to be declared with the Stdcall calling convention For examples of function pointers and callbacks see Example Using Callbacks on page 351 and Example Using the Message Handler on page 298 CPXCHARptr CPXCCHARptr and CPXVOIDptr The types CPXCHARptr and CPXVOIDptr are used in the header file cplex h to avoid the complicated syntax of using the CPXPUBLIC designation on functions that return char const char Or void File Pointers File pointer arguments for Callable Library routines should be declared with the type CPXFILEptr On UNIX platforms this practice is equivalent to using the file pointer type On Win32 platforms the file pointers declared this way will correspond to the environment of the ILOG CPLEX DLL Any file pointer passed to a Callable Library routine should be obtained with a call to CPX open and closed with CPX c1ose Callable Library routines with file pointer arguments include CPXsetlogfile CPXaddfpdest ILOG CPLEX 8 1 USER S MANUAL 95 2 D ie D D o A 5 lt ILOG CPLEX PROGRAMMING PRACTICES 96 CPXdelfpdest and CPXfputs Handling Message Channels Callable Library Routines on page 297 discusses most of those routines String Functions Se
187. Could not register CPLEX license status d n status goto TERMINATE env CPXopenCPLEX amp status if env NULL char errmsg 1024 fprintf stderr Could not open CPLEX environment n CPXgeterrorstring env status errmsg fprintf stderr s errmsg goto TERMINATE a o O 2 oS nom R mo Q The registerLicense Routine for Java Users Here is an example using IloCplex registerLicense for Java users static String ilm_CPLEX_license LICENSE ILOG Test n RUNTIME CPLEX 8 000 021 Apr 2002 R81GM34ECZTS N IRIX options m static int ilm CPLEX license signature 2756133 public static void main String args ILOG CPLEX 8 1 USER S MANUAL 383 CPLEX RUNTIME DEVELOPMENT AND LICENSING PROCEDURES try IloCplex registerLicense ilm CPLEX license ilm CPLEX license signature IloCplex cplex new IloCplex catch IloException e System err println Exception caught for runtime license e Summary ILM runtime license keys come in two forms Users of file based RTNODE RTSTOKEN and TOKEN keys should use the CPXputenv or I1oCplex putenv routine to identify the location CPXputenv Users of memory based RUNTIME keys should use the CPXRegisterLicense or IloCplex registerLicense routine to pass the key to the ILOG License Manager embedded inside the CPLEX Component Libraries Refer to the ILOG License Manager online documentation that comes with
188. Dietary Optimization esee RII 49 Program Description rs nllsxI be RB LIes Peder ti Reque dedu weg re eet der d 51 Solving the Model with lloCplex lseeeeseeee RR 53 Complete Program seis ues dues ex xus Re eig bac Eqox eu Re Wea x dnm I RR e RR Te 54 ILOG Concert Technology for Java Users 000 cee eee eee 59 Modeling with Concert Technology e cece cece eee RIAM 60 Modeling with lloModeler 0 0 ete 61 TheActive Mod l tent tide det nese dre Reese erectos ete det PO o CRUS 64 Building the Model 525 cea ceeds eave koh er E Fa RR RR RERO CR 64 Solving the Model 2 crnisss oh ep x Er RR eee name ke eee a ea 66 Accessing Solution Information 00 c cece eee eee nnn 68 Choosing an Optimizer vuerhibRLx nc pee head ande es uade jhe dees 69 Solving a Single LP or QP 1 nsn 69 Solving Subsequent LPs or QPs ina MIP 0 0 0 c eect eee 70 Controlling ILOG CPLEX Optimizers 00 0 e eee eee eee 70 ILOG CPLEX 8 1 USER S MANUAL Chapter 3 TABLE OF CONTENTS Paramete Seegen ta pex heed ebur bete dedi i BE ha le ta a Men are dete ees 70 More Solution Information sleseeeeeee IRI 72 Dual Solution Information l lllsleieleeeee eae 72 Basis Information 55s o rp ER IS RI x PIS Ie IS LPRERL URN OIM ts 72 Infeasible Solution Information liiis 73 Solution Quali ss s ion ends tice od Opto atit Reque a eR Ros eee 74 Advanced Mo
189. E E Copyright C 1997 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products M lpex7 c Reading in and optimizing a problem Printing names with the answer This is a modification of lpex2 c To run this example command line arguments are required i e lpex7 filename method where filename is the name of the file with mps lp or sav extension method is the optimization method default primal simplex dual simplex network with dual simplex cleanup barrier with crossover barrier without crossover sifting concurrent Qqaunors5ato Example lpex7 example mps o ay Bring in the CPLEX function declarations and the C library header file stdio h with the following single include 310 ILOG CPLEX 8 1 USER S MANUAL USING QUERY ROUTINES IN THE CALLABLE LIBRARY finclude lt ilcplex cplex h gt Bring in the declarations for the string and character functions and malloc include lt ctype h gt include lt stdlib h gt include lt string h gt Include declarations for functions in this program static void free_and_null char ptr usage char progname int main int argc char argv Declare and allocate space for the variables and arrays where we will store the optimization results including the status ob
190. ER DISPLAY BarEpComp Num CPX PARAM BAREPCOMP BARRIER CONVERGETOL BarGrowth Num CPX PARAM BARGROWTH BARRIER LIMITS GROWTH BarItLim Int CPX PARAM BARITLI BARRIER LIMITS ITERATIONS BarMaxCor Int CPX PARAM BARMAXCOR BARRIER LIMITS CORRECTIONS BarObjRng Num CPX PARAM BAROBJRNG BARRIER LIMITS OBJRANGE 386 ILOG CPLEX 8 1 USER S MANUAL ILOG CPLEX Parameter Names Table A 1 Parameter Name Equivalents Concert Type Callable Library Interactive Optimizer BarOOC Bool CPX PARAM BAROOC BARRIER OUTOFCORE BarOrder Int CPX PARAM BARORDER BARRIER ORDERING BarStartAlg Int CPX PARAM BARSTARTALG BARRIER STARTALG BarThreads Int CPX PARAM BARTHREADS BARRIER LIMITS THREADS BarVarUp Num CPX PARAM BARVARUP BARRIER LIMITS VARUPPER BasInterval Int CPX PARAM BASINTERVAL SIMPLEX BASISINTERVAL BBInterval Int CPX PARAM BBINTERVAL IP STRATEGY BBINTERVAL BndStrenInd Int CPX PARAM BNDSTRENIND PREPROCESSING BOUNDSTRENGTH BrDir Int CPX PARAM BRDIR IP STRATEGY BRANCH BtTol Num CPX PARAM BTTOL IP STRATEGY BACKTRACK Clique
191. For MIP problems if the callback returns a nonzero value the solution process will terminate and the status returned by IloCplex getStatus or CPXgetstat will be one of the values in Table 9 5 Table 9 5 Status of Nonzero Callbacks for MIPs Value Symbolic constant Meaning 113 CPXMIP_ABORT_FEAS current solution integer feasible 114 CPXMIP_ABORT_INFEAS no integer feasible solution found Interaction Between Callbacks and ILOG CPLEX Parallel Optimizers When you use callback routines and invoke the parallel version of ILOG CPLEX optimizers you need to be aware that the ILOG CPLEX environment passed to the callback routine corresponds to an individual ILOG CPLEX thread rather than to the original environment created ILOG CPLEX frees this environment when finished with the thread This does not affect most uses of the callback function However keep in mind that ILOG CPLEX associates problem objects parameter settings and message channels with the environment that specifies them ILOG CPLEX therefore frees these items when it removes that environment if the callback uses routines like CPXcreateprob CPXcloneprob or CPXgetchannels those objects remain allocated only as long as the associated environment does Similarly setting parameters with routines like CPXsetintparam affects settings only within the thread So applications that access ILOG CPLEX objects in the callback should use the original en
192. Include declaration for functions at end of program static int readarray FILE in int num_p double data_p readdata char file int nfoods_p double cost_p double lb_p double ub_p int nnutr_p double nutrmin_p double nutrmax_p double nutrper_p populatebyrow CPXENVptr env CPXLPptr lp int nfoods double cost double lb double ub int nnutr double nutrmin double nutrmax double nutrper populatebycolumn CPXENVptr env CPXLPptr lp int nfoods double cost double lb double ub int nnutr double nutrmin double nutrmax double nutrper static void 102 ILOG CPLEX 8 1 USER S MANUAL EXAMPLE DIETARY OPTIMIZATION free_and_null char ptr usage char progname int main int argc char argv int status 0 int nfoods int nnutr double cost NULL double lb NULL double ub NULL double nutrmin NULL double nutrmax NULL double nutrper NULL double x NULL double objval int solstat Declare and allocate space for the variables and arrays where we will store the optimization results including the status objective value variable values dual values row slacks and variable reduced costs J 7 CPXENVptr env NULL m CPXLPptr lp NULL int i j o Check the command line arguments r cs if arge 3 Ll D argv 1 0 t N zZ strchr rc argv 1 1 NULL usage argv 0
193. Java API offers to solve mathematical programming problems An overview of the architecture is given then techniques for creating models are explained Chapter 3 The ILOG CPLEX Callable Library introduces the ILOG CPLEX Callable Library It describes the architecture of the product explains the relation between the Interactive Optimizer and the Callable Library and offers an example of programming with the Callable Library It also provides an overview about the parameters you control in ILOG CPLEX Chapter 4 Further Programming Considerations provides tips on developing applications with ILOG CPLEX suggests ways to debug your applications built around ILOG CPLEX and provides a checklist to help avoid common programming errors Chapter 5 Solving Linear Programming Problems goes deeper into aspects of linear programming with ILOG CPLEX It explains how to tune performance how to diagnose infeasibility in a model and how to use the primal dual logarithmic barrier algorithm implemented in the ILOG CPLEX Barrier Optimizer on large sparse linear programming problems It also offers an example showing you how to start optimizing from an advanced basis Chapter 6 Solving Network Flow Problems describes how to use the ILOG CPLEX Network Optimizer on linear programming problems based on a network model Chapter 7 Solving Quadratic Programming Problems takes up programming problems in which the objective function may be quadratic It too inclu
194. LEX Concert Technology Library 31 Bora PEPTIDE 32 Compiling and Linking llseseeseee IRR II 32 Creating an Application with the Concert Technology Library 33 Modeling an Optimization Problem with Concert Technology 33 ILOG CPLEX 8 1 USER S MANUAL 5 TABLE OF CONTENTS Chapter 2 Modeling Classes 2 edze seni rb er ex e e e ebi ae DRE Leg p Ron rung 33 Data Management Classes 2 0 0 c cece ect ene eens 36 Solving Concert Technology Models with lloCplex 0 00 e cece eee eee eee 37 Extracting a Model yl p REL EIER Heder ie a eea a e E E E 38 Solving a Model ebenso RR bb band eee abre aaae 39 Ghoosing am Optimizer errs nenas Rcx Re actae RR E Rua Roa e OR R RUP HUS 39 Accessing Solution Information 000 c cece eee eee nn 41 Querying Solution Data scoene eese0 es Suede ierd Ru exci yu pu depu i 43 Accessing Basis Information llle 43 Performing Sensitivity Analysis 0 0 0 6 cee ett 44 Analyzing Infeasible Problems 0 00 cece ett 44 Solution Quality sinc Lett a ddd bidedbedaieetd abba dielhisadei baht 45 Modifying a Model 0 00 cece eee eee n hh hn 45 Deleting and Removing Modeling Objects 0 000 cece eee 46 Changing Variable Type 0 0 0 0 cece teen eee 47 Hanallng EtrOts ii ascccsconiei a risanni RE nace rece wens ah ada RR ie R RR RR RR a ca mg 47 Example
195. LOG CPLEX 8 1 USER S MANUAL 85 USING THE CALLABLE LIBRARY IN AN APPLICATION 86 Instantiate the Problem Object Once you have initialized a ILOG CPLEX environment your next step is to instantiate that is create and initialize a problem object by calling CPXcreateprob This routine returns a C pointer to the problem object Your application then passes this pointer to other routines of the Callable Library Most applications will use only one problem object though ILOG CPLEX allows you to create multiple problem objects within a given ILOG CPLEX environment Put Data in the Problem Object When you instantiate a problem object it is originally empty In other words it has no constraints no variables and no coefficient matrix ILOG CPLEX offers you several alternative ways to put data into an empty problem object that is to populate your problem object You can assemble arrays of data and then call CPXcopylp to copy the data into the problem object You can make a sequence of calls in any convenient order to these routines e CPXnewcols e CPXnewrows e CPXaddcols e CPXaddrows e CPXchgcoeflist If data already exist in MPS or LP format in a file you can call CPXreadcopyprob to read that file and copy the data into the problem object MPS Mathematical Programming System is an industry standard format for organizing data in mathematical programming problems LP linear progr
196. MANUAL 359 USING CALLBACKS 360 see Diagnostic Callbacks on page 341 for a discussion of how macros and callback implementation classes relate IloCplex MIPCallbackI ILOMIPCALLBACKn IloCplex NodeCallbackI ILONODECALLBACKn IloCplex IncumbentCallbackI ILOINCUMBENTCALLBACKn _ IloCplex ControlCallbackI ILOCONTROLCALLBACKn E IloCplex BranchCallbackI ILOBRANCHCALLBACKn MR IloCplex CutCallbackI ILOCUTCALLBACKn NN IloCplex HeuristicCallbackI ILOHEURISTICCALLBACKn e IloCplex SolveCallbackI ILOSOLVECALLBACKn Again the callback class hierarchy for Java is exactly the same but the class names differ in that there is no 1 at the end For example the corresponding Java implementation class for IloCplex BranchCallbackI is IloCplex BranchCallback Similar to class I1oCplex CallbackI IloCplex Callback class IloCplex ControlCallbackI IloCplex ControlCallback is not provided for deriving user callback classes but for defining the common interface for its derived classes This interface provides methods for querying information about the current node such as current bounds or solution information for the current node See class IloCplex ControlCallbackI IloCplex ControlCallback in the LOG CPLEX Reference Manual for more information Example Controlling Cuts This example shows how to use the cut callback in the context of solving the noswot model This is a relatively small model from the MIPLIB 3 0 test set con
197. NUAL CHOOSING AN OPTIMIZER FOR YOUR LP PROBLEM and the symbolic names for these in an application program are as follows Table 5 2 Symbolic Names for LP Solution Methods Concert C Concert Java Callable Library TloCplex AutoAlg loCplex Algorithm Auto PX ALG AUTOMATIC IloCplex Primal loCplex Algorithm Primal PX ALG PRIMAL IloCplex Dual loCplex Algorithm Dual PX ALG DUAL IloCplex Barrier loCplex Algorithm Barrier PX ALG BARRIER IloCplex Sifting loCplex Algorithm Sifting PX ALG SIFTING oO 1 BY W MB FI oO I C I e I C IloCplex Network IloCplex Algorithm Network CPX ALG NET I C I C I c IloCplex Concurrent loCplex Algorithm Concurrent PX ALG CONCURRENT Automatic Selection of Optimizer The default Aut omat ic setting of LPMethod lets ILOG CPLEX determine the algorithm to use to optimize your problem Most models are solved well with this setting and we recommend using this option except when you have a compelling reason to tune performance for a particular class of model On a serial computer or on a parallel computer where only one thread will be invoked the automatic setting will in most cases choose the dual simplex optimizer An exception to this rule is when an advanced basis is present that is ascertained to be primal feasible in that case primal simplex will be called On a computer where parallel threads are availa
198. NUAL 329 GOALS 330 IN ILOCPLEX rhs lhs rhs lhs rhs ILOG CPLEX 8 1 add x21 x22 0000 0000 00000000 0 00 000 00000000 0 if IF if if iT LI if if if if af ce TE if if If xa TE LT if if if TE AT AF Af if if IF LE TE ise ise ise LSe LSe LSG LSe LSe LSe LSe ise ise ise se se LSe LSe LSG LSe ise ise ise LSe se LSG LSe LSe LSe ise ise ise add 0 0 add x22 x23 add 0 0 add x23 x24 add 0 0 add 2 08 x11 0 25 w11 add 20 25 add 2 08 x12 0 25 w12 add 20 25 add 2 08 x13 0 25 w13 add 20 25 strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars B H H H BR BR H H He He H H BR BR He Beo He H RR H He BR He BR He H H H H H H SB x21 25 w21 98 x22 25 w22 98 x23 25 w23 getName getName getName getName getName getName getName getName getName getName getName getName getName getName getName getName get
199. Name getName getName getName getName getName getName getName getName getName getName getName getName getName getName f f f f 47 x31 25 w31 47 x32 25 w32 3 0 AT x33 25 w33 X45 X51 X52 X53 X54 X55 W11 W12 W13 W14 W15 W21 W22 W23 W24 W25 W31 W32 W33 W34 W35 W41 W42 W43 W44 W45 W51 W52 W53 W54 W55 tj y 2 24 x41 0 25 w41 2 24 x42 25 w42 2 24 x43 0 25 w43 0 0 Oo CT OO 0 Oo Oo OU QU 0 O Q0 0 oOo OO OO O OO OG UsER S MANUAL x45 vars x51 vars x52 vars x53 vars x54 vars x55 vars w11 vars w12 vars w13 vars w14 vars w15 vars w21 vars w22 vars w23 vars w24 vars w25 vars w31 vars w32 vars w33 vars w34 vars w35 vars w41 vars w42 vars w43 vars w44 vars w45 vars w51 vars w52 vars w53 vars w54 vars w55 vars 08 x51 25 w51 08 x52 25 w52 08 x53 25 w53 B p H peo BR BR He He He He He RR BR BR BR RR He Beo RR RR RR BR BR BR He BR BS He B H H GOALS IN ILOCPLEX 2 24 x44 2 08 x54 0 25 w44 0 25 w54 lhs add 2 08 x1
200. Network in case of QPs Controlling ILOG CPLEX Optimizers 70 Though ILOG CPLEX defaults will prove sufficient to solve most problems ILOG CPLEX offers a variety of other parameters to control various algorithmic choices ILOG CPLEX parameters can take values of type boolean int double and st ring The parameters are accessed via parameter names defined in classes IloCplex BooleanParam IloCplex IntParam IloCplex DoubleParam and IloCplex StringParam corresponding to the parameter type Parameters Parameters are manipulated using I1oCplex setParam For example ILOG CPLEX 8 1 USER S MANUAL CONTROLLING ILOG CPLEX OPTIMIZERS cplex setParam IloCplex BooleanParam PreInd false sets the Boolean parameter PreInd to false instructing ILOG CPLEX not to apply presolve before solving the problem Integer parameters often indicate a choice from a numbered list of possibilities rather than a quantity For example the class IloCplex PrimalPricing defines constants with the integer parameters shown in Table 2 4 Constants in IloCplex PrimalPricing for better maintainability of the code Table 2 4 Constants in IloCplex PrimalPricing Integer g Constant in class IloCplex PrimalPricing Q Parameter 0 IloCplex PrimalPricing Auto S lt 4 2 o 1 IloCplex PrimalPricing Devex 2 o 5 i 2 TloCplex PrimalPricing Steep o 2 Ke 3 TloCplex PrimalPricing SteepQStart 7 4 IloCplex PrimalPricing F
201. O 2 oS Us a UE Q the number of threads indicated by the licensed values of the thread limit parameters Table 9 7 summarizes the values of those thread limit parameters Table 9 7 Thread Limit Parameters Concert Technology Enumeration Value Callable Library Parameter Interactive Commands set threads Threads CPX_PARAM_THREADS set barrier limits threads BarThreads CPX_PARAM_BARTHREADS ILOG CPLEX 8 1 USER S MANUAL 371 USING PARALLEL OPTIMIZERS 372 Table 9 7 Thread Limit Parameters Interactive Commands Concert Technology Enumeration Value Callable Library Parameter set simplex limits threads SimThreads CPX_PARAM_SIMTHREADS set mip limits threads MIPThreads CPX PARAM MIPTHREADS set mip limits strongthreads StrongThreadLim CPX PARAM STRONGTHREADLIM The global thread parameter Threads establishes a default thread count for all parallel optimizers Thread limits for specific optimizers can be set to values that differ from the global default for example by setting IloCplex MIPThreads The notion of the number of threads used when running a parallel CPLEX optimizer is entirely separate from the limit on licensed uses A typical ILOG CPLEX license permits one licensed use that is a single concurrent execution on one licensed computer If the license also contains the parallel option with a thread limit of say four on a machine with at least fo
202. OG CPLEX 8 1 USER S MANUAL 89 ILOG CPLEX PROGRAMMING PRACTICES 90 Copying in MIP and QP The ILOG CPLEX Mixed Integer Optimizer the routine CPXcopyctype copies information about variable types in a mixed integer programming MIP application The routines CPXcopyasep and CPXcopyquad are for copying information about quadratic objective coefficients in a convex quadratic programming QP application Problem Size and Memory Allocation Issues As we indicated in Change the Problem Object on page 87 after you have created a problem object by calling CPXcreateprob you can modify the problem in various ways through calls to routines from the Callable Library There is no need for you to allocate extra space in anticipation of future problem modifications Any limit on problem size is determined by system resources and the underlying implementation of the system function malloc not by artificial limits in ILOG CPLEX As you modify a problem object through calls to modification routines from the Callable Library ILOG CPLEX automatically handles memory allocations to accommodate the increasing size of the problem In other words you do not have to keep track of the problem size nor make corresponding memory allocations yourself as long as you are using library modification routines such as CPXaddrows or CPXaddcols However the sequence of Callable Library routines that you invoke can influence the efficiency
203. OG CPLEX Network Optimizer works What You Need to Know In order to use ILOG CPLEX effectively you need to be familiar with your operating system whether UNIX or Windows In this manual we assume you are familiar with the concepts of mathematical programming particularly linear programming In case those concepts are new to you the bibliography on page 30 in this preface indicates references to help you there This manual also assumes you already know how to create and manage files In addition if you are building an application that uses the Component Libraries this manual assumes that you know how to compile link and execute programs written in a high level language The ILOG CPLEX 8 1 USER S MANUAL 23 IN THIS MANUAL In This Manual 24 Callable Library is written in the C programming language while Concert Technology is written in C and Java This manual also assumes that you already know how to program in the appropriate language and that you will consult a programming guide when you have questions in that area Chapter 1 ILOG Concert Technology for C Users introduces the Concert Technology Library It provides an overview of the design of the library explains modeling techniques and offers an example of programming with the Concert Technology Library It also provides information on controlling parameters Chapter 2 ILOG Concert Technology for Java Users explores the full range of features the ILOG CPLEX
204. OG CPLEX Reference Manual Use an SOS file to set priorities Use an ORD file to set priorities ILOG CPLEX derives the branching priority of a set from the branching priorities of its members the entire set is assigned the highest priority among its members To specify SOS priorities Inthe Concert Technology Library use the functions IloCplex setPriority and TloCplex setPriorities In the Callable Library use the routines CPXcopysos or CPXcopyorder ILOG CPLEX 8 1 USER S MANUAL 245 USING SEMI CONTINUOUS VARIABLES Assigning SOS Weights Members of an SOS should be given unique weights that in turn define the order of the variables in the set These unique weights are also called reference row values The most flexible way for you to assign weights is through an SOS MPS or LP file An alternative is to use MPS format to assign a single reference row containing weights Such a reference row may be a free row with specific weighting information or it may be the objective function or it may be a constraint row In the Callable Library the routine CPXcopysos lets you specify weights directly in an application In our SOS example page 244 we used the coefficients of the warehouse capacity constraint to assign weights Using Semi Continuous Variables Semi continuous variables are variables that may take either the value 0 or values in a finite range a b Semi continuous variables can be sp
205. P PROBLEM FROM A FILE int mai n int argc char argv Declare and allocate space for the variables and arrays where we will store the optimization results including the status objective value and variable values int solstat double objval double tx NULL CPXENVptr env NULL CPXLPptr lp NULL int status int is int cur numcols Check the command line arguments if arge 2 usage argv 0 goto TERMINATE Initialize the CPLEX environment env CPXopenCPLEX amp status If an error occurs the status value indicates the reason for failure A call to CPXgeterrorstring will produce the text of the error message Note that CPXopenCPLEX produces no output so the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines the errors will be seen if the CPX PARAM SCRIND indicator is set to CPX ON if env NULL char errmsg 1024 fprintf stderr Could not open CPLEX environment n CPXgeterrorstring env status errmsg fprintf stderr s errmsg goto TERMINATE Turn on output to the screen status CPXsetintparam env CPX PARAM SCRIND CPX ON if status fprintf stderr Failure to turn on screen indicator error d n status goto TERMINATE Create the problem using the filename as the problem name lp CPXoreateprob env amp status argv 1 ILOG CPLEX 8 1 USER S MANUAL
206. PMRK SIMPLEX TOLERANCES MARKOWITZ EpOpt um CPX PARAM EPOP SIMPLEX TOLERANCES OPTIMALITY EpPer um CPX PARAM EPPER SIMPLEX PERTURBATION EpRHS um CPX PARAM EPRHS SIMPLEX TOLERANCES FEASIBILITY FlowCovers Int CPX PARAM FLOWCOVERS IP CUTS FLOWCUTS FlowPaths Int CPX PARAM FLOWPATHS IP CUTS PATHCU FracCand Int CPX PARAM FRACCAND IP LIMITS GOMORYCAND FracCuts Int CPX PARAM FRACCUTS IP CUTS GOMORY FracPass Int CPX PARAM FRACPASS IP LIMITS GOMORYPASS GUBCovers Int CPX PARAM GUBCOVERS IP CUTS GUBCOVERS HeurFreq Int CPX PARAM HEURFREQ IP STRATEGY HEURISTICFREQ IISInd Int CPX PARAM IISIND SIMPLEX IISFIND ImplBd Int CPX PARAM IMPLBD IP CUTS IMPLIED IntSolLim Int CPX PARAM INTSOLLIM IP LIMITS SOLUTIONS ItLim Int CPX PARAM ITLIM SIMPLEX LIMITS ITERATIONS IPDisplay Int CPX PARAM MIPDISPLAY IP DISPLAY IPEmphasis Int CPX PARAM MIPEMPHASIS IP EMPHASIS IPInterval Int CPX PARAM MIPINTERVAL IP INTERVAL IPOrdInd Bool CPX_PARAM_MIPORDIND IP STRATEGY ORDER IPOrdType Int CPX PARAM MIPORDTYPE IP ORDERTYPE IPStart Bool CPX PARAM MIPSTART IP STRATEGY MIPSTART IPThreads Int CPX PARA IPTHREADS IP LIMITS THREADS 388 ILOG CPLEX 8 1 USER S MANUAL Table A 1 Parameter Name Equivalents ILOG CPLEX Parameter Names
207. ROCESSING LINEAR PrePass Int CPX PARAM PREPASS PREPROCESSING NUMPASS PreslvNd Int CPX PARAM PRESLVND MIP STRATEGY PRESOLVENODE PriceLim Int CPX PARAM PRICELIM SIMPLEX PRICING ILOG CPLEX 8 1 USER S MANUAL 389 ILOG CPLEX Parameter Names Table A 1 Parameter Name Equivalents Concert Type Callable Library Interactive Optimizer Probe Int CPX PARAM PROBE MIP STRATEGY PROBE QPmakePSDInd Bool CPX_PARAM_QPMAKEPSDIND PREPROCESSING QPMAKEPSD QPNzGrowth Int CPX PARAM QPNZGROWTH READ QPNONZEROS Reduce Int CPX PARAM REDUCE PREPROCESSING REDUCE ReInv Int CPX PARAM REINV SIMPLEX REFACTOR RelaxPreInd Bool CPX PARAM RELAXPREIND PREPROCESSING RELAX RelObjDif Num CPX PARAM RELOBJDIF MIP TOLERANCES RELOBJDIFFERENCE ReverseInd Bool CPX PARAM REVERSEIND READ REVERSE RootAlg Int CPX PARAM LPMETHOD LPMETHOD RootAlg Int CPX PARAM QPMETHOD QPMETHOD RootAlg Int CPX PARAM STARTALG MIP STRATEGY STARTALGORITHM RowGrowth Int CPX PARAM ROWGROWTH READ CONSTRAINTS ScaInd Int CPX PARAM SCAIND READ SCALE ScrInd Int CPX PARAM SCRIND SiftAlg Int CPX PAR
208. Rights Reserved Permission is expressly granted to use this example in the ef course of developing applications that use ILOG products p netexl c Entering and optimizing a network problem Import the CPLEX function declarations and the C library 182 ILOG CPLEX 8 1 USER S MANUAL EXAMPLE USING THE NETWORK OPTIMIZER WITH THE CALLABLE LIBRARY header file stdio h with the include of cplex h finclude ilcplex cplex h include lt stdlib h gt Import the declarations for the string functions include lt string h gt v BS fej ES 3 Forward declaration for function at end of program TEXT Bley NET NB UIAJOS static int buildNetwork CPXENVptr env CPXNETptr net static void free and null char ptr int main void Declare variables and arrays for retrieving problem data and solution information later on int narcs int nnodes int solstat double objval double c NULL double pi NULL double slack NULL double dj NULL CPXENVptr env NULL CPXNETptr net NULL int status int Ls 4 Initialize the CPLEX environment env CPXopenCPLEX amp status If an error occurs the status value indicates the reason for failure A call to CPXgeterrorstring will produce the text of the error message Note that CPXopenCPLEX produces no output s
209. S WITH THE BARRIER OPTIMIZER and the dual constraints are written as Aly z we c Asa result in the log file the infeasibilities represent norms as summarized in Table 5 10 Table 5 10 Infeasibilities and Norms in the Log File of a Barrier Optimization Infeasibility In log file Norm primal Prim Inf b Ax upper Upper Inf lu x s dual Dual Inf lc yYA z w If solution values are large in absolute value then the infeasibilities may appear inordinately large because they are recorded in the log file in absolute terms The optimizer uses relative infeasibilities as termination criteria Infeasibility Ratio in the Log File If you are using one of the barrier infeasibility algorithms available in the ILOG CPLEX Barrier Optimizer that is if you have set BarAlg to either 1 or 2 as discussed later in this chapter then ILOG CPLEX records an additional column of output titled Inf Ratio the infeasibility ratio This ratio always positive is a measure of progress for that particular algorithm In a problem with an optimal solution you will see this ratio increase to a large number In contrast in a problem that is infeasible or unbounded this ratio will decrease to a very small number Understanding Solution Quality from the Barrier LP Optimizer When ILOG CPLEX successfully solves a problem with the ILOG CPLEX Barrier Optimizer it reports the optimal objective value and solution time in a l
210. S a eS Se SS eS aes ILOG CPLEX 8 1 USER S MANUAL 347 USING CALLBACKS 348 Copyright C 1999 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products ilolpex4 cpp Illustrating the CPLEX callback functionality This is a modification of ilolpexl c where we use a callback function to print the iteration info rather than have CPLEX do it finclude lt ilcplex ilocplex h gt ILOSTLBEGIN ILOSIMPLEXCALLBACKO MyCallback cout lt lt Iteration lt lt getNiterations lt lt if isFeasible cout lt lt Objective lt lt getObjValue lt lt endl else cout lt lt Infeasibility measure lt lt getInfeasibility lt lt endl static void populatebycolumn IloModel model IloNumVarArray var IloRangeArray rng int main int argc char argv IloEnv env try IloModel model env example IloNumVarArray var env IloRangeArray rng env populatebycolumn model var rng IloCplex cplex model cplex setOut env getNullStream cplex setParam IloCplex RootAlg IloCplex Primal cplex use MyCallback env cplex solve env out lt lt Solution status lt lt cplex getStatus lt lt endl env out lt lt Solution value lt lt cplex getObjValue lt lt endl IloNumArray vals env cplex getValues vals v
211. TPUT Write the output to the screen We will also write it toa file as well by setting up a file destination and a function destination ourchannel CPXaddchannel env if ourchannel NULL CPXmsg cpxerror Failed to set up our private channel n goto TERMINATE fpout CPXfopen lpex5 msg w if fpout NULL CPXmsg cpxerror Failed to open lpex5 msg file for output Wn goto TERMINATE status CPXaddfpdest env ourchannel fpout if status CPXmsg cpxerror Failed to set up output file destination Mn goto TERMINATE status CPXaddfuncdest env ourchannel ourlabel ourmsgfunc if status CPXmsg cpxerror Failed to set up our output function n goto TERMINATE Now any message to channel ourchannel will go into the file and into the file opened above CPXmsg ourchannel nSolution status d n solstat CPXmsg ourchannel Solution value f n n objval The size of the problem should be obtained by asking CPLEX what the actual size is rather than using sizes from when the problem was built cur_numrows and cur_numcols store the current number of rows and columns respectively cur numrows CPXgetnumrows env 1p cur numcols CPXgetnumcols env 1p for i 0 i lt cur numrows i CPXmsg ourchannel Row d Slack 10f Pi 10f n i slack i pil il z EN 563 O 2 oS Us a UE Q for
212. UMCOLS numrows_p NUMROWS objsen_p CPX_MAX The problem is maximization probname_p zprobname obj p zobj rhs p zrhs dp sense_p zsense y o matbeg p zmatbeg matcnt_p zmatcnt oo matind p zmatind E matval_p zmatval o UU lb p zlb ub p zub ctype p zctype return status END setproblemdata static int setsosandorder CPXENVptr env CPXLPptr lp Priority order information int colindex 2 int priority 2 int direction 2 SOS set information char sostype 1 int sospri 1 int sosbeg 1 ILOG CPLEX 8 1 USER S MANUAL 285 EXAMPLE 286 USING SOS AND PRIORITY int sosind 2 double sosref 2 int status 0 Note for this example the priority order and SOS information are just made up for illustrative purposes The priority order is not necessarily a good one for this particular problem Set order info Variables 1 and 3 will be in the priority order with respective priorities of 8 and 7 and with respective branching directions of up and down colindex 0 1 colindex 1 3 priority 0 8 priority 1 7 direction 0 CPX BRANCH UP direction 1 CPX BRANCH DOWN status CPXcopyorder env lp 2 colindex priority direction if status fprintf stderr CPXcopyorder failed n goto TERMINATE Set SOS set info Create one SOS type 1 set with variables 2 and 3 in it wit
213. WS 2 define NUMCOLS 3 define NUMNZ 6 define NUMONZ 7 int main void Declare pointers for the variables and arrays that will contain the data which define the LP problem The setproblemdata routine allocates space for the problem data char probname NULL int numcols int numrows int objsen double obj NULL double rhs NULL char sense NULL int matbeg NULL int matcnt NULL int matind NULL double matval NULL double lb NULL double ub NULL int gmatbeg NULL int gmatcnt NULL int qmatind NULL 208 ILOG CPLEX 8 1 USER S MANUAL EXAMPLE CREATING A QP OPTIMIZING FINDING A SOLUTION double gmatval NULL Declare and allocate space for the variables and arrays where we will store the optimization results including the status objective value variable values dual values row slacks and variable reduced costs int solstat double objval double x NUMCOLS double pi NUMROWS double slack NUMROWS double dj NUMCOLS CPXENVptr env NULL CPXLPptr lp NULL int status int Hye int cur numrows cur numcols Initialize the CPLEX environment env CPXopenCPLEX amp status o 5 Q 9 U v E O D 3 2 If an error occurs the status value indicates the reason for failure A call to CPXgeterrorstring will produce the text of the error message Note that CPXopenCPLEX produces no output so th
214. X2 3x3 x subject to Xj Xp X3 10x4 lt 20 Xj c 3X2 x3 lt 30 X2 35x 0 with these bounds 0 lt x lt 40 0 S x X 0 S xj S o 2 lt x lt 3 X4 integer ILOG CPLEX 8 1 USER S MANUAL CONSIDERING PRELIMINARY ISSUES Considering Preliminary Issues When you are optimizing a MIP there are a few preliminary issues that you need to consider to get the most out of ILOG CPLEX The following sections cover such topics as entering variable type displaying MIPs in the Interactive Optimizer determining the problem type and switching to fixed versions of your problem Entering MIP Problems You enter MIPs into ILOG CPLEX as explained in Put Data in the Problem Object on page 86 with this additional consideration you need to indicate which variables are binary general integer semi continuous and semi integer and which are contained in special ordered sets SOS Concert Technology Library users can specify this information by passing a type value to the appropriate constructor when creating the variable Use IloNumVar objects of type ILOBOOL IloNumVarType Bool in Java for binary variables and of type ILOINT IloNumVarType Int in Java for general integer variables Use 11o0SemiContVar objects of type ILONUM IloNumVarType Float in Java for semi continuous variables and IloSemiContVar oftype ILOINT IloNumVarType Int in Java for semi integer variables Callable Library users can specify this informa
215. a By default the lower bound on an arc is 0 zero u the upper bound determines the maximum flow allowed through the arc a By default the upper bound on an arc is positive infinity c the objective value determines the contribution to the objective function of one unit of flow through the arc ILOG CPLEX 8 1 USER S MANUAL EXAMPLE NETWORK OPTIMIZER IN THE INTERACTIVE OPTIMIZER Each node n is associated with one value s isthe supply value at node n 7 By convention a node with strictly positive supply value that is s gt 0 is called a supply 2 node or a source and a node with strictly negative supply value that is s lt 0 is called a v amp demand node or a sink A node where s 0 is called a transshipment node The sum of all MN supplies must match the sum of all demands if not then the network flow problem is Z infeasible 3 9 0 s T is the set of arcs whose tails are node n H is the set of arcs whose heads are node n The Ru usual form of a network problem looks like this 2 Minimize or maximize bs C4X4 ac A subject to by X37 b X SNE N ae Ta ae H with these bounds l Xa Su Na e A That is for each node the net flow entering and leaving the node must equal its supply value and all flow values must be within their bounds The solution of a network flow problem is an assignment of flow values to arcs that is the modeling variables to satisfy the problem formulation
216. able Library routine CPXNETprimopt If CPXNETprimopt returns a nonzero value an error has occurred otherwise the optimization was successful Before retrieving that solution we allocate arrays to hold it Then we use CPXNETsolution to copy the solution into those arrays After we display the solution on screen we write the network problem into a file netex1 net in the NET file format The TERMINATE label is used as a place for the program to exit if any type of error occurs Therefore code following this label cleans up it frees the memory that has been allocated for the solution data it frees the network object by calling CPXNET reeprob and it frees the ILOG CPLEX environment by calling CPXcloseCPLEX All freeing should be done only if the data is actually available The Callable Library routine CPXcloseCPLEX should always be the last ILOG CPLEX routine called in a ILOG CPLEX Callable Library application In other words all ILOG CPLEX objects that have been allocated should be freed before the call to CPXcloseCPLEX Complete Program netex1 c The complete program netex1 c appears here and online in the standard distribution po File examples src netexl c a Version 8 1 zy D Copyright C 1997 2002 by ILOG All
217. able Library routines only However equivalent Concert Technology examples are also provided in the distribution Using Surplus Arguments for Array Allocations Most of the ILOG CPLEX query routines in the Callable Library require your application to allocate memory for one or more arrays that will contain the results of the query In many cases your application the calling program does not know the size of these arrays in advance For example in a call to CPXget cols requesting the matrix data for a range of columns your application needs to pass the arrays cmat ind and cmatva1 for ILOG CPLEX to populate with matrix coefficients and row indices However unless your application has carefully kept track of the number of nonzeros in each column throughout the problem specification and if applicable throughout its modification the actual length of these arrays remains unknown Fortunately the ILOG CPLEX query routines in the Callable Library contain a surplus p argument that when used in conjunction with the array length arguments enables you first to call the query routine to determine the length of the required array Then when the length is known your application can properly allocate these arrays Afterwards your application makes a second call to the query routine with the correct array lengths to obtain the requested data For example consider a program that needs to call CPXget cols to access a range of columns Here
218. about the progress of an optimization algorithm They can also return a value to indicate ILOG CPLEX 8 1 USER S MANUAL ILOG CPLEX PROGRAMMING PRACTICES whether an optimization should be aborted CPXget callbackinfo is the only routine of the Callable Library that a user defined callback may call Of course calls to routines not in the Callable Library are permitted Using Callbacks on page 341 describes callback facilities in greater detail Portability ILOG CPLEX contains a number of features to help you create Callable Library applications that can be easily ported between UNIX and Windows platforms CPXPUBLIC All ILOG CPLEX Callable Library routines except CPXmsg have the word CPXPUBLIC as part of their prototype On UNIX platforms this has no effect On Win32 platforms the CPXPUBLIC designation tells the compiler that all of the ILOG CPLEX functions are compiled with the Microsoft stdca11 calling convention The exception CPXmsg cannot be called by st cal11 because it takes a variable number of arguments Consequently CPXmsg is declared as CPXPUBVARARGS that calling convention is defined as cdecl for Win32 systems Function Pointers All ILOG CPLEX Callable Library routines that require pointers to functions expect the passed in pointers to be declared as CPXPUBLIC Consequently when your application uses the ILOG CPLEX Callable Library routines CPXaddfuncdest CPXsetlpcallbackfunc and
219. aces To create a new modeling object you must first create the 110Modeler which will be used to create the modeling object For the discussion here the model will be an instance of IloCplex and it will be created as follows IloCplex cplex new IloCplex ILOG CPLEX 8 1 USER S MANUAL MODELING WITH CONCERT TECHNOLOGY Since class IloCplex implements 110MPModeler and thus its parent interface IloModeler all methods from IloMPModeler and 11oModeler can be used for building a model 11oModeler defines the methods to e create modeling variables of type integer float or Boolean e construct simple expressions using modeling variables e create objective functions and e create ranged constraints that is constraints of the form lb Sexpression Sub Models that consist only of such constructs can be built and solved with any ILOG optimizer implementing the 11oModeler interface including 11oCplex which implements the IloMPModeler extension The 11oMPModeler interface extends IloModeler by adding functionality specific to mathematical programming applications This functionality includes these additional modeling object types e semi continuous variables e special ordered sets and e piecewise linear functions It also includes these modeling features to support specific needs e change of type for previously declared variables e modeling by column and e general manipulations of model entities Modeling with l
220. ack Macro Class presolve ILOPRESOLVECALLBACKn TloCplex PresolveCallbackI continuous ILOCONTINUOUSCALLBACKn IloCplex ContinuousCallbackI simplex ILOSIMPLEXCALLBACKn IloCplex SimplexCallbackI primal ILOPRIMALSIMPLEXCALLBACKn IloCplex SimplexCallbackI simplex dual ILODUALSIMPLEXCALLBACKn IloCplex SimplexCallbackI simplex barrier ILOBARRIERCALLBACKn IloCplex BarrierCallbackI crossover ILOCROSSOVERCALLBACKn TloCplex CrossoverCallbackI network ILONETWORKCALLBACKn TloCplex NetworkCallbackI MIP ILOMIPCALLBACKn loCplex MIPCallbackI probing ILOPROBINGCALLBACKn loCplex ProbingCallbackI fractional ILOFRACTIONALCUTCALLBACKn loCplex FractionalCutCallbackI cut disjunctive ILODISJUNCTIVECUTCALLBACKn IloCplex DisjunctiveCutCallbackI cut The protected member functions of the corresponding class and its base classes determine the functions that can be called for implementing your callback see the ILOG CPLEX Reference Manual Here is an example of how to implement a simplex callback with the name MyCallback that takes one parameter ILOSIMPLEXCALLBACK1 MyCallback IloInt num if getNiterations num abort This callback aborts the simplex algorithm at the num iteration It queries the current iteration number by calling function getNiterations which is a protected member function of class 11o0Cplex ContinuousCallbackI 344 ILOG CPLEX 8 1 USER S MANUAL USING CALLBACKS To use this
221. age 229 netopt page 178 page 258 optimize primopt page 374 quit read filename type page 130 page 178 page 130 set advance yes page 130 set barrier page 159 set barrier algorithm page 163 page 170 set barrier colnonzeros page 171 set barrier convergetol set barrier crossover set barrier display page 160 page 171 ILOG CPLEX 8 1 USER S MANUAL 395 Interactive Optimizer Commands 396 Command Options Example set barrier limits corrections page 170 set barrier limits growth set barrier limits iterations set barrier limits objrange page 172 set barrier limits threads set barrier limits varupper set barrier ordering set barrier outofcore set barrier startalg set clocktype set defaults set logfile filename set lpmethod set mip cuts class page 237 set mip display set mip emphasis set mip interval set mip limits aggforcut set mip limits cutpasses set mip limits cutsfactor page 237 set mip limits gomorycand set mip limits gomorypass set mip limits nodes page 242 set mip limits solutions page 242 set mip limits strongcand set mip limits strongit ILOG CPLEX 8 1 USER S MANUAL Interactive Optimizer Commands Command Options Example set mip limi
222. agnosing Barrier Optimizer Infeasibility llle 172 Solving Network Flow Problems seesseeeee eene 175 Choosing an Optimizer Network Considerations leslesses 175 Formulating a Network Problem 000 e eee eee eee n nnn 176 Example Network Optimizer in the Interactive Optimizer Lue 177 Understanding the Network Log File 0 0 cece BB 178 Tuning Performance of the Network Optimizer 0 00000 cece eee eee eee 179 Solving Problems with the Network Optimizer 0 000 cece eee eee eee 179 Network Extractions ecse crei ostet rere exte dg Po ROREM ee ae eae glee exe ee 180 Preprocessing and the Network Optimizer 0 0 0 cece eee ee 181 Example Using the Network Optimizer with the Callable Library 181 Complete Program netex1 C 12 cette tenes 182 Solving Network Flow Problems as LP Problems 00200eeeeeeeeeeees 188 Example Network to LP Transformation 00 ccc eee eee eee eee eee 189 Complete Program netex2 C 1 2 cette tenes 190 Solving Quadratic Programming Problems lese 195 Identifying Convex Quadratic Programming Problems sese 195 Entering QPS sls RE e x RR ERG x RR UR REF ek ee ee eee 196 Saving QP Problems 0 0c eee e eee eee eee ee n n n n nnn 198 Changing Problem Type in QPS 0 0 cece eee eee eee ee 198 Changing Quadratic TermS
223. aken as though the run had not been interrupted due simply to the dynamic nature of the branch amp cut algorithm A TRE file may be quite large corresponding to the current size of an active tree so it may consume considerable disk space If you modify the model of a MIP after you create its TRE file then the TRE file will be of no use to you ILOG CPLEX will accept the old TRE file if the basic dimensions of the problem have not changed but the results it produces from it will likely be invalid for the modified model ILOG CPLEX 8 1 USER S MANUAL USING SENSITIVITY INFORMATION IN A MIP Post Solution Information in a MIP Interpreting Solution Statistics on page 141 explains how to use the display command in the Interactive Optimizer to see post solution information from the linear optimizers However because of the way integer solutions are generated the display command shows you only limited information from the MIP optimizer In fact ILOG CPLEX generates integer solutions by solving subproblems that have different bounds from the original problem so computing solution values with the original bounds will not usually give the same solution Nevertheless the following solution statistics are available from the MIP optimizer objective function value for the best integer solution if one exists best bound that is best objective function value among remaining subproblems solution quality 9 9 primal v
224. algorithm the limit on barrier corrections and the choice of starting point heuristic topics introduced in Tuning Barrier Optimizer Performance on page 165 and recapitulated here in the following subsections Change the Ordering Algorithm As we explain about tuning performance in Choosing an Ordering Algorithm on page 167 you can choose one of several ordering algorithms to use in the ILOG CPLEX Barrier Optimizer To improve the quality of a solution in some problems change the ordering algorithm Change the Barrier Algorithm The ILOG CPLEX Barrier Optimizer implements the algorithms listed in Table 5 13 The selection of barrier algorithm is controlled by the BarAlg parameter The default option invokes option 3 for LPs and QPs and option 1 for MIPs where the ILOG CPLEX Barrier Optimizer is used on the subproblems Naturally the default is the fastest for most problems but it may not work well on problems that are primal infeasible or dual infeasible Options 1 and 2 in the ILOG CPLEX Barrier Optimizer implement a barrier algorithm that also detects infeasibility They differ from each other in how they compute a starting point Though ILOG CPLEX 8 1 USER S MANUAL 169 o 2 Q T U Uv al D 3 7 SOLVING LP PROBLEMS WITH THE BARRIER OPTIMIZER 170 they are slower than the default option in a problem demonstrating numerical difficulties they may eliminate the numerical difficulties and thus improve th
225. alues Assuming your variables are stored in an IloNumVarArray var you can use IloNumArray x env cplex getValues x var to access the solution values for all variables in var at once Value x i contains the solution value for variable var i Solution data is not restricted to the solution values of variables It also includes values of slack variables for linear constraints and the objective value If the extracted model does not contain an objective object IloCplex assumes a 0 expression objective The objective value is returned by calling method cplex getObjValue Slack values are accessed with the methods getS1ack and getSlacks which take linear constraints as a parameter For LPs and QPs solution data includes information such as dual variables and reduced cost Such information can be queried with the methods getDual getDuals getReducedCost and getReducedCosts Accessing Basis Information When solving the LPs or QPs with a simplex algorithm or when solving LPs using the barrier optimizer with crossover enabled basis information is available as well Basis information can be consulted using method I1oCplex getBasisStatuses which returns basis status information for variables and constraints Such information is encoded by the nested enumeration type ILOG CPLEX 8 1 USER S MANUAL 43 ACCESSING SOLUTION INFORMATION IloCplex BasisStatus Basic AtLower AtUpper FreeOrSuperbasic
226. alues and symbolic constants are the same for the NodeAlg parameter as for the Root A1g parameter in Table 8 13 To set the NodeA1g parameter Inthe Concert Technology library use the 11oCplex method setParam with the parameter NodeA1g and the appropriate algorithm enumeration value In the Callable Library use the routine CPXsetintparam with the parameter CPX PARAM SUBALG and the appropriate symbolic constant In the Interactive Optimizer use the command set mip strategy subalgorithm with the value to indicate the optimizer you want Example Optimizing a Basic MIP Problem This example illustrates how to optimize a MIP with the ILOG CPLEX Component Libraries 258 ILOG CPLEX 8 1 USER S MANUAL EXAMPLE OPTIMIZING A BASIC MIP PROBLEM Complete Program ilomipex1 cpp The example derives from ilolpex8 cpp Here are the differences between that linear program and this mixed integer program The problem to solve is slightly different It appears in Sample Stating a MIP Problem on page 224 The routine populatebyrow added the variables objective and constraints to the model created by the method IloModel model env EE QR File examples src ilomipexl cpp Version 8 1 Copyright C 1999 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products ilomipexl cpp Entering and o
227. alues for the best integer solution if one has been found slack values for best integer solution if one has been found If you request other solution statistics ILOG CPLEX will issue the error message Not available for mixed integer problems use CHANGE PROBLEM to change the problem type Using Sensitivity Information in a MIP i e ES D diN Bulnjos Other post solution information does not have the same meaning in a mixed integer program as in a linear program because of the special nature of the integer variables in the MIP The reduced costs dual values and sensitivity ranges give you information about the effect of making small changes in problem data so long as feasibility is maintained Integer variables however lose feasibility if a small change is made in their value so this post solution information cannot be used to evaluate changes in problem data in the usual way of LPs Integer variables typically represent major structural decisions in a model and often many continuous variables of the model are related to these major decisions With that observation in mind if you take the integer variable values as given then you can use post solution information applying only to the continuous variables in the usual way To access this limited sensitivity information in a MIP In the Interactive Optimizer use the command change problem fixed to fix the values of the integer variables In
228. am s behavior in the Interactive Optimizer 1 If you can reproduce the behavior with a SAV file but not with an MPS file this suggests corruption or errors in the problem data arrays Use the Dat aCheck parameter or diagnostic routines in the source file check c to track down the problem 2 If you can reproduce the behavior in neither the SAV file nor the MPS file the most likely cause of the problem is that your program has some sort of memory error Memory debugging tools such as Purify or Insure will usually find such problems quickly 3 When solving a problem in MPS or LP format if the Interactive Optimizer issues a message about a segmentation fault or similar ungraceful interruption and exits contact ILOG CPLEX technical support to arrange for transferring the problem file The Interactive Optimizer should never exit with a system interrupt when solving a problem from a text file even if the program that created the file has errors Such cases are extremely rare If the peculiar behavior that you observed in your application persists in the Interactive Optimizer then you must examine the LP or MPS or SAV problem file to determine whether the problem file actually defines the problem you intended If it does not define the problem you intended to optimize then the problem is being passed incorrectly from your application to ILOG CPLEX so you need to look at that part of your application Make sure the problem statistics and matr
229. ameters ssiseseeeeeeee e rn 130 Diagnosing Performance Problems 0c e cece eee n n nn nnn 134 Lack Of Memoty sx eR e RE she 2 ENS A Ea pans ae ae dea ARS 134 Numerical Difficulties 0 00 0 c eee eee eens 135 Diagnosing LP Infeasibility 2 0 0 cece eee 139 The Effect of Preprocessing on Feasibility llle 140 Coping with an Ill Conditioned Problem or Handling Unscaled Infeasibilities 140 Interpreting Solution Statistics 0 ketene 141 Finding a Set of Irreducibly Inconsistent Constraints 00 000 ee eee 143 Example Using a Starting Basis in an LP Problem 0020e cece ee eeeee 148 Exairiplealolpexe cpp ss sd nbd wate eo ia ed vee E RI Been Vee eee 148 Example lp6x6 C s uoc but ie VES Dak bd Wer were ve que ug d 150 Solving LP Problems with the Barrier Optimizer else 156 Identifying LPs for Barrier Optimization llle 157 Using the Barrier Optimizer llslsseeeeleeee RI I 159 Special ODIIOLS cs tacuit donaca Meotee ae nee iode o nee alana Lace c cies es 159 ILOG CPLEX 8 1 USER S MANUAL 9 TABLE OF CONTENTS Chapter 6 Chapter 7 10 Controlling Crossover ms 160 Interpreting the Barrier Log File llle 160 Understanding Solution Quality from the Barrier LP Optimizer 0 0 163 Tuning Barrier Optimizer Performance l l ee 165 Overcoming Numerical Difficulties lle 169 Di
230. amming is an ILOG CPLEX specific format for expressing linear programming problems as equations or inequalities Understanding File Formats on page 290 explains these formats in greater detail Whenever possible compute your problem data in double precision 64 bit Computers are finite precision machines and truncating your data to single precision 32 bit can result in unnecessarily ill conditioned problems For more information refer to Numerical Difficulties on page 135 Optimize the Problem Call one of the ILOG CPLEX optimizers to solve the problem object that you have instantiated and populated Choosing an Optimizer for Your LP Problem on page 124 explains in greater detail how to choose an appropriate optimizer for your problem ILOG CPLEX 8 1 USER S MANUAL ILOG CPLEX PROGRAMMING PRACTICES Change the Problem Object In analyzing a given mathematical program you may make changes in a model and study their effect As you make such changes you must keep ILOG CPLEX informed about the modifications so that ILOG CPLEX can efficiently re optimize your changed problem Always use the problem modification routines from the Callable Library to make such changes and thus keep ILOG CPLEX informed In other words do not change a problem by altering the original data arrays and calling CPXcopylp again That tempting strategy usually will not make the best use of ILOG CPLEX Instead modify your problem by means of the pr
231. ample file 145 isDualFeasible member function IloCplex class 43 isPrimalFeasible member function IloCplex class 43 J Java parameter names 385 K knapsack constraint 235 236 L le method 63 license CPLEX 32 parallel 371 limiting network iterations 179 strong branching candidate list 252 strong branching iterations 252 linear expression 35 linear objective function 37 Linear Programming LP problem see LP linear relaxation network flow and 190 log file barrier optimizer 160 Cholesky factor in 162 clones and 379 closing 295 contents 131 163 creating 295 default 295 description 295 diagnostic routines and 94 iteration 135 naming 295 network 179 UsER S MANUAL 413 INDEX parallel MIP optimizer and 379 parameter 295 parameter specifications and 401 records IISs 144 records infeasibilities 141 records infeasibility information 143 records singularities 138 relocating 295 renaming 295 lower bound values choosing 63 LP barrier optimizer 156 choosing algorithm 39 network optimizer 175 problem formulation 22 157 solving 123 to 173 LP file format defined 290 IISs and 145 QPs and 198 row column order 292 special considerations 292 managing log file 295 Markowitz tolerance 138 139 maximal cliques recorded in MIP node log file 248 maximization concave QPs 196 lower cutoff parameter 253 see also optimization maximize 64 maximum bound infeasibility 142 maximum reduced cost infeasibility 142
232. an empty constraint nutrMin i S lt nutrMax i where is left to be filled once you walk into the store Also you set up the objective function to minimize the cost We refer to constraint i as range i and to the objective as COSL Now you walk into the store and for each food you check the price and nutritional content With this data you create a variable representing the amount you want to buy of the food type and install it in the objective function and constraints That is you create the following column cost foodCost j sum_i range i nutrPer i j 66 0 where the notation and sum indicate that you add the new variable j to the objective cost and constraints range i The value in parentheses is the linear coefficient that is used for the new variable We chose this notation for its similarity to the syntax actually used in Concert Technology as demonstrated in the function buildModelByColumn in example ilodiet cpp Creating Multi Dimensional Arrays with lloArray All data defining the problem are read from a file The nutrients per food are stored in a two dimensional array Concert Technology does not provide a predefined array class however by using the template class IloArray you can create your own two dimensional array class This class is defined with the type definition typedef IloArray IloNumArray IloNumArray2 and is then ready to use just like any predefined
233. anspose e In computer generated samples such as log files where only ASCII characters are available we denote the product of A and its transpose like this A A The asterisk indicates matrix multiplication and the prime indicates the matrix transpose Related Documentation The complete documentation set for ILOG CPLEX 8 1 consists of the following materials ILOG CPLEX 8 1 Getting Started We recommend that new ILOG CPLEX users start with this manual It introduces ILOG CPLEX through the interactive optimizer and contains tutorials on ILOG CPLEX Concert Technology for C and Java applications and the ILOG CPLEX Callable Library The ILOG CPLEX 8 1 Getting Started manual is supplied in HTML form in Microsoft compiled HTML help CHM form and as a PDF file ILOG CPLEX 8 1 User s Manual This manual explains the topics covered in the Getting Started Manual in greater depth with individual chapters on e LP Linear Programming problems e Network Flow problems e QP Quadratic Programming problems and e MIP Mixed Integer Programming problems There is also detailed information on e managing input and output e using query routines ILOG CPLEX 8 1 USER S MANUAL 27 RELATED DOCUMENTATION 28 e using callbacks and e using parallel optimizers The ZLOG CPLEX 6 1 User s Manual is supplied in HTML form in Microsoft compiled HTML help CHM form and as a PDF file ILOG CPLEX 8 1 Referenc
234. ant factor which changes the unit of measurement for the objective but does not alter the meaning of the variables or the sense of the problem as a whole If your objective function itself contains a wide variation of coefficient magnitudes you may also want to consider scaling the individual columns to achieve a closer range ILOG CPLEX 8 1 USER S MANUAL EXAMPLE CREATING A QP OPTIMIZING FINDING A SOLUTION Example Creating a QP Optimizing Finding a Solution This example shows you how to build and solve a QP The problem being created and solved is Maximize Xi 2o 3X9 05 83x 22x 11x 12xyxXp 23xoxj subject to X1 X2 X3 lt 20 X1 i 3x2 X3 lt 30 5 with these bounds 0 lt x 40 Co i o 0 X x2 lt to v v 0 lt X3 lt 00 c D 3 D Example iloqpex1 cpp This example is almost identical to ilolpex1 cpp with only function populatebyrow to create the model Also this function differs only in the creation of the objective from its ilolpex1 cpp counterpart Here the objective function is created and added to the model like this model add IloMaximize env x 0 2 x 1 3 x 2 0 5 33 x 0 x 0 22 x 1 x 1 11 x 2 x 2 12 x 0 x 1 23 x 1 x 2 In general any expression built of basic operations constant and brackets that amounts to a quadratic and optional linear term can be used for building QP objective function Note that if the ex
235. ar env out Values lt lt vals lt lt endl cplex getSlacks vals rng ILOG CPLEX 8 1 USER S MANUAL USING CALLBACKS env out lt lt Slacks lt lt vals lt lt endl cplex getDuals vals rng env out lt lt Duals lt lt vals lt lt endl cplex getReducedCosts vals var env out lt lt Reduced Costs lt lt vals lt lt endl cplex exportModel lpex4 1p catch IloException amp e cerr Concert exception caught e endl catch cerr lt lt Unknown exception caught lt lt endl env end return 0 END main To populate by column we first create the rows and then add the columns static void populatebycolumn IloModel model IloNumVarArray x IloRangeArray c IloEnv env model getEnv IloObjective obj IloMaximize env c add IloRange env IloInfinity 20 0 c add IloRange env IloInfinity 30 0 x add IloNumVar obj 1 0 c 0 1 0 c 1 1 0 0 0 40 0 x add obj 2 0 c 0 1 0 c 1 3 0 x add obj 3 0 c 0 1 0 c 1 1 0 model add obj model add c END populatebycolumn z E 563 O 2 oS Us a UE Q Implementing Callbacks in the Callable Library ILOG CPLEX optimization routines in the Callable Library incorporate a callback facility to allow your application to transfer control temporarily from ILOG CPLEX to the calling application Using call
236. arity total sum of slack yj row complementarity max maximum of slack yil primal norm x total sum of absolute values of all primal variables primal norm x max maximum of absolute values of all primal variables dual norm rc total sum of absolute values of all reduced costs dual norm rc max maximum of absolute values of all reduced costs primal error Ax b total max total and maximum error in satisfying primal equality constraints dual error A pi rc c total max total and maximum error in satisfying dual equality constraints primal x bound error total max total and maximum error in satisfying primal lower and upper bound constraints primal slack bound error total max total and maximum violation in slack variables dual pi bound error total max total and maximum violation with respect to zero of dual variables on inequality rows dual rc bound error total max total and maximum violation with respect to zero of reduced costs 164 ILOG CPLEX 8 1 USER S MANUAL SOLVING LP PROBLEMS WITH THE BARRIER OPTIMIZER Table 5 11 Barrier Solution Quality Display Continued Item Meaning primal normalized error Ax b max accuracy of primal constraints dual normalized error A pi rc c accuracy of dual constraints max Table 5 11 lists the items ILOG CPLEX displays and explains their meaning In the solution quality display the term pi refer
237. asible active model take part in the IIS ILOG CPLEX 8 1 USER S MANUAL 73 ADVANCED MODELING WITH ILOMPMODELER Solution Quality The ILOG CPLEX optimizer uses finite precision arithmetic to compute solutions To compensate for numerical errors due to this tolerances are used by which the computed solution is allowed to violate feasibility or optimality conditions Thus the solution computed by the solve method may in fact slightly violate the bounds specified in the active model IloCplex provides the method getQuality to allow you to analyze the quality of the solution Several quality measures are defined in class IloCplex QualityType For example to query the maximal bound violation of variables or slacks of the solution found by cplex solve call IloCplex QualityType inf cplex getQuality IloCplex QualityType MaxPrimalInfeas double maxinfeas inf getValue The variable or constraint for which this maximum infeasibility occurs can be queried by calling inf getNumVar or inf getRange one of which returns nu11 Not all quality measures are available for solutions generated by different optimizers See the CPLEX Java Reference Manual for further details Advanced Modeling with lloMPModeler 74 So far we have only considered the constraints individually as ranged constraints of type IloRange this is termed a modeling by row approach However mathematically the models that can be solved with 11oCplex a
238. asis Variables 1 and 2 are basic while variable 0 is at its upper bound cstat 0 CPX AT UPPER estat 1 CPX BASIC cstat 2 CPX BASIC The row statuses are all nonbasic for this problem rstat 0 CPX AT LOWER rstat 1 CPX AT LOWER Now copy the basis status CPXcopybase env lp cstat rstat if status fprintf stderr Failed to copy the basis Mn goto TERMINATE Optimize the problem and obtain solution status CPXlpopt env lp ILOG CPLEX 8 1 USER S MANUAL 153 o 2 Q T U Ru E e D 3 7 EXAMPLE USING A STARTING BASIS IN AN LP PROBLEM if status fprintf stderr Failed to optimize LP n goto TERMINATE status CPXsolution env lp amp solstat amp objval x pi slack dj if status i1 fprintf stderr Failed to obtain solution n goto TERMINATE Write the output to the screen printf nSolution status d n solstat printf Solution value f n objval printf Iteration count d n n CPXgetitcnt env 1p The size of the problem should be obtained by asking CPLEX what the actual size is rather than using sizes from when the problem was built cur_numrows and cur_numcols store the current number of rows and columns respectively cur numrows CPXgetnumrows env 1p cur numcols CPXgetnumcols env 1p for i 0 i lt cur numrows i printf Row d Slack 10f P
239. ation F ile s CPXaddchannel ES CPXmsg p gt Channel s CPXdelchannel CPXaddfuncdest CPXdelfuncdest Destination F unction s Figure 9 1 ILOG CPLEX Message Handling Routines Example Using the Message Handler This example shows you how to use the ILOG CPLEX message handler from the Callable Library It captures all messages generated by ILOG CPLEX and displays them on screen along with a label indicating which channel sent the message It also creates a user channel to receive output generated by the program itself The user channel accepts user generated messages displays them on screen with a label and records them in a file without the label This example derives from 1pex1 c a program described in the ILOG CPLEX Getting Started manual There are a few differences between the two examples ILOG CPLEX 8 1 USER S MANUAL MANAGING INPUT amp OUTPUT In this example the function ourmsgfunc rather than the C functions printf or fprintf stderr manages all output The program itself or CPXmsg from the ILOG CPLEX Callable Library calls ourmsgfunc In fact CPXmsg isa replacement for printf allowing a message to appear in more than one place for example both on screen and in a file Only after you initialize the ILOG CPLEX environment by calling CPXopenCPLEX can you call CPXmsg And only after you call CPXgetchannels can you use the
240. ation takes significantly longer to solve the problem than does the Interactive Optimizer then you can probably improve the performance of your application In such a case look closely at issues like memory fragmentation unnecessary compiler options inappropriate linker options and programming practices that slow the application without causing incorrect results such as operations within a loop that should be outside the loop Using the Interactive Optimizer for Debugging 118 The ILOG CPLEX Interactive Optimizer distributed with the Component Libraries offers a way to see what is going on within the ILOG CPLEX part of your application when you observe peculiar behavior in your optimization application The commands of the Interactive Optimizer correspond exactly to routines of the Component Libraries so anomalies due to the ILOG CPLEX part of your application will manifest themselves in the Interactive Optimizer as well and contrariwise if the Interactive Optimizer behaves appropriately on your problem you can be reasonably sure that routines you call in your application from the Component Libraries work in the same appropriate way The first step in using the Interactive Optimizer for debugging is to write a version of the problem from the application into a formatted file that can then be loaded into the Interactive Optimizer To do so insert a call to the method 11oCplex exportModel or to the routine CPXwriteprob into your app
241. atus 0 Inky 34 int zero 0 int ind NULL double val NULL char sense NULL double rngval NULL sense char malloc nnutr sizeof char if sense NULL Status CPXERR NO MEMORY goto TERMINATE for i 0 i lt nnutr itt sense i R val double malloc nnutr sizeof double if val NULL Status CPXERR NO MEMORY goto TERMINATE rngval double malloc nnutr sizeof double if rngval NULL Status CPXERR NO MEMORY goto TERMINATE ILOG CPLEX 8 1 USER S MANUAL 107 2 co ie D 7 ley o y lt EXAMPLE 108 DIETARY OPTIMIZATION for i 0 i lt nnutr itt rngval i nutrmax i nutrmin il ind int malloc nfoods sizeof int if ind NULL status CPXERR NO MEMORY goto TERMINATE for i 0 i lt nnutr itt ind i ij status CPXnewrows env lp nnutr nutrmin sense rngval NULL if status goto TERMINATE for j 0 j lt nfoods j for i 0 i lt nnutr itt val i nutrper i j status CPXaddcols env lp 1 nnutr costtj amp zero ind val lb j ub j NULL if status goto TERMINATE TERMINATE free and null char amp sense free and null char amp rngval free and null char amp ind free and null char amp val return status END populatebycolumn This simple routine frees
242. atus Bounded 67 error 67 Feasible 67 Infeasible 67 InfeasibleOrUnbounded 67 Optimal 67 Unbounded 67 Unknown 67 return value 91 debugging with 120 routines to access parameters 98 REW file format 291 RHS see right hand side right hand side RHS file formats for 293 rim vectors 293 root relaxation parallel processing 376 RootAlg 69 TOW growth parameter 182 index number 92 name 92 referencing 92 residual 141 row ordering algorithms 167 approximate minimum degree AMD 167 ILOG CPLEX 8 1 INDEX approximate minimum fill AMF 168 automatic 167 nested dissection ND 168 rowwise modeling 49 100 S SAV file format 130 198 291 saving advanced basis 130 best factorable basis 138 DPE file 257 MIP tree 242 parameter specification file 400 perturbed problem 257 SAV file 257 TRE file 242 scaling 140 142 alternative methods of 132 definition 132 in network extraction 180 infeasibility and 140 singularities and 138 search tree 319 semi continuous variable 37 246 semi continuous variables 61 sensitivity analysis 73 MIPs 243 performing 44 separable 196 set Interactive Optimizer command 400 setDefaults 71 setDefaults member function IloCplex class 41 setDirection 72 setDirections 72 setExpr member function IloObjective class 200 setLB 82 setLinearCoef 82 setOut 295 setParam 69 70 setParam member function IloCplex class 41 setPriorities 72 UsER S MANUAL 419 INDEX setPriority 72 setting
243. ault uses the dual simplex optimizer ILOG CPLEX 8 1 USER S MANUAL 101 EXAMPLE DIETARY OPTIMIZATION After this the program finishes by making a call to CPXsolution to obtain the values for each variable in this optimal solution printing these values and writing the problem to a disk file for possible evaluation by the user via the call to CPXwriteprob It then terminates after freeing all the arrays that have been allocated along the way Complete Program The complete program diet c appears here and online in the standard distribution HOHER DEUM BS NEU File examples src diet c Version 8 1 m Copyright C 1997 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the x course of developing applications that use ILOG products he E EE diet c reading data for a dietary problem building the model and solving it methods for creating the model diet r lt datafile gt generates the problem by adding rows diet c lt datafile gt generates the problem by adding columns Bring in the CPLEX function declarations and the C library header file stdio h with the following single include include lt ilcplex cplex h gt Bring in the declarations for the string functions include lt stdlib h gt include lt string h gt
244. backs your application can implement interrupt capability for example or create displays of optimization progress Once control is transferred back to a function in the calling application the calling application can retrieve specific information about the current optimization from the routine CPXgetcallbackinfo Optionally the calling application can then tell ILOG CPLEX to discontinue optimization ILOG CPLEX 8 1 USER S MANUAL 349 USING CALLBACKS 350 To implement and use a callback in your application you must first write the callback function and then tell ILOG CPLEX about it For more information about the ILOG CPLEX Callable Library routines for callbacks see the ILOG CPLEX Reference Manual Setting Callbacks In the Callable Library diagnostic callbacks are grouped into two groups LP callbacks and MIP callbacks For each group one callback function can be set by calling functions CPXset lpcallbackfunc and CPXsetmipcallbackfunc respectively You can distinguish between the actual callbacks by querying the parameter wherefrom which is passed to the callback function as parameter by ILOG CPLEX Callbacks for LPs and for MIPs ILOG CPLEX will evaluate two user defined callback functions one during the solution of LP and QP problems and one during the solution of MIP problems ILOG CPLEX calls the LP callback once per iteration during the solution of an LP or QP problem and periodically during the presolve ILOG
245. been passed as parameters to a new goal Also user code in the execute method is not allowed to modify existing ILOG Concert Technology objects in any way 11oCplex uses an optimized memory management system within goals for dealing with temporary objects However this memory management system cannot be mixed with the default memory management system used by ILOG Concert Technology Thus for example it is illegal to add an element to array vars in the example since this array has been created outside of the goal Cuts and Goals Goals can also be used to add global cuts Whereas local cuts are respected only in a subtree global cuts are added to the entire problem and are therefore respected at every node after they have been added Global cuts can be added similarly to local cuts by using a global cut goal A global cut goal is created with method I1oCplex GoalI GlobalCutGoal IloCplex globalCutGoal This method takes an 11oRange or an I1oRangeArray IloRange object as its ILOG CPLEX 8 1 USER S MANUAL 327 EN E O 2 oS US a UE Q GOALS 328 IN ILOCPLEX parameter and returns a goal When the goal executes it adds the constraints as global cuts to the problem Example ilogoalex2 cpp shows the use of IloCplex GoalI GlobalCutGoal for solving the noswot MILP model This is a relatively small model from the MIPLIB 3 0 test set consisting only of 128 variables Nonetheless it is ver
246. bject will not correspond to your intentions One possible result may be a segmentation fault or other disruption of your application In other cases ILOG CPLEX may solve a different model from the one you intended and that situation may or may not result in error messages from ILOG CPLEX Using the Data Checking Parameter E 2 D ie D D E ey A 5 lt To help you detect this kind of error you can set the parameter CPX_PARAM_DATACHECK to the value CPX_ON to activate additional checking of array arguments for CPXcopy CPXread and CPXchg functions The additional checks include invalid sense ctype sostype values indexes out of range for example rowind 2 numrows duplicate entries matbeg or sosbeg array with decreasing values NANs in double arrays NULLsin name arrays When the parameter is set to CPX_OFF only simple checks for example checking for the existence of the environment are performed ILOG CPLEX 8 1 USER S MANUAL 93 ILOG CPLEX PROGRAMMING PRACTICES 94 Using Diagnostic Routines for Debugging ILOG CPLEX also provides diagnostic routines to look for common errors in the definition of problem data In the standard distribution of ILOG CPLEX the file check c contains the source code for these routines CPXcheckcopylp CPXcheckcopylpwnames CPXcheckcopyapsep CPXcheckcopyquad CPXcheckaddrows CPXcheckaddcols CPXcheckchgcoeflist
247. ble to ILOG CPLEX the automatic setting results in the Concurrent optimizer being called An exception is when an advanced basis is present in that case it will behave as the serial algorithm would Dual Simplex Optimizer If you are familiar with linear programming theory then you recall that a linear programming problem can be stated in primal or dual form and an optimal solution if one exists of the dual has a direct relationship to an optimal solution of the primal model ILOG CPLEX s Dual Simplex Optimizer makes use of this relationship but still reports the solution in terms of the primal model Recent computational advances in the dual simplex method have made it the first choice for optimizing a linear programming problem This is especially true for primal degenerate problems with little variability in the right hand side coefficients but significant variability in the cost coefficients Primal Simplex Optimizer ILOG CPLEX s Primal Simplex Optimizer also can effectively solve a wide variety of linear programming problems with its default parameter settings With recent advances in the dual simplex method the primal simplex method is no longer the obvious choice for a first try at o 2 Q T U Uv e D 3 7 ILOG CPLEX 8 1 USER S MANUAL 125 CHOOSING AN OPTIMIZER FOR YOUR LP PROBLEM 126 optimizing a linear programming problem However this method will sometimes work better on problems wher
248. blparam accepts arguments to indicate e the environment that is a pointer of type CPXENVptr returned by CPXopenCPLEX e the parameter to set this routine sets parameters of type double e the value you want the parameter to assume CPXsetstrparam accepts arguments to indicate e the environment that is a pointer of type CPXENVptr returned by CPXopenCPLEX e the parameter to set this routine sets parameters of type const char e the value you want the parameter to assume The ILOG CPLEX Reference Manual documents the type of each parameter int double char along with the symbolic constant and reference number representing the parameter The routine CPXsetdefaults resets all parameters except the log file to their default values including the ILOG CPLEX callback functions This routine resets the callback functions to NULL Like other Callable Library routines to manage parameters this one accepts an argument indicating the environment and it returns 0 for success or a nonzero value in case of error 2 D ie D D D o A 5 lt Example Dietary Optimization The optimization problem solved in this example is to compose a diet from a set of foods so that the nutritional requirements are satisfied and the total cost is minimized Example diet c illustrates Creating a Model Row by Row Creating a Model Column by Column Solving the Model with CPX1popt
249. branch One branch restricts xj x2 x4 to O zero This branch results in x5 being set to J one The other branch where x is set to O zero results in an infeasible solution so we remove it from further consideration If a warehouse must be built then we need the additional constraint that Xj X2 X4 X5 1 The implicit constraint for an SOS Type 1 is less than or equal to one The continuous relaxation may more closely resemble the MIP if we add that constraint Declaring SOS Members ILOG CPLEX offers you several ways to declare an SOS in a problem Use an SOS file that is one in SOS format with the file extension sos SOS files offer you the most powerful and flexible alternative because the SOS file structure allows you to do several tasks at once e provide branching priorities for sets e assign weights to individual set members e define overlapping sets Use SOS declarations within an MPS or LP file that is one in MPS format with the file extension mps or in LP format with the file extension 1p If you already have MPS files with SOS information you may prefer this option Conventions for declaring SOS information in MPS files are documented in the ILOG CPLEX Reference Manual a e ES D di Buinjos Setting Branching Priority for an SOS An entire SOS can be given a branching priority There are two alternative ways to give an SOS branching priority both documented in the IL
250. brary so that the Callable Library is fully reentrant and thread safe The names of all library routines begin ILOG CPLEX 8 1 USER S MANUAL 87 ILOG CPLEX PROGRAMMING PRACTICES 88 with the three character prefix CPX to prevent namespace conflicts with your own routines or with other libraries Also to avoid clutter in the namespace there is a minimal number of routines for setting and querying parameters Variable Names and Calling Conventions Routines in the ILOG CPLEX Callable Library obey the C programming convention of call by value as opposed to call by reference for example in FORTRAN and BASIC Ifa routine in the Callable Library needs the address of a variable in order to change the value of the variable then that fact is documented in the ILOG CPLEX Reference Manual by the suffix _p in the parameter name in the synopsis of the routine In C you create such values by means of the amp operator to take the address of a variable and to pass this address to the Callable Library routine For example let s look at the synopses for two routines CPXgetobjval and CPXgetx as they are documented in the ILOG CPLEX Reference Manual to clarify this calling convention Here is the synopsis of the routine CPXgetobjval int CPXgetobjval CPXCENVptr env CPXCLPptr lp double objval p In that routine the third parameter is a pointer to a variable of type double To call this routine from C declare double objval
251. cessing dual page 168 set preprocessing fill page 127 set preprocessing linear set preprocessing numpass set preprocessing presolve page 135 page 239 set preprocessing qpmakepsd set preprocessing reduce page 127 page 140 set preprocessing relax page 239 set preprocessing symmetry set qpmethod set read constraints 398 ILOG CPLEX 8 1 USER S MANUAL Interactive Optimizer Commands Command Options Example set read datacheck set read nonzeroes set read qpnonzeroes set read reverse set read scale page 132 set read variables set sifting algorithm set sifting display set sifting iterations set simplex basisinterval set simplex crash page 133 set simplex dgradient set simplex display set simplex iisfind set simplex limits iterations set simplex limits lowerobj set simplex limits perturbation page 138 set simplex limits singularity page 138 set simplex limits threads set simplex limits upperobj set simplex perturbation page 138 set simplex pgradient set simplex pricing set simplex refactor page 134 set simplex tolerances feasibility page 142 set simplex tolerances markowitz page 139 ILOG CPLEX 8 1 USER S MANUAL 399 Interactive Optimizer Commands Command Options Example set simplex tolerances optimality page 142 set simplex xxxs
252. chapter we assume you have some familiarity with quadratic programming For a more complete explanation of quadratic programming generally we recommend you consult a text such as one of those listed in Further Reading on page 30 of the preface of this manual ILOG CPLEX supports two views of quadratic objective functions a matrix view and an algebraic view ILOG CPLEX 8 1 USER S MANUAL ENTERING QPS In the matrix view commonly found in textbook presentations of QP the objective function is defined as 1 7 xTQx cx where Q must be symmetric and positive semi definite for a minimization problem or negative semi definite for a maximization problem This view is supported by the MPS file format and the Callable Library routines where the quadratic objective function information is specified by providing matrix Q Thus by definition the factor of 2 must be considered when entering a model using the matrix view as it will be implicitly assumed by the optimization routines Similarly symmetry of the Q matrix data is required the MPS reader will return an error status code if the file contains unequal off diagonal components such as a nonzero value for one and zero or omitted for the other In the algebraic view a quadratic objective function is specified as an expressions of the form Cl xl cn xn gll xl x1 q12 xl x2 qnn xn xn This view is supported by the LP format when entering quadratic objective f
253. cnt NULL int matind NULL double matval NULL double lb NULL double ub NULL char ctype NULL Declar store variab e and allocate space for the optimization results including the le values and row slacks int solstat double objval double x NUMCOLS double slack NUMROWS CPXENVptr env NULL CPXLPptr lp NULL int status int ipg int cur_numrows cur_numcols status the variables and arrays where we will objective value Initialize the CPLEX environment env CPXopenCPLEX amp status the status value indicates the reason for A call to CPXgeterrorstring will produce the text of the error message Note that CPXopenCPLEX produces no output so the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines the errors will be seen if the CPX_PARAM_SCRIND indicator is set to CPX_ON If an error occurs failure g if env NULL 262 ILOG CPLEX 8 1 USER S MANUAL EXAMPLE OPTIMIZING A BASIC MIP PROBLEM char errmsg 1024 fprintf stderr Could not open CPLEX environment n CPXgeterrorstring env status errmsg fprintf stderr s errmsg goto TERMINATE Turn on output to the screen status CPXsetintparam env CPX PARAM SCRIND CPX ON if status fprintf stderr Failure to turn on screen indicator error d n status goto TERMINATE Fill in the data for th
254. cols routine 94 PXcheckaddrows routine 94 PXcheckchgcoeflist routine 94 PXcheckcopyctype routine 94 PXcheckcopylp routine 94 PXcheckcopylpwnames routine 94 PXcheckcopyqsep routine 94 PXcheckcopyquad routine 94 PXcheckcopysos routine 94 PXcheckvals routine 94 PXchgcoeflist routine 86 114 PXchgprobtype routine 202 243 261 PXchgqpcoef routine 200 PXcloseCPLEX routine 87 151 182 215 271 299 352 PXCLPptr 89 PXCNETptr 89 PXcopybase routine 150 151 PXcopycttype routine 246 PXcopyctype routine 90 119 225 260 PXcopylp routine 86 114 PXcopynettolp routine 188 PXcopyorder routine 245 277 PXcopyqsep routine 90 PXcopyquad routine 90 207 PXcopysos routine 245 246 277 PXcreateprob 351 PXcreateprob routine 86 89 101 151 207 215 H I USER S MANUAL 260 271 CPXdelchannel routine 298 299 CPXdelfpdest routine 95 298 299 CPXdelfuncdest routine 298 299 CPXdisconnectchannel routine 298 CPXdisplayiis routine 144 CPXdualopt routine 379 CPXENVptr data type 89 CPXERR NEGATIVE SURPLUS symbolic constant 308 cpxerror message channel 297 299 CPXfclose routine 95 CPXFILEptr data type 95 CPXflushchannel routine 298 CPXfopen routine 95 295 CPXfput s routine 96 CPXfreeprob routine 87 151 215 271 352 CPXgetcallbackinfo routine 94 349 350 352 CPXgetchannels routine 89 297 299 CPXgetcolindex routine 93 CPXgetcolname routine 309 310
255. constraint Since the branch callback function allows branching only on individual variables the determination of the appropriate branch may be quite difficult for constraints not modelled with linear expressions With goals the feasibility test and the resulting branching can be implemented with a single goal The second big difference between goals and callbacks is that with goals you can easily specify different search strategies in different subtrees To do this simply provide different search goals as a parameter to the Or goal when creating the root nodes for the subtrees in question To achieve a similar result with callbacks requires an implementation that is too complex for a presentation here The only functionality that is not supported via goals is that provided by the solve callback Because of this the solve callbacks can be used at the same time as goals However this callback is very rarely used In summary goals can be advantageous if you want to take control over several steps of the branch amp cut search simultaneously or if you want to specify different search strategies in different subtrees On the other hand if you only need to control a single aspect of the search for example adding cuts using the appropriate callback may involve a smaller API and thus be quicker and easier to understand and implement ILOG CPLEX 8 1 USER S MANUAL USING PARALLEL OPTIMIZERS Using Parallel Optimizers This section
256. constructor methods methodName there is also a constructor method addMet hodName which immediately adds the newly constructed modeling object to the active model For example the call IloObjective obj cplex addMaximize expr is equivalent to IloObjective obj cplex add cplex maximize expr Not only do the addMet hodName methods simplify the program they are also more efficient than the two equivalent calls because an intermediate copy can be avoided Building the Model All the building blocks are now in place to implement a method that creates a model The diet problem consists of finding the least expensive diet using a set of foods such that all nutritional requirements are satisfied In this chapter we build the specific diet model 64 ILOG CPLEX 8 1 USER S MANUAL BUILDING THE MODEL choose an optimizing algorithm and see how to access more detailed information about the solution We have a set of foods where food j has a unit cost of oodCost 3 The minimum and maximum amount of food j which can be used in the diet is designated foodMin 4 and foodMax j respectively Each food j also has a nutritional value nutrPerFood il j for all possible nutrients i The nutritional requirement states that in the diet the amount of every nutrient i consumed must be within the bounds nut rMin i and nutrMax i Mathematically this problem can be modeled using a variable Buy j for each food j indicat
257. controls the kinds of pivots permitted If you set it near its maximum value of 0 99999 it may make iterations slower but more numerically stable Inability to Stay Feasible on page 139 shows how to change the Markowitz tolerance If none of these ideas help you may need to alter the model of your problem Consider removing the offending variables manually from your model and review the model to find other ways to represent the functions of those variables Stalling Due to Degeneracy Highly degenerate linear programs tend to stall optimization progress in the primal and dual simplex optimizers When stalling occurs with the primal simplex optimizer ILOG CPLEX automatically perturbs the variable bounds when stalling occurs with the dual simplex optimizer ILOG CPLEX perturbs the objective function In either case perturbation creates a different but closely related problem Once ILOG CPLEX has solved the perturbed problem it removes the perturbation by resetting problem data to their original values ILOG CPLEX 8 1 USER S MANUAL DIAGNOSING LP INFEASIBILITY If ILOG CPLEX automatically perturbs your problem early in the solution process you should consider starting the solution process yourself with a perturbation Starting in this way will save the time that would be wasted if you first allowed optimization to stall and then let ILOG CPLEX perturb the problem automatically To start perturbation yourself set the parameter Per
258. ct added to the IloMode1 objects that represent the individual scenarios Data Management Classes Usually the data describing an optimization problem must be collected before or during the creation of the Concert Technology representation of the model Though in principle modeling does not depend on how the data is generated and represented this task may be facilitated by using the array or set classes provided by Concert Technology For example objects of class IloNumArray can be used to store numerical data in arrays Elements of the class 11o0NumArray can be accessed like elements of standard C arrays but the class also offers a wealth of additional functions For example Concert Technology arrays are extensible in other words they transparently adapt to the required size when new elements are added using the method aaa Conversely elements can be removed from anywhere in the array with the method remove Concert Technology arrays also provide debugging support when compiled in debug mode by using assert to ensure that no element beyond the array bounds is accessed Input and output operators that is operator and operator are provided for arrays For example the code IloNumArray data env 3 1 0 2 0 3 0 cout data endl produces the following output 1 0 2 0 3 0 When you are done using an array and want to reclaim its memory call method end for example data end However when ending
259. d Performance Considerations If you set the number of threads to a value greater than the number of available processors performance will usually degrade If you set the number of threads to a value less than the number of processors the remaining processors will be available for other jobs on your platform Simultaneously running multiple parallel jobs with a total number of threads ILOG CPLEX 8 1 USER S MANUAL USING PARALLEL OPTIMIZERS exceeding the number of processors may impair the performance of each individual process as its threads compete with one another If you are using the OpenMP libraries and set the OMP_NUM_THREADS environment variable to a greater value than the actual thread count used with ILOG CPLEX your operating system may create idle threads that still consume system resources If you know in advance how many threads you want to use we recommend that you set the environment variable to that number before you start ILOG CPLEX The benefit of applying more threads to optimizing a specific problem varies depending on the optimizer you use and the characteristics of the problem You should experiment to assess performance improvements and degradation when you apply more or fewer processors For example when you optimize the root relaxation using the dual simplex method there may be little or no benefit in applying more than four processors to the task In contrast if you use 16 processors during the MIP phase of
260. d Upper Bound Values lb ub method rhs rhs eq Double MAX VALUI rhs le rhs Double MAX VALUI ge The last column contains the method provided with 11o0Modeler that can be used to directly create the appropriate ranged constraint specifying parameters re1 and rhs For example the constraint expr 1 0 is created by calling IloRange le cplex le expr 1 0 Again all constructors for ranged constraints come in pairs one constructor with and one without a name parameter Objective Functions The objective function in Concert Technology is represented by objects of type IloObjective Such objects are defined by an optimization sense an expression and an optional name The objective expression is represented by an 11oNumExpr The objective sense is represented by an object of class IloObjectiveSense and can take two values IloObjectiveSense Maximize or IloObjectiveSense Minimize The most general constructor for an objective function object is IloObjective obj cplex objective sense expr name where sense is of type I100bjectiveSense expr is of type IloNumExpr and name is a string ILOG CPLEX 8 1 USER S MANUAL 63 BUILDING THE MODEL For convenience the methods maximize andminimize are provided to create a maximization or minimization objective respectively without using an IloObjectiveSense parameter Names for objective function objects are optional so al
261. d change problem 1p After this change you can apply any of the LP optimizers to this problem When you change a network flow problem into an LP problem the basis information that is available in the network flow problem is passed along to the LP formulation In fact if you have already solved the network flow problem to optimality then if you call the primal or dual simplex optimizers for example with the Interactive Optimizer command primopt or tranopt that simplex optimizer will perform no iterations Generally you can also use the same basis from a basis file for both the LP and the network optimizers However there is one exception in order to use an LP basis with the network optimizer at least one slack variable or one artificial variable needs to be basic Starting from an Advanced Basis on page 129 explains more about this topic in the context of LP optimizers If you have already read the LP formulation of a problem into the Interactive Optimizer you can transform it into a network with the command change problem network Given any LP problem and this command ILOG CPLEX will try to find the largest network embedded in the LP problem and transform it into a network flow problem However as it does so it discards all rows and columns that are not part of the embedded network At the same time ILOG CPLEX passes along as much basis information as possible to the network optimizer Example Network to LP Transformation This e
262. d in calls to external functions or subroutines causes its argument to be passed by value rather than by the default FORTRAN convention of passed by reference For example with that extension you can call the routine CPXprimopt with this FORTRAN statement status CPXprimopt val env val lp i z Pointers ie Certain ILOG CPLEX routines return a pointer to memory In FORTRAN 77 such a pointer cannot be dereferenced however you can store its value in an appropriate integer type and you can then pass it to other ILOG CPLEX routines On most operating systems the default E integer type of four bytes is sufficient to hold pointer variables On some systems such as o DEC Alpha a variable of type INTEGER 8 may be needed Consult your system g documentation to determine the appropriate integer type to hold variables that are C pointers Strings When you pass strings to routines of the Callable Library they expect C strings that is strings terminated by an ASCII NULL character denoted 0 in C Consequently when you pass a FORTRAN string you must add a terminating NULL character you do so by means of the FORTRAN intrinsic function CHAR 0 C Interface The ILOG CPLEX header file cplex h includes the extern C statements necessary for use with C If you wish to call the ILOG CPLEX C interface from a C application rather than using Concert Technology you can include cplex h in your C sourc
263. d of optimality often also speeds up the processing of the root node If your purposes are compatible with this emphasis consider using it Trouble Finding More than One Feasible Solution For some models ILOG CPLEX finds an integer feasible solution early in the process and then does not find a better one for quite a while One possibility of course is that the first feasible solution is optimal In that case there are no better solutions One possible approach to finding more feasible solutions is to increase the frequency of the node heuristic by setting the HeurFreq parameter to a value like 10 or 5 or even 1 This heuristic can be expensive so exercise caution when setting this parameter to values less than 10 Another approach to finding more feasible solutions is to try a node selection strategy alternative Setting the NodeSe1 parameter to 2 invokes a best estimate search which sometimes does a better job of locating good quality feasible solutions than the default node selection strategy i A fa E D 7 di Bulnjos Large Number of Unhelpful Cuts While the cuts added by ILOG CPLEX reduce runtime for most problems on occasion they can have the opposite effect If you notice for example that ILOG CPLEX adds a large number of cuts at the root but the objective value does not change significantly then you may want to experiment with turning off cuts In the Interactive Optimizer you can turn cuts
264. d once the size of the tree exceeds the value of TreLim the tree limit parameter Under default settings the limit is infinity le gt but you can set it to a lower value in megabytes Write a Tree File and Restart On some platforms even when the current tree size is within system limits memory fragmentation may be so great that performance becomes poor To overcome that kind of fragmentation we recommend that you stop optimization write a tree file using the TRE format exit ILOG CPLEX restart it read in the model and tree file and continue optimization then Use Node Files for Storage ILOG CPLEX offers a node file storage feature to store some parts of the branch amp cut tree in files If you use this feature ILOG CPLEX will be able to explore more nodes within a smaller amount of computer memory This feature includes several options to reduce the use of physical memory and it entails a very small increase in runtime Node file storage offers a much better option than relying on swap space This feature is especially helpful when you are using steepest edge pricing as the subproblem simplex pricing strategy because pricing information itself consumes a great deal of memory There are several parameters that control the use of node files They are WorkMem NodeFileInd TreLim WorkDir When tree storage size exceeds the limit defined by WorkMem what happens next is determined by the setting of NodeFileInd
265. d right hand side names extraneous uncommented characters blanks in lieu of repeated name fields such as bound vector names and right hand side names You can convert fixed format MPS files that contain those conventions into acceptable ILOG CPLEX extended MPS files To do so use the convert utility supplied in the standard distribution of ILOG CPLEX The convert utility removes unreadable features from fixed format MPS BAS SOS and ORD files It runs from the operating system prompt of your platform Here is the syntax of the convert utility convert option inputfilename outputfilename Your command must include an input file name and an output file name they must be different from each other The options summarized in Table 9 1 indicate the file type You ILOG CPLEX 8 1 USER S MANUAL MANAGING INPUT amp OUTPUT may specify only one option If you do not specify an option ILOG CPLEX attempts to deduce the file type from the extension in the file name Table 9 1 Options for the convert Utility and Corresponding File Extensions Option File type File extension m MPS Mathematical Programming System mps s SOS Special Ordered Set SOS b BAS basis file according to MPS conventions bas 0 ORD priority orders ord Managing Log Files the Log File Parameter As ILOG CPLEX is working it can record messages to a log file By default the Interactive Optimiz
266. de that first pivots the variable out of the basis before removing it The resulting basis is not guaranteed to be feasible or optimal but it will still constitute a valid basis To select this mode call method cplex setDeleteMode IloCplex FixBasis Similarly when removing a constraint with the FixBasis delete mode ILOG CPLEX will pivot the corresponding slack or artificial variable into the basis before removing it to assure maintaining a valid basis In either case if no valid basis was available in the first place no pivot operation is performed To set the delete mode back to its default setting call cplex setDeleteMode IloCplex LeaveBasis ILOG CPLEX 8 1 USER S MANUAL Handling Errors HANDLING ERRORS Changing Variable Type The type of a variable cannot be changed by calling modification methods Instead Concert Technology provides the modeling class IloConversion the objects of which allow you to override the type of a variable in a model This design allows you to use the same variable in different models with different types Consider for example mode11 containing integer variable x You can then create mode12 as a copy of mode11 that treats x as a continuous variable with the following code IloModel model2 env model2 add modell model2 add IloConversion env x ILOFLOAT Q e O D ES 7 ey i ES Q lt A conversion object that is an instance of IloConversio
267. default n primal simplex n dual simplex n network simplex n barrier n oO 5 att o ILOG CPLEX 8 1 USER S MANUAL 221 EXAMPLE READING A QP FROM A FILE 222 ILOG CPLEX 8 1 USER S MANUAL Solving Mixed Integer Programming Problems The ILOG CPLEX Mixed Integer Optimizer enables you to solve models in which one or more variables must take integer solution values This chapter tells you more about optimizing mixed integer programming MIP problems with ILOG CPLEX It includes sections on i A fej ES D 7 diN Buinjos Sample Stating a MIP Problem Considering Preliminary Issues Using the Mixed Integer Optimizer Using Sensitivity Information in a MIP Using Special Ordered Sets Using Semi Continuous Variables Progress Reports Interpreting the Node Log Troubleshooting MIP Performance Problems Example Optimizing a Basic MIP Problem Example Reading a MIP Problem from a File 9 9 9 9 9 o 99 Example Using SOS and Priority ILOG CPLEX 8 1 USER S MANUAL 223 SAMPLE STATING A MIP PROBLEM Sample Stating a MIP Problem 224 A mixed integer programming MIP problem may contain both integer and continuous variables If the problem contains an objective function with no quadratic term a linear objective then the problem is termed a Mixed Integer Linear Program MILP If there is a quadratic term in the objective function the problem is termed a Mixed Int
268. del could give unintended answers that are accurate in the context of the specific data being fed to the optimizer Be particularly wary of data in your model that has been computed within your program or transmitted to your program from another via an input file using single precision 32 bit arithmetic For example in C this would come from using type float instead of double Such data will be accurate to only about 8 decimal digits so that for instance if you print the data you might see values like 0 3333333432674408 instead of 0 3333333333333333 ILOG CPLEX uses double precision 64 bit arithmetic in its computations and truncated single precision data carries the risk that it will convey a different meaning than the user intends The underlying principle behind all the cautions in this section is that information contained in the data needs to reflect actual meaning or the optimizer may reach unstable solutions or encounter algorithmic difficulties Measuring Problem Sensitivity with Basis Condition Number Ill conditioned matrices are sensitive to minute changes in problem data That is in such problems small changes in data can lead to very large changes in the reported problem solution ILOG CPLEX provides a basis condition number to measure the sensitivity of a linear system to the problem data You might also think of the basis condition number as the number of places in precision that can be lost For example if the bas
269. deling with lloMPModeler 000 e cece eee nnn nn RR 74 Modeling by Column 2 0 02 0 0 75 Solving the Diet Model with the Java API 0 0 c eee ee eee eee nets 76 Creating the Optimizer 2 2 0 ete n 76 Example Diet java Source Code 1 1 cette eee 78 Modifying the Model 1 2 2 0 0 0 cece eee eee 82 The ILOG CPLEX Callable Library llle 83 Architecture of the ILOG CPLEX Callable Library 00 0 c cece eee eee 83 EDD Rr 84 Compiling and Linking gt es se sanee i a IRR 85 Using the Callable Library in an Application 0 0020 e eee eee eee eee 85 Initialize the ILOG CPLEX Environment 0 0 cece eects 85 Instantiate the Problem Object 0 0 c cece ete 86 Put Data in the Problem Object slslsssssesse eee eh 86 Optimize the Problem 0 0 0 cece ee rn 86 Change the Problem Object 1 0 0 00 0 cece ett men 87 Destroy the Problem Object saaana nennen 87 Release the ILOG CPLEX Environment 000 cece eee nes 87 ILOG CPLEX Programming Practices 0 cece eee eee eee eee eee 87 Variable Names and Calling Conventions lille 88 Data TY PCS E 89 Ownership of Problem Data en 89 Copying in MIP and QP sssssessseseeeeeee rs 90 Problem Size and Memory Allocation Issues llle 90 Status and Return Values 0 0 0 e ec rn 91 ILOG CPLEX 8 1 USER S MANUAL 7 TABLE OF CONTENTS Chapter
270. derr Failure to turn on screen indicator error d n status goto TERMINATE Create the problem using the filename as the problem name lp CPXoreateprob env amp status argv l1 A returned pointer of NULL may mean that not enough memory was available or there was some other problem In the case of failure an error message will have been written to the error channel from inside CPLEX In this example the setting of the parameter CPX PARAM SCRIND causes the error message to appear on stdout Note that most CPLEX routines return an error code to indicate the reason for failure if lp NULL fprintf stderr Failed to create LP n goto TERMINATE Now read the file and copy the data into the created lp status CPXreadcopyprob env lp argv 1 NULL if status fprintf stderr Failed to read and copy the problem data n goto TERMINATE Optimize the problem and obtain solution ILOG CPLEX 8 1 USER S MANUAL USING QUERY ROUTINES IN THE CALLABLE LIBRARY switch argv 2 0 case o method break case p method CPX ALG PRIMAL break case d method CPX ALG DUAL break case n method CPX ALG NET break CPX ALG AUTOMATIC case h method CPX ALG BARRIER break case b method CPX ALG BARRIER status CPXsetintparam env CPX PARAM BARCROSSALG CPX ALG NONE if status fprintf stderr Failed to set the crossover method
271. des examples Chapter 8 Solving Mixed Integer Programming Problems shows you how to handle MIPs It particularly emphasizes performance tuning and offers a series of examples Chapter 9 More About Using ILOG CPLEX includes several sections on working with important aspects of the ILOG Component Libraries Managing Input amp Output explains how to enter mathematical programs efficiently and how to generate meaningful output from your ILOG CPLEX applications It also lists the ILOG CPLEX 8 1 USER S MANUAL IN THIS MANUAL available file formats for entering data into ILOG CPLEX and writing bases and solutions from ILOG CPLEX Using Query Routines in the Callable Library shows how to access information about the model you currently have in memory through query routines of the Callable Library Goals in ILOG CPLEX shows how to use goals to control the MIP search Using Callbacks shows how to use callbacks to control the MIP search A Comparison of Goals and Callbacks compares the two different approaches Using Parallel Optimizers explains how to exploit parallel optimizers in case your hardware supports parallel execution Appendix B Interactive Optimizer Commands lists the commands available in the ILOG CPLEX Interactive Optimizer with cross references to examples of their use in this manual It also provides an overview about controlling parameters with the Interactive Optimizer Examples Online For the e
272. dividual nodes are computationally challenging then it may be possible to achieve speed increases by leaving the global thread limit at its default of 1 and setting the continuous optimizer thread limit SimThreads or BarThreads to a value greater than 1 The global thread limit of 1 will inhibit the parallelism of the branching process while the explicit thread limit of more than 1 will permit the optimization of each node in parallel Nested Parallel Processing Nested parallelism represents a further way to exploit the flexibility of independent thread parameters For example it might be determined from experience on a given family of models that only a modest degree of parallelism is beneficial at the nodes and additional processors do not help speed up the branching In such a case better speed increases might be obtained by combining a parallelization of the work that the LP or QP optimizer does at ILOG CPLEX 8 1 USER S MANUAL USING PARALLEL OPTIMIZERS each node On an 8 processor computer you might opt to solve a model by setting the MipThreads limit to 4 instead of its maximum of 8 and the BarThreads limit to 2 thus keeping all 8 processors busy as much of the time as possible with the four MIP threads each invoking two threads for the simplex optimizer If you do decide to try a nested parallel approach keep in mind the rule of thumb that it is usually better to keep a higher degree of parallelism of the nodes themselves
273. duplicateCallback const 0 which must be implemented for your callback class This method will be called to create the copies needed for using a callback on different cplex objects or on one cplex object with a parallel optimizer In most cases you can avoid writing callback classes by hand using supplied macros that make the process as easy as implementing a function You must implement a callback by hand only if the callback manages internal data not passed as arguments or if the callback requires eight or more parameters Writing Callbacks with Macros This is how to implement a callback using macros Since macros are not supported in java this technique will only apply to C Start by determining which callback you want to implement and how many arguments to pass to the callback function These two pieces of information determine the macro you need to use For example to implement a simplex callback with one parameter the macro is ILOSIMPLEXCALLBACK1 Generally for every callback type Xxx and any number of ILOG CPLEX 8 1 USER S MANUAL 343 z EN D3 qe oS US a UE Q USING CALLBACKS parameters n from 0 to 7 there is a macro called ILOXXXCALLBACKn The following table lists the callbacks and the corresponding macros and classes where n is a placeholder for 0 7 Table 9 4 Callback Macros Callb
274. e ILOG CPLEX 8 1 USER S MANUAL 97 MANAGING PARAMETERS FROM THE CALLABLE LIBRARY Managing Parameters from the Callable Library 98 Some ILOG CPLEX parameters assume values of type double others assume values of type int others are strings that is C type char Consequently in the Callable Library there are sets of routines one for int one for double one for char to access and to change parameters that control the ILOG CPLEX environment and guide optimization For example the routine CPXinfointparam shows you the default the maximum and the minimum values of a given parameter of type int whereas the routine CPXinfodblparam shows you the default the maximum and the minimum values of a given parameter of type double and the routine CPXinfostrparam shows you the default value of a given string parameter Those three Callable Library routines observe the same conventions they return 0 from a successful call and a nonzero value in case of error The routines CPXinfointparam and CPXinfodblparam expect five arguments a pointer to the environment that is a pointer of type CPXENVptr returned by CPXopenCPLEX anindication of the parameter to check this argument may be a symbolic constant such as CPX_PARAM_CLOCKTYPE or a reference number such as 1006 the symbolic constants and reference numbers of all ILOG CPLEX parameters are documented in the ILOG CPLEX Reference Manual and they are defined in
275. e ub p char ctype p setsosandorder CPXENVptr env CPXLPptr lp static void free and null char ptr The problem we are optimizing will have 2 rows 3 columns and 6 nonzeros define NUMROWS define NUMCOLS 4 define NUMNZ 9 int main void Declare and allocate space for the variables and arrays that will contain the data which define the LP problem char probname NULL int numcols int numrows int objsen double obj NULL double rhs NULL char sense NULL int matbeg NULL 278 ILOG CPLEX 8 1 USER S MANUAL EXAMPLE USING SOS AND PRIORITY int matcnt NULL int matind NULL double matval NULL double lb NULL double ub NULL char ctype NULL Declare and allocate space for the variables and arrays where we will store the optimization results including the status objective value variable values and row slacks int solstat double objval double x NUMCOLS double slack NUMROWS CPXENVptr env NULL CPXLPptr lp NULL int status int dy cs int cur numrows cur numcols Initialize the CPLEX environment env CPXopenCPLEX amp status If an error occurs the status value indicates the reason for failure A call to CPXgeterrorstring will produce the text of the error message Note that CPXopenCPLEX produces no output so the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX rout
276. e log file from the Interactive Optimizer with the command set logfile ILOG CPLEX 8 1 USER S MANUAL 295 MANAGING INPUT amp OUTPUT By default routines from the Callable Library do not write to a log file However if you want to close a log file that you created by a call to CPXset logfile call CPXset logfile again and this time pass a NULL pointer as its second argument From Concert use the setOut method with env getNullStream as argument where env is an I1oEnv object to stop sending logging output to an output stream Handling Message Channels the Output Channel Parameter Besides the log file parameter Interactive Optimizer and the Callable Library offer you output channel parameters to give you finer control over when and where messages appear in the Interactive Optimizer Output channel parameters indicate whether output should or should not appear on screen They also allow you to designate log files for message channels The output channel parameters do not affect the log file parameter so it is customary to use the command set logfile before the command set output channel valuel value2 In the output channel command you can specify a channel to be one of dialog errors logonly results Or warnings Table 9 2 summarizes the information carried over each channel Table 9 2 Options for the Output Channel Command Channel Information dialog messages related to interactiv
277. e solution with objective value z there exists a feasible solution with objective value z 1 for a minimization problem or z 1 for a maximization problem InfeasibleOrUnbounded The active model has been proven to be infeasible or unbounded For example an Opt imal status indicates that an optimal solution has been found and can be queried whereas an Infeasible status indicates that the active model has been proven to be infeasible See the online CPLEX Java Reference Manual for more information about these statuses More detailed information about the status of the optimizer can be queried with method getCplexStatus returning an object corresponding to ILOG CPLEX status codes Again the online CPLEX Java Reference Manual contains further information about this ILOG CPLEX 8 1 USER S MANUAL 67 ACCESSING SOLUTION INFORMATION Accessing Solution Information 68 If a solution was found with the solve method it can be accessed and then queried using a variety of methods The objective function can be accessed by calling double objval cplex getObjValue The values of individual modeling variables for the solution are accessed by calling methods IloCplex getValue for example double xl cplex getValue varl Frequently solution values for an array of variables are needed Rather than having to implement a loop to query the solution values variable by variable the method IloCplex getValues
278. e Manual This manual supplies detailed definitions of the classes and functions in the ILOG CPLEX callable library and the Concert Technology for C ILOG CPLEX Library It is available only in online form as HTML Microsoft compiled HTML help CHM form and as a PDF file You will find the searching facilities and cross links of these formats very useful ILOG CPLEX 8 1 Java Reference Manual This manual supplies detailed definitions of the Concert Technology interfaces and ILOG CPLEX Java classes It is available only in online form as HTML and Microsoft compiled HTML help CHM form ILOG License Manager ILM ILOG products are protected by the ILOG License Manager Before you can use ILOG CPLEX you need to set up the ILM This online documentation explains how to do it step by step for different platforms It is in HTML form included with your distribution ILOG Concert Technology Documentation Kit This includes the ILOG Concert Technology Reference Manual which documents the classes methods and functions of the Concert Technology library the LOG Concert Technology User s Manual which provides examples that show how to use Concert Technology to model problems the ILOG Concert Technology Hybrid Optimizers User s Guide amp Reference which documents the class IloLinConstraint and shows how to use ILOG s main algorithm classes IloSolver and 11oCplex in cooperation and the ILOG Concert Technology Migration Guide which shows how to
279. e largest objective coefficients among the variables with largest integer infeasibility That index is recorded in variable best j Then we create a new goal handle object res By default this is initialized to an empty goal However if an integer infeasible variable was found among those in vars variable best j will be 0 and we assign a non empty goal to res res AndGoal OrGoal vars bestj gt IloFloor x bestj 1 vars bestj lt IloFloor x bestj this This goal creates two branches one for vars bestj lt x bestj and one for vars bestj gt Lxlbestj 1 and continues branching in both subtrees with the same goal this Finally we call method end for all temporary arrays and return goal res Since Java objects are garbage collected there is no need for variable res Instead depending on the availability of an integer infeasible variable the nu11 goal is returned or the returned goal is created in the return statement itself return cplex and cplex or cplex geGoal _vars best j Math floor x bestj 1 cplex leGoal _vars best j Math floor x bestj this The Goal Stack To better understand how goals are executed we need to understand the concept of the goal stack Every node has its own goal stack When calling cplex solve goal the goal stack of the root node is simply initialized with goa1 and then calls the regular cplex solve method When 11oCplex processes a node it pops the fi
280. e only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines the errors will be seen if the CPX PARAM SCRIND indicator is set to CPX ON if env NULL char errmsg 1024 fprintf stderr Could not open CPLEX environment Mn CPXgeterrorstring env status errmsg fprintf stderr s errmsg goto TERMINATE Turn on output to the screen status CPXsetintparam env CPX PARAM SCRIND CPX ON if status fprintf stderr Failure to turn on screen indicator error d n status goto TERMINATE Fill in the data for the problem status setproblemdata amp probname amp numcols amp numrows amp objsen amp obj amp rhs amp sense amp matbeg amp matcnt amp matind amp matval amp lb amp ub amp qmatbeg amp qmatcnt amp gmatind amp qmatval if status fprintf stderr Failed to build problem data arrays n goto TERMINATE ILOG CPLEX 8 1 USER S MANUAL 209 EXAMPLE CREATING A QP OPTIMIZING FINDING A SOLUTION Create the problem lp CPXcreateprob env amp status probname A returned pointer of NULL may mean that not enough memory was available or there was some other problem In the case of failure an error message will have been written to the error channel from inside CPLEX In this example the setting of the parameter CPX PARAM SCRIND causes the error message to appear on stdout if lp
281. e problem status setproblemdata amp probname amp numcols amp numrows amp objsen amp obj amp rhs amp sense amp matbeg amp matcnt amp matind amp matval amp lb amp ub amp ctype if status fprintf stderr Failed to build problem data arrays n goto TERMINATE Create the problem lp CPXcreateprob env amp status probname A returned pointer of NULL may mean that not enough memory was available or there was some other problem In the case of failure an error message will have been written to the error channel from inside CPLEX In this example the setting of the parameter CPX PARAM SCRIND causes the error message to appear on stdout if lp NULL fprintf stderr Failed to create LP n goto TERMINATE Now copy the problem data into the lp status CPXcopylp env lp numcols numrows objsen obj rhs sense matbeg matcnt matind matval lb ub NULL if status fprintf stderr Failed to copy problem data n goto TERMINATE ILOG CPLEX 8 1 USER S MANUAL 263 i Le ES D 2 di Buinjos EXAMPLE 264 OPTIMIZING A BASIC MIP PROBLEM Now copy the ctype array status CPXcopyctype env lp ctype if status fprintf stderr Failed to copy ctype n goto TERMINATE Optimize the problem and obtain solution status CPXmipopt env lp if status i fprintf stderr Failed to opti
282. e quality of the solution Table 5 13 BarAlg Parameter Values for Barrier Optimizer Algorithm sett Meaning 0 default 1 algorithm starts with infeasibility estimate 2 algorithm starts with infeasibility constant 3 standard barrier algorithm Change the Limit on Barrier Corrections The default barrier algorithm in the ILOG CPLEX Barrier Optimizer computes an estimate of the maximum number of centering corrections that ILOG CPLEX should make on each iteration You can see this computed value by setting barrier display level two as explained in Interpreting the Barrier Log File on page 160 and checking the value of the parameter to limit corrections Its default value is 1 If you see that the current value is 0 zero then you should experiment with greater settings Setting the parameter BarMaxCor to a value greater than 0 may improve numerical performance but there may also be an increase in computation time Choose a Different Starting Point Heuristic As we explained in Using a Starting Point Heuristic on page 168 the default starting point heuristic works well for most problems suitable to barrier optimization But for a model that is exhibiting numerical difficulty it is possible that setting the BarStartAlg to select a different starting point will make a difference However if you are preprocessing your problem as dual for example in the Interactive Optimizer you issued the command set preprocessing dua
283. e several message channels for flexible control over message output cpxresults for messages containing status and progress information cpxerror for messages issued when a task cannot be completed cpxwarning for messages issued when a nonfatal difficulty is encountered or when an action taken may have side effects or when an assumption made may have side effects cpxlog for messages containing information that would not conventionally be displayed on screen but could be useful in a log file Output messages flow through message channels to destinations Message channels are associated with destinations through their destination list Messages from routines of the ILOG CPLEX Callable Library are assigned internally to one of those predefined channels Those default channels are C pointers to ILOG CPLEX objects they are initialized by CPXopenCPLEX they are not global variables Your application accesses these objects by calling the routine CPXget channels You can use these predefined message channels for your own application messages You can also define new channels lt 2 E O 2 oS US a UE Q An application using routines from the ILOG CPLEX Callable Library produces no output messages unless the application specifies message handling instructions through one or more calls to the message handling routines of the Callable Library In other words the destination list of each channel is initially empty
284. e the number of variables exceeds the number of constraints significantly or on problems that exhibit little variability in the cost coefficients Few problems exhibit poor numerical performance in both primal and dual form Consequently if you have a problem where numerical difficulties occur when you use the dual simplex optimizer then consider using the primal simplex optimizer instead Network Optimizer If a major part of your problem is structured as a network then the ILOG CPLEX Network Optimizer may have a positive impact on performance The ILOG CPLEX Network Optimizer recognizes a special class of linear programming problems with network structure It uses highly efficient network algorithms on that part of the problem to find a solution from which it then constructs an advanced basis for the rest of your problem From this advanced basis ILOG CPLEX then iterates to find a solution to the full problem Chapter 6 Solving Network Flow Problems describes this optimizer in greater detail Barrier Optimizer The barrier optimizer offers an approach particularly efficient on large sparse problems for example more than 1000 rows or columns and no more than perhaps a dozen nonzeros per column The barrier optimizer is sufficiently different in nature from the other optimizers that it is discussed in detail at the end of this chapter in Solving LP Problems with the Barrier Optimizer on page 156 Sifting Optimizer Sifting was
285. e the other columns contain less than five entries you may benefit by setting the column nonzeros parameter to 30 This setting allows ILOG CPLEX to recognize that column as dense and thus invoke techniques to handle it To set the dense column threshold set the parameter BarColNz to a positive integer The default value of 0 means that ILOG CPLEX will determine the threshold Choosing an Ordering Algorithm ILOG CPLEX offers several different algorithms in the ILOG CPLEX Barrier Optimizer for ordering the rows of a matrix automatic the default indicated by the value 0 approximate minimum degree AMD indicated by the value 1 ILOG CPLEX 8 1 USER S MANUAL 167 o Q T U Ru cA D 3 7 SOLVING LP PROBLEMS WITH THE BARRIER OPTIMIZER 168 approximate minimum fill AMF indicated by the value 2 nested dissection ND indicated by the value 3 The log file as we explain in Ordering Algorithm Time in the Log File on page 162 records the time spent by the ordering algorithm in a barrier optimization so you can experiment with different ordering algorithms and compare their performance on your problem Automatic ordering the default option will usually be the best choice This option attempts to choose the most effective of the available ordering methods and it usually results in the best order It may require more time than the other settings The ordering time is usually small relati
286. e use e g prompts help messages greetings errors messages to inform user that operation could not be performed and why logonly message to record only in file not on screen e g multiline messages results information explicitly requested by user state change progress information warnings messages to inform user request was performed but unexpected condition may result The option value2 lets you specify a file name to redirect output from a channel Also in that command va1ue1 allows you to turn on or off output to the screen When valuel is y output is directed to the screen when its value is n output is not directed to the screen Table 9 3 summarizes which channels direct output to the screen by default If a 296 ILOG CPLEX 8 1 USER S MANUAL MANAGING INPUT amp OUTPUT channel directs output to the screen by default you can leave value1 blank to get the same effect as set output channel y Table 9 3 Channels Directing Output to Screen or to a File Channel Default value1 Meaning dialog y blank directs output to screen but not to a file errors y blank directs output to screen and to a file logonly n blank directs output only to a file not to screen results y blank directs output to screen and to a file warnings y blank directs output to screen and to a file Handling Message Channels Callable Library Routines Interactive Optimizer and the Callable Library defin
287. echnology application are imported by including the file lt ilcplex ilocplex h gt The line 1LOSTLBEGIN is a macro that is needed for portability Microsoft Visual C code varies depending on whether you use the STL or not This macro allows you to switch between both types of code without the need to otherwise change your source code Function usage is called in case the program is executed with incorrect command line arguments o i i i i i i i i et i i i ie i i i i i i i i i i i i i i m i m n C File examples src ilodiet cpp Version 8 1 a a ce Copyright C 1999 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products 4 m cre e uL epu HELP WeoeoeeE LEE A dietary model Input data oodMin j minimum amount of food j to use oodMax j maximum amount of food j to use foodCost j cost for one unit of food j nutrMin i minimum amount of nutrient i nutrMax i maximum amount of nutrient i nutrPer i j nutrition amount of nutrient i in food j Modelling variables Buy 3 amount of food j to purchase Objective minimize sum j Buy j foodCost j Constraints forall foods i nutrMin i lt sum j Buy j nutrPer i j lt nutrMax jl finclude ilcplex ilocplex h ILOSTLBEGIN 54 ILOG CPLEX 8 1
288. ecified in MPS and LP files In the Concert Technology Library semi continuous variables are instances of the class IloSemiContVar In the Callable Library semi continuous variables can be entered with type CPX_SEMICONT Or CPX SEMIINT via the routine CPXcopyctype Progress Reports Interpreting the Node Log As we explained earlier when ILOG CPLEX optimizes mixed integer programs it builds a tree with the linear relaxation of the original MIP at the root and subproblems to optimize at the nodes of the tree ILOG CPLEX reports its progress in optimizing the original problem in a node log file as it traverses this tree You control how information in the log file is recorded and displayed through two ILOG CPLEX parameters The MIPDisplay parameter controls the general nature of the output that goes to the node log as follows Table 8 11 Values of the MIP Display Parameter Value Effect 0 no display 1 display integer feasible solutions 2 display nodes under mip interval control 3 same as 2 but add information on node cuts 246 ILOG CPLEX 8 1 USER S MANUAL PROGRESS REPORTS INTERPRETING THE NODE LOG Table 8 11 Values of the MIP Display Parameter Value Effect 4 same as 3 but add LP display for root node 5 same as 3 but add LP display for all nodes The MIPInterval parameter controls how frequently node log lines are printed Its default is 100 and can be set
289. ed with ILOG CPLEX except with the class IloSolution as described in the ILOG Concert Technology User s Manual Extracting a Model In this manual we describe only one optimization model and use only one instance of IloCplex at a time to solve the model Consequently we talk about these as the model and the cplex object It should be noted however that in Concert Technology an arbitrary number of models and algorithm objects can be created The cplex object can be created using the constructor IloCplex cplex env To use it to solve the model the model must first be extracted to cplex by calling cplex extract model This method copies the data from the model into the appropriate optimized data structures which ILOG CPLEX uses for solving the problem It does so by extracting each of the modeling objects added to the model and each of the objects referenced by them For every extracted modeling object corresponding data structures are created internally in the cplex object For readers familiar with the sparse matrix representation used internally by ILOG CPLEX a variable becomes a column and a constraint becomes a row As we will discuss later these data structures are kept synchronized with the modeling objects even if the modeling objects are modified If you consider a variable to be part of your model even though it is not initially used in any constraint you should add this variable explicitly to the model This ens
290. eduction is so important that even when you turn off preprocessing ILOG CPLEX still applies minimal presolving before barrier optimization For problems that contain linearly dependent rows it is a good idea to turn on the preprocessing dependency parameter By default it is off This dependency checker may add some preprocessing time but it can detect and remove linearly dependent rows to improve overall performance To turn on dependency checking set parameter DepInd to 1 Detecting and Eliminating Dense Columns Dense columns can significantly degrade barrier optimizer performance A dense column is one in which a given variable appears in many rows The interactive optimizer contains a display feature that shows a histogram of the number of nonzeros in the columns of your model display problem histogram c In fact when a few dense columns are present in a problem it is often effective to reformulate the problem to remove those dense columns from the model Otherwise you can control whether ILOG CPLEX perceives columns as dense by setting the column nonzeros parameter At its default setting ILOG CPLEX calculates an appropriate value for this parameter automatically However if your problem contains one or a few dense columns that remain undetected at the default setting you can adjust this parameter yourself to help ILOG CPLEX detect it or them For example in a large problem in which one column contains forty entries whil
291. ee I I i i MM C File examples src ilogoalexl cpp Version 8 1 Jj a Copyright C 1999 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the z a D3 qe oS Us a UE Q course of developing applications that use ILOG products ilogoalexl cpp A simple goal example ILOG CPLEX 8 1 USER S MANUAL 321 GOALS 322 IN ILOCPLEX Create a branch goal that chooses the variable with the largest objective from amongst those with the largest integer infeasibility finclude lt ilcplex ilocplex h gt ILOSTLBEGIN static void usage const char progname Branch on var with largest objective coefficient among those with largest infeasibility ILOCPLEXGOAL1 MyBranchGoal IloNumVarArray vars IloNumArray x TloNumArray obj IntegerFeasibilityArray feas I x IloNumArray getEnv obj IloNumArray getEnv feas IntegerFeasibilityArray getEnv getValues x vars getObjCoefs obj vars getFeasibilities feas vars IloInt bestj 1 IloNum maxinf 0 0 IloNum maxobj 0 0 IloInt cols vars getSize for IloInt j 0 J lt cols 3 if feas j Infeasible IloNum xj inf x j IloFloor x j if xj inf gt 0 5 xj inf 1 0 xj inf if xj inf gt maxinf amp amp xj inf gt maxinf IloAbs obj j gt maxobj bestj j maxinf xj in
292. eger Quadratic Program MIQP In ILOG CPLEX documentation if the discussion pertains specifically to either the MILP or MIQP case then that term is used For the majority of topics that pertain equally to MILP and MIQP the comprehensive term MIP is used The integer variables may be restricted to the values 0 zero and one in which case they are referred to as binary variables Or they may take on any integer values in which case they are referred to as general integer variables A variable of any MIP that may take either the value 0 or a value between a lower and an upper bound is referred to as semi continuous A semi continuous variable that is restricted to integer values is referred to as semi integer Special Ordered Sets SOS are discussed elsewhere in this chapter Continuous variables in a MIP problem are those which are not restricted in any of these ways and are thus permitted to take any solution value within their possibly infinite lower and upper bounds In ILOG CPLEX documentation the comprehensive term integer variable means any of the various types just mentioned except for continuous or SOS The presence or absence of a quadratic term in the objective function for a given variable has no bearing on its being classified as continuous or integer The following illustrates a mixed integer programming problem which is solved in the example program ilomipex1 cpp mipexl c discussed later in this chapter Maximize X 2
293. elaxation problem itself is taking a long time The standard screen display will print a line telling Root relaxation solution time once this root solve is complete and a large solution time would be an indicator of an opportunity for tuning If you set the MIPDisplay parameter to 4 you may get a further indication of the difficulties this root solve has run into Tuning techniques found in Chapter 5 Solving Linear Programming Problems or Chapter 7 Solving Quadratic Programming Problems would be applicable to tuning the root solve of a MIP model too In particular it is worth considering setting the Root A1g parameter to a nondefault setting such as the Barrier optimizer to see if a simple change in algorithm will speed up this step sufficiently ILOG CPLEX 8 1 USER S MANUAL TROUBLESHOOTING MIP PERFORMANCE PROBLEMS For some problems ILOG CPLEX will spend a significant amount of time performing computation at node 0 apart from solving the LP or QP relaxation While this investment of time normally saves in the overall branch amp cut it does not always do so Time spent at node 0 can be reduced by two parameters First you can try turning off the node heuristic by setting the parameter HeurF req to 1 Second try a less expensive variable selection strategy by setting the parameter VarSel to 4 pseudo reduced costs Itis worth noting that setting the MIPEmphasis parameter to 1 resulting in an emphasis on feasibility instea
294. emoved ILOG CPLEX uses node file storage most effectively when the amount of working memory is reasonably large so that it does not have to create node files too frequently A reasonable amount is to use approximately half the memory but no more than 128 megabytes Higher values result in only marginally improved efficiency Node files could grow very large Use the TreMem parameter to limit the size of the tree so that it does not exceed available disk space when you choose NodeFileInd settings 2 or 3 It is usually better to let ILOG CPLEX terminate the run gracefully with whatever current feasible solution has been found than to trigger an error message or even a program abort When ILOG CPLEX uses node file storage the sequence of nodes processed may differ from the sequence in which nodes are processed without node file storage Nodes in node file storage are not accessible to user written callback routines Change Algorithms The best approach to reduce memory use is to modify the solution process Here are some ways to do so Switch the node selection strategy to best estimate or more drastically to depth first as explained on page 237 Depth first search rarely generates a long memory consuming list of unexplored nodes since ILOG CPLEX dives deeply into the tree instead of jumping around A narrowly focused search like depth first also often results in faster processing times for individual nodes However overall solution t
295. en copied into the problem object the basis is copied by a call to cplex setBasisStatuses After the problem has been optimized the iteration count is printed For the given data and basis the basis is optimal so no iterations are required to optimize the problem The main program starts by declaring the environment and terminates by calling method end for the environment The code in between is encapsulated in a try block that catches all Concert Technology exceptions and prints them to the C error stream cerr All other exceptions are caught as well and a simple error message is issued Next the model object and the cplex object are constructed The function populatebycolumn builds the problem object and as we noted earlier cplex setBasisStatuses copies the advanced starting basis The call to cplex solve optimizes the problem and the subsequent print of the iteration count demonstrates that the advanced basis took effect In fact this basis is immediately determined to be the optimal one resulting in zero iterations being performed in contrast to the behavior seen in the example program ilolpex1 cpp where the same model is solved without the use of an advanced basis 148 ILOG CPLEX 8 1 USER S MANUAL EXAMPLE USING A STARTING BASIS IN AN LP PROBLEM Complete Program The complete program ilolpex6 cpp appears here and online in the standard distribution jf Mii eins He SS SS eee en k CHF File examp
296. enCPLEX amp status If an error occurs the status value indicates the reason for failure The error message will be printed at the end of the program if env NULL fprintf stderr Could not open CPLEX environment n goto TERMINATE Turn off output to the screen since we ll be producing it via the callback function This also means we won t see any CPLEX generated errors but we ll handle that at the end of the program status CPXsetintparam env CPX PARAM SCRIND CPX OFF if status fprintf stderr Failure to turn off screen indicator error d n status goto TERMINATE Create the problem strcpy probname example lp CPXcreateprob env amp status probname A returned pointer of NULL may mean that not enough memory was available or there was some other problem In the case of failure an error message will have been written to the error channel from inside CPLEX In this example we wouldn t see an error message from CPXcreateprob since we turned off the CPX PARAM SCRIND parameter above The only way to see this message would be to use the CPLEX message handler but that clutters up the simplicity of this example which has a point of illustrating the CPLEX callback functionality x if lp NULL fprintf stderr Failed to create LP n goto TERMINATE Now populate the problem with the data status populatebycolumn env lp if status fp
297. end these findings to your screen as well use the command set output logonly y cplex log You can also write an IIS file from the Interactive Optimizer and then examine it with your preferred text editor to see all the constraints and bounds in the irreducibly inconsistent set For an example of how to use the infeasibility finder and how to interpret its results see Example Output from the Infeasibility Finder in the Interactive Optimizer on page 144 ILOG CPLEX 8 1 USER S MANUAL 143 o 2 Q T me Uv al D 3 7 DIAGNOSING LP INFEASIBILITY 144 Infeasibility Finder in the Component Libraries Its alternative value of 1 one may take longer but generates a minimal set of irreducibly inconsistent constraints Use the method cplex out or the routines CPXdisplayiis or CPXiiswrite to output the results for review Correcting Multiple Infeasibilities The infeasibility finder will find only one irreducibly inconsistent set IIS though a given problem may contain many independent IISs Consequently even after you detect and correct one such IIS in your problem it may still remain infeasible In such a case you need to run the infeasibility finder more than once to detect those multiple causes of infeasibility in your problem Example Output from the Infeasibility Finder in the Interactive Optimizer After you have optimized a problem and ILOG CPLEX has terminated with a primal infeasible basic
298. entifying Convex Quadratic Programming Problems Conventionally a quadratic program QP is formulated this way Minimize J x Qx c x ILOG CPLEX 8 1 USER S MANUAL 195 ENTERING QPS Entering QPs 196 subject to Ax b with these bounds xx lt u where the relation may be any combination of equal to less than or equal to greater than or equal to or range constraints As in other problem formulations indicates lower and u upper bounds Q is a matrix of ares function coefficients That is the elements Q are the coefficients of the quadratic terms x7 and the elements Qj and Qj are summed topeflier to be the coefficient of the term x ij ILOG CPLEX distinguishes two kinds of Q matrices Ina separable problem only the diagonal terms of the matrix are defined Inanonseparable problem at least one off diagonal term of the matrix is nonzero ILOG CPLEX optimizes only convex quadratic minimization problems or equivalently only concave quadratic maximization problems as illustrated in Figure 7 1 For convex QPs Q must be positive semi definite that is the term xT Qx 2 0 for all x whether or not x is feasible For concave maximization problems the requirement is that Q must be negative semi definite that is xT Qx 30 for all x In a minimization problem if Q is separable and positive semi definite then Q 2 0 Figure 7 1 Maximize a Concave Objective Function Minimize a Convex Objective Function In this
299. eps gives a tolerance by which a cut must at least be violated in order to be added to the problem being solved The implementation of this example cut callback looks for cuts that are violated by the current LP solution of the node where the callback is invoked We loop over the potential cuts checking each for violation by querying the value of the 1ns expression with respect to the current solution This is done by calling get Value with this expression as a parameter This is tested for violation of more than the tolerance parameter eps with the corresponding right hand side value Tip A numerical tolerance is always a wise thing to consider when dealing with any non trivial model to avoid certain logical inconsistencies that could otherwise occur due to numerical roundoff Here we use the standard ILOG CPLEX simplex feasibility tolerance for this purpose to insure some consistency with the way ILOG CPLEX is treating the rest of the model ILOG CPLEX 8 1 USER S MANUAL USING CALLBACKS If a violation is detected the callback creates an IloRange object to represent the cut lhs i lt rhs i It is added to the LP by calling method add Adding a cut to ILOG CPLEX unlike extracting a model only copies the cut into the ILOG CPLEX data structures without maintaining a notification link between the two Thus after a cut has been added it can be deleted by calling its method end In fact it should be deleted as otherwise
300. er creates the log file in the directory where it is running and it names the file cplex log If such a file already exists ILOG CPLEX adds a line indicating the current time and date and then appends new information to the end of the existing file That is it does not overwrite the file and it distinguishes different sessions within the log file By default there is no log file for Component Library applications You can locate the log file where you like and you can rename it Some users for example like to create a specifically named log file for each session Also you can close the log file in case you do not want ILOG CPLEX to record messages to its default log file The following sections show you the commands for creating renaming relocating and closing a log file Creating Renaming Relocating Log Files In the Interactive Optimizer use the command set logfile filename substituting the name you prefer for the log file In other words use this command to rename or relocate the default log file From the Callable Library first use the routine CPX open to open the target file then use the routine CPXsetlogfile The ILOG CPLEX Reference Manual documents both routines s 2 E O 2 oS US a UE Q From Concert use the setOut method to send logging output to the specified output stream Closing Log Files If you do not want ILOG CPLEX to record messages in a log file then you can close th
301. ere in this chapter in Solving LP Problems with the Barrier Optimizer on page 156 The simplex tuning suggestions are arranged according to the following groupings Pricing Algorithm and Gradient Parameters Scaling Crash Memory Management and Problem Growth Pricing Algorithm and Gradient Parameters The parameters in Table 5 3 determine the pricing algorithms that ILOG CPLEX uses Consequently these are the algorithmic parameters most likely to affect simplex linear programming performance The default setting of these gradient parameters choose the pricing algorithms that are best for most problems When you are selecting alternate pricing algorithms look at these values as guides ILOG CPLEX 8 1 USER S MANUAL TUNING LP PERFORMANCE overall solution time number of Phase I iterations that is iterations before I LOG CPLEX arrives at an initial feasible solution total number of iterations ILOG CPLEX records those values in the log file as it works By default ILOG CPLEX creates the log file in the directory where it is executing and it names the log file cplex log Managing Log Files the Log File Parameter on page 295 tells you how to rename and relocate this log file If the number of iterations required to solve your problem is approximately the same as the number of rows then you are doing well If the number of iterations is three times greater than the number of rows or more then it may ver
302. error d n status goto TERMINATE break case s method CPX ALG SIFTING break case c method CPX ALG CONCURRENT break default method CPX ALG NONE break status CPXsetintparam env CPX PARAM LPMETHOD method if status fprintf stderr Failed to set the optimization method error d n status goto TERMINATE z EN 563 O 2 oS Us a UE Q status CPXlpopt env lp if status fprintf stderr Failed to optimize LP n goto TERMINATE solnstat CPXgetstat env lp ILOG CPLEX 8 1 USER S MANUAL 313 USING QUERY ROUTINES IN THE CALLABLE LIBRARY 314 if solnstat CPX_STAT_UNBOUNDED printf Model is unbounded n goto TERMINATE else if solnstat CPX_STAT_INFEASIBLE printf Model is infeasible n goto TERMINATE else if solnstat CPX_STAT_INForUNBD printf Model is infeasible or unbounded n goto TERMINATE status CPXsolninfo env lp amp solnmethod amp solntype NULL NULL if status 4 fprintf stderr Failed to obtain solution info n goto TERMINATE printf Solution status d solution method d n solnstat solnmethod if solntype CPX_NO_SOLN fprintf stderr Solution not available n goto TERMINATE status CPXgetobjval env lp amp objval if status fprintf stderr Failed to obtain objective value n goto TERMINATE print
303. ertain nutritional constraints which were described earlier in this chapter This example was chosen because it is simple enough to be viewed from a row as well as from a column perspective Both ways are shown in the example In this example either perspective can be viewed as natural Only one approach will seem natural for many models but there is no general way of determining which is more appropriate in a particular case The example accepts a filename and two options c and i as command line arguments Option i allows you to create a MIP model where the quantities of foods to purchase must be integers Option c can be used to build the model by columns The example starts by evaluating the command line arguments and reading the input data file The input data of the dietary problem is read from a file using an object of the embedded class Diet Data Its constructor requires a file name as parameter from which it reads the data using class InputDataReader This class is distributed with the examples but will not be described here as it does not make use of any ILOG CPLEX or Concert Technology functionality Creating the Optimizer Once the data has been read the 11o0Cplex modeler optimizer is created IloCplex cplex new IloCplex IloNumVar Buy new IloNumVar nFoods if byColumn buildModelByColumn cplex data Buy varType else buildModelByRow cplex data Buy varType Array IloNumVar Buy is also created where
304. es no output so the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines the errors will be seen if the CPX PARAM SCRIND indicator is set to CPX ON if status char errmsg 1024 fprintf stderr Could not close CPLEX environment Nn CPXgeterrorstring env status errmsg fprintf stderr s errmsg Free up the problem data arrays if necessary free and null char amp probname free and null char amp obj free and null char amp rhs free and null char amp sense free and null char amp matbeg ILOG CPLEX 8 1 UsER s MANUAL EXAMPLE USING SOS AND PRIORITY free_and_null char free_and_null char amp matcnt amp matind free and null char amp matval free and null char amp 1b free and null char amp ub free and null char amp ctype return status END main This function fills in the data structures for the mixed integer program Maximize obj xl 2 x2 3 x3 x4 Subject To Cl xl x2 x3 10x4 lt 20 C2 xl 3 x2 x3 lt 30 cat x2 3 5x4 0 Bounds 0 lt x1 lt 40 2 lt x4 lt 3 Integers x2 x3 x4 End Ayr static int setproblemdata char probname p int numcols p int numrows p i AS fe ES D di Buinjos int objsen_p double obj_p double rhs_p char sense_p int matbeg_p int matcnt_p
305. et mip cuts cliques Cliques CPX_PARAM_CLIQUES Cover set mip cuts covers Covers CPX_PARAM_COVERS Disjunctive set mip cuts disjunctive DisjCuts CPX PARAM DISJCUTS Flow Cover set mip cuts flowcuts FlowCovers CPX PARAM FLOWCOVERS Flow Path set mip cuts pathcut FlowPaths CPX PARAM FLOWPATHS Gomory set mip cuts gomory FracCuts CPX PARAM FRACCUTS GUB Cover set mip cuts gubcovers GUBCovers CPX PARAM GUBCOVERS Implied Bound set mip cuts implied ImplBd CPX PARAM IMPLBD Mixed Integer set mip cuts mircut MIRCuts CPX PARAM MIRCUTS Rounding MIR The default value of each of those parameters is 0 zero By default ILOG CPLEX automatically determines how often if at all it should try to generate that class of cut A setting of 1 indicates that no cuts of the class should be generated a setting of 1 indicates that cuts of the class should be generated moderately and a setting of 2 indicates that cuts of the class should be generated aggressively For disjunctive cuts a setting of 3 is permitted which indicates that disjunctive cuts should be generated very aggressively Be x fej ES D 7 diN Bulnjos In the Interactive Optimizer the command set mip cuts all iapplies the value i to all classes of cut parameters That is you can set them all at once The CutsFactor parameter controls the number of cuts ILOG CPLEX adds to the model The problem can grow to Cut sFactor times the original number of rows in the model or in the
306. eter In the dual simplex optimizer the CraInd setting determines whether ILOG CPLEX aggressively uses primal variables instead of slack variables while it still tries to preserve as much dual feasibility as possible If its value is 1 one it indicates the default starting basis if its value is 0 zero or 1 it indicates an aggressive starting basis These values are summarized in Table 5 6 Table 5 6 Cralnd Parameter Values for the Dual Simplex Optimizer pir Meaning for Dual Simplex Optimizer 1 Use default starting basis 0 Use an aggressive starting basis 1 Use an aggressive starting basis In the primal simplex optimizer the CraInd setting determines how ILOG CPLEX uses the coefficients of the objective function to select the starting basis If its value is 1 one ILOG CPLEX uses the coefficients to guide its selection if its value is 0 zero ILOG CPLEX ignores the coefficients if its value is 1 ILOG CPLEX does the opposite of what the coefficients normally suggest These values are summarized in Table 5 7 Table 5 7 Cralnd Parameter Values for the Primal Simplex Optimizer Cralnd Tm Value Meaning for Primal Simplex Optimizer 1 Use coefficients of objective function to select basis 0 Ignore coefficients of objective function 1 Select basis contrary to one indicated by coefficients of objective function Memory Management and Problem Growth ILOG CPLEX automatical
307. etting the Optimizer Use Disk for Storage Preprocessing the Presolver and Aggregator Detecting and Eliminating Dense Columns Choosing an Ordering Algorithm Using a Starting Point Heuristic In addition several parameters set termination criteria With them you control when ILOG CPLEX stops optimization ILOG CPLEX 8 1 USER S MANUAL 165 o 2 Q T U Uv al e D 3 7 SOLVING LP PROBLEMS WITH THE BARRIER OPTIMIZER 166 You can also control convergence tolerance another factor that influences performance Convergence tolerance determines how nearly optimal a solution ILOG CPLEX must find tight convergence tolerance means ILOG CPLEX must keep working until it finds a solution very close to the optimal one loose tolerance means ILOG CPLEX can return a solution within a greater range of the optimal one and thus stop calculating sooner Performance of the ILOG CPLEX Barrier Optimizer is most highly dependent on the number of floating point operations required to compute the Cholesky factor at each iteration When you adjust barrier parameters always check their impact on this number At default output settings this number is reported at the beginning of each barrier optimization in the log file as we explain in Cholesky Factor in the Log File on page 162 Another important performance issue is the presence of dense columns By a dense column we mean that a given variable appears in a relatively large
308. example shows how to implement and use a goal for controlling the branch strategy used by IloCplex As we discussed goals are implemented as subclasses of class IloCplex GoalI IloCplex Goal In the C version of the example listed above we do so by using the macro ILOCPLEXGOAL1 MyBranchGoal IloNumVarArray vars instead This macro defines two things class MyBranchGoalI and function IloCplex Goal MyBranchGoal IloEnv env IloNumVarArray vars The class MyBranchGoalT is defined as a subclass of class 11o0Cplex GoalI IloCplex Goal and has a private member IloNumVarArray vars The function MyBranchGoal creates an instance of class MyBranchGoalI initializes the member vars to the parameter vars passed to the function and returns a handle to the new goal object The braces following the macro enclose the implementation of method MyBranchGoalI execute containing the actual code of the goal The use of the macro is very convenient as the amount of user code is equivalent to the amount for defining a function but with a slightly unusual syntax 11oCplex provides 7 such macros that can be used for defining goals with 0 to 6 private members If more than 6 members are needed IloCplex GoalI IloCplex Goal must be subclassed by hand Since the Java programing language does not provide macros a subclass of IloCplex Goal must always be implemented by hand In this example this class is called MyBranchGoal and we do not provide a hel
309. f maxobj IloAbs 0obj jl IloCplex Goal res if bestj gt 0 res AndGoal OrGoal vars bestj gt IloFloor x bestj 1 vars bestj lt IloFloor x bestj this x end ILOG CPLEX 8 1 USER S MANUAL GOALS IN ILOCPLEX obj end feas end return res int main int argc char argv IloEnv env try IloModel model env IloCplex cplex env if arge 2 usage argv 0 throw 1 IloObjective obj IloNumVarArray var env IloRangeArray rng env cplex importModel model argv 1 obj var rng cplex extract model cplex solve MyBranchGoal env var IloNumArray vals env cplex getValues vals var cout lt lt Solution status lt lt cplex getStatus lt lt endl cout lt lt Solution value lt lt cplex getObjValue lt lt endl cout lt lt Values lt lt vals lt lt endl catch IloException amp e cerr Concert exception caught e endl env end return 0 z EN 563 O 2 oS Us a UE Q static void usage const char progname cerr lt lt Usage lt lt progname lt lt filename lt lt endl cerr lt lt where filename is a file with extension lt lt endl cerr lt lt MPS SAV or LP lower case is allowed lt lt endl cerr lt lt Exiting lt lt endl ILOG CPLEX 8 1 USER S MANUAL 323 GOALS 324 IN ILOCPLEX This
310. f Objective value 10g n objval The size of the problem should be obtained by asking CPLEX what the actual size is cur_numrows and cur_numcols store the current number of rows and columns respectively cur numcols CPXgetnumcols env 1p cur numrows CPXgetnumrows env 1p Retrieve basis if one is available if solntype CPX BASIC SOLN estat int malloc cur numcols sizeof int rstat int malloc cur numrows sizeof int if cstat NULL rstat NULL fprintf stderr No memory for basis statuses Wn goto TERMINATE status CPXgetbase env lp cstat rstat if status fprintf stderr Failed to get basis error d n status ILOG CPLEX 8 1 USER S MANUAL USING QUERY ROUTINES IN THE CALLABLE LIBRARY goto TERMINATE else printf No basis available n Retrieve solution vector x double malloc cur_numcols sizeof double if x NULL fprintf stderr No memory for solution Wn goto TERMINATE status CPXgetx env lp x 0 cur numcols 1 if status fprintf stderr Failed to obtain primal solution Mn goto TERMINATE Now get the column names for the problem First we determine how much space is used to hold the names and then do the allocation Then we call CPXgetcolname to get the actual names status CPXgetcolname env lp NULL NULL 0 amp surplus 0 cur numcols 1 if
311. f 0 MIPEmphasisBalanced or CPX MIPEMPHASIS BALANCED ILOG CPLEX uses tactics intended to quickly find a proven optimal solution for models of a broad range of difficulty That is considerable analysis of the model is performed before branching ever begins in the expectation that the investment will result in a faster total run time yet not every possible analysis is performed And then branching is performed in a manner that seeks to find good quality feasible ILOG CPLEX 8 1 USER S MANUAL 229 USING THE MIXED INTEGER OPTIMIZER 230 solutions without sacrificing too much time that could be spent proving the optimality of any solution that has already been found In many situations the user will desire a greater emphasis on feasibility and less emphasis on analysis and proof of optimality For instance a restrictive time limit set by the user using the TiLim parameter may be in force due to a real time application deployment where a model is of sufficient difficulty that a proof of optimality is unlikely and the user wants to have simply as good a solution as is practicable when the time limit is reached The MIPEmphasis Setting of 1 MIPEmphasisFeasibility or CPX_MIPEMPHASIS_FEASIBILITY directs ILOG CPLEX to adopt this emphasis Less computational effort is applied at the outset toward the analyses that aid in the eventual proof of optimality and more effort is spent in immediately beginning computations that search
312. f ranged rows the bound indicates whether the row lies at the lower or upper end of the range of right hand side values For other kinds of rows there is only one possible right hand side value at ILOG CPLEX 8 1 USER S MANUAL DIAGNOSING LP INFEASIBILITY which the row can lie Greater than constraints must lie at their lower bound Less than constraints must lie at their upper bound Equality constraints are fixed Example Writing an IIS Type File After you have invoked the infeasibility finder with the display iis command if you want additional information to determine the cause of infeasibility use the write command and the file type iis to generate a ILOG CPLEX LP format file containing each individual constraint and bound in the IIS You can then use the xecute command to call an ordinary text editor during your ILOG CPLEX session to examine the contents of that IIS file It will look something like this example CPLEX gt write infeas iis Starting Infeasibility Finder Algorithm Performing row sensitivity filter Performing column sensitivity filter Irreducibly inconsistent set written to file infeas iis CPLEX xecute edit infeas iis Minimize subject to NRows in the iis NODES T25 T35 T57 T58 0 Ds T47 T57 gt 20 D8 T58 gt 30 Columns in the iis Bounds T25 lt 10 T35 lt 10 T47 lt 2 Non iis columns intersecting iis rows T57 Free T58 Free In this example you see that the bou
313. failure it returns a NULL pointer The parameter status p that is one of its arguments is set to 0 if the routine is successful in case of failure that parameter is set to a nonzero value that indicates the reason for the failure Each failure value is unique and documented in the ILOG CPLEX Reference Manual The Callable Library routine CPXcreateprob returns a pointer to a ILOG CPLEX problem object and sets its parameter status pto 0 zero to indicate success In case of failure it returns a NULL pointer and sets status p to a nonzero value indicating the reason for the failure Some query routines in the Callable Library return a nonzero value when they are successful For example CPXgetnumcols returns the number of columns in the constraint matrix that is the number of variables in the problem object However most query routines return 0 zero indicating success of the query and entail one or more parameters such as a buffer or character string to contain the results of the query For example CPXgetrowname returns the name of a row in its name parameter Most other routines in the Callable Library return an integer value 0 zero indicating success of the call A nonzero return value indicates a failure Each failure value is unique and documented in the ILOG CPLEX Reference Manual We strongly recommend that your application check the status whether the status is indicated by the return value or by a parameter
314. fined as static class MyCallback extends IloCplex ContinuousCallback public void main throws IloException System out print Iteration getNiterations if isFeasible System out println Objective getObjValue else System out println Infeasibility measure getInfeasibility The callback prints the iteration number Then depending on whether the current solution is feasible or not it prints the objective value or infeasibility measure The functions getNiterations isFeasible getObjValue and getInfeasibility are member functions provided in the callback s base class IloCplex ContinuousCallbackI IloCplex ContinuousCallback See the ILOG CPLEX Reference Manual for the complete list of methods provided for each callback class 346 ILOG CPLEX 8 1 USER S MANUAL USING CALLBACKS Here is how the macro ILOSIMPLEXCALLBACKO is expanded class MyCallbackI public IloCplex SimplexCallbackI void main IloCplex CallbackI duplicateCallback const return new getEnv MyCallbackI this IloCplex Callback MyCallback IloEnv env return IloCplex Callback new env MyCallbackI void MyCallbackI main cout lt lt Iteration lt lt getNiterations lt lt if isFeasible cout lt lt Objective lt lt getObjValue lt lt endl else cout lt lt Infeasibility measure lt lt getInfeasibility lt lt
315. g CPXputenv Routine char inststr NULL char envstr NULL Initialize the CPLEX environment envstr char malloc 256 if envstr NULL fprintf stderr Memory allocation for CPXputenv failed Wn status FAIL goto TERMINATE else inststr char getenv MYAPP_HOME if inststr NULL fprintf stderr Unable to find installation directory n status FAIL goto TERMINATE strcpy envstr ILOG LICENSE FILE strcat envstr inststr strcat envstr license access ilm CPXputenv envstr env CPXopenCPLEX amp status 382 ILOG CPLEX 8 1 USER S MANUAL CPLEX RUNTIME DEVELOPMENT AND LICENSING PROCEDURES The putenv Routine for Java Users Here is an example using Concert Technology for Java users TloCplex putenv ILOG_LICENSE_FILE license access ilm try cplex new IloCplex catch IloException e System err println Exception caught for runtime license e CPXRegisterLicense Routine The following is an example illustrating the usage of the CPXRegisterLicense routine static char ilm_license LICENSE ILOG Incline n RUNTIME CPLEX 8 000 21 Apr 2002 R81GM34ECZTS N IRIX options m static int ilm license signature 2756133 CPXENVptr env NULL int status Initialize the CPLEX environment status CPXRegisterLicense ilm license ilm license signature if status 0 fprintf stderr
316. g Crossover on page 160 explains how to control crossover in the Interactive Optimizer Differences between Barrier and Simplex Optimizers The barrier optimizer and the simplex optimizers primal and dual are fundamentally different approaches to solving linear programming problems The key differences between them have these implications Simplex and barrier optimizers differ with respect to the nature of solutions Barrier solutions tend to be midface solutions In cases where multiple optima exist barrier solutions tend to place the variables at values between their bounds whereas in basic solutions from a simplex technique the values of the variables are more likely to be at either their upper or their lower bound While objective values will be the same the nature of the solutions can be very different The fact that barrier without crossover does not produce a basic solution has other consequences Without a basis you will not be able to optimize the same or similar ILOG CPLEX 8 1 USER S MANUAL SOLVING LP PROBLEMS WITH THE BARRIER OPTIMIZER problems repeatedly using advanced start information You will also not be able to obtain range information for performing sensitivity analysis Simplex and barrier optimizers have different numerical properties sensitivity and behavior For example the barrier optimizer is sensitive to the presence of unbounded optimal faces whereas the simplex optimizers are not As a res
317. g on the operating system s virtual memory swap space To activate out of core Barrier set the parameter BarOOC to 1 instead of its default value of 0 Note that out of core barrier uses some working memory to store the portion of the factor on which it is currently performing computation You can improve performance by allocating more working memory using the WorkMem parameter More working memory allows the algorithm to transfer less factor data to and from disk In fact the factor matrix will not be written to disk at all if its size does not exceed the value of WorkMem The default for this parameter is 128 meaning 128 megabytes When Barrier is being run out of core the location of disk storage is controlled by the Working Directory parameter WorkDir For example to use the directory tmp mywork ILOG CPLEX 8 1 USER S MANUAL SOLVING LP PROBLEMS WITH THE BARRIER OPTIMIZER set WorkDir to the string tmp mywork WorkDir should be specified as the name of a directory that already exists and ILOG CPLEX will create its working directory under that Preprocessing the Presolver and Aggregator For best performance of the ILOG CPLEX Barrier Optimizer preprocessing should almost always be on That is we recommend that you use the default setting where the presolver and aggregator are active While they may use more memory they also reduce the problem and problem reduction is crucial to barrier optimizer performance In fact r
318. g the Environment The lloEnv Object Before creating modeling objects an object of class IloEnv must be constructed We refer to this object as the environment object It is constructed with the statement IloEnv env which is usually the first Concert Technology statement in an application At the end the environment must be closed by calling env end This is usually the last Concert Technology statement in an application The end method must be called because like most Concert Technology classes the 11oEnv class is a handle class This means that IloEnv objects are really only pointers to implementation objects Implementation objects are destroyed by calling the end method Failing to call the end method can result in memory leaks Please see the LOG Concert Technology User s Manual and the ILOG Concert Technology Reference Manual for more details about handle classes in Concert Technology Users familiar with the ILOG CPLEX Callable Library are cautioned not to confuse the Concert Technology environment object with the ILOG CPLEX environment object of type CPXENVpt r used for setting ILOG CPLEX parameters Such an object is not needed with Concert Technology as parameters are handled directly by each instance of the IloCplex class Thus when talking about the environment in Concert Technology we always refer to the object of class 11oEnv required for all other Concert Technology objects Defining Variab
319. getEnv this for C or for Java cplex and cplex branchAsCplex this The method BranchAsCplexGoal getEnv cplex branchAsCplex creates a goal that branches in the same way as the built in branch procedure By adding this goal the current goal will be executed for the entire subtree Thus the goal returned by CutGoal will add all currently violated constraints as global cuts one by one Then it will branch in the way 11oCplex would branch without any goals and execute the CutGoal again in the child nodes Injecting Solutions At any time in the execution of a goal you may find that for example by slightly manipulating the current node subproblem solution you may construct a solution to your model Such solutions are called heuristic solutions and a procedure that generates them is called a heuristic Heuristic solutions can be injected into the branch amp cut search by creating a solution goal with method I1oCplex GoalI SolutionGoal IloCplex solutionGoal Such a goal can be returned typically as a subgoal of And goal much like global cut goals When 110oCplex executes a solution goal it does not immediately use the specified solution as a potential new incumbent The reason is that with goals part of the model may be ILOG CPLEX 8 1 USER S MANUAL GOALS IN ILOCPLEX specified via global cuts or through specialized branching strategies Thus the solution needs first to be tested for feasibili
320. goals Your heuristic can still safely be used as IloCplex will ensure feasibility for the entire model However there are some performance considerations to observe If parts of the model specified with goals are dominant heuristic solutions you generate might need to be rejected so frequently that you do not get enough payoff for the work of running the heuristic Also your heuristic should account for the global and local cuts that have been added at the node where you run your heuristic so that a solution candidate is not rejected right away and the work wasted Controlling Goal Controlled Search So far we have discussed how to control the branching and cut generation of IloCplex branch amp cut search The remaining missing piece is the node selection strategy The node selection strategy determines which of the active nodes in the tree IloCplex chooses when it selects the next node for processing 11oCplex has several built in node selection strategies selected through parameter NodeSel When using goal controlled search node evaluators are used to override the built in node selection strategy The process is as follows You combine a goal with a node evaluator by calling method 11oCplex Goal Apply IloCplex apply This method returns a new goal that implements the same search strategy as the goal passed as the parameter but adds the node evaluator to every node in the subtree defined by the goal Therefore nodes may have a l
321. h set priority 3 and reference values 25 and 18 for the 2 variables respectively sostype 0 CPX TYPE SOS sospri 0 3 sosbeg 0 0 sosind 0 2 sosind 1 3 sosref 0 25 sosref 1 18 status CPXcopysos env lp 1 2 sostype sospri sosbeg sosind sosref if status fprintf stderr CPXcopysos failed n goto TERMINATE To assist in debugging write the order and SOS to a file status CPXordwrite env lp mipex3 ord if status fprintf stderr CPXordwrite failed n goto TERMINATE status CPXsoswrite env lp mipex3 sos if status 4 fprintf stderr CPXsoswrite failed n goto TERMINATE ILOG CPLEX 8 1 USER S MANUAL EXAMPLE USING SOS AND PRIORITY TERMINATE return status This simple routine frees up the pointer ptr and sets ptr to NULL static void free_and_null char ptr if ptr NULL free ptr ptr NULL END free_and_null i Le ES D 2 di Buinjos ILOG CPLEX 8 1 USER S MANUAL 287 EXAMPLE USING SOS AND PRIORITY 288 ILOG CPLEX 8 1 USER S MANUAL More About Using ILOG CPLEX This chapter provides information designed to help you master several important aspects of ILOG CPLEX It includes sections on Managing Input amp Output Using Query Routines in the Callable Library Goals in IloCplex Using Callbacks A Comparison of Goals and Callbacks
322. h the file containing the key You must communicate the location of this file to your application In order to avoid potential conflicts with other runtime applications we recommend that you locate the key in a directory specific to your application by using the CPXputenv routine in C or C or IloCplex putenv in java These are the most commonly used runtime licenses Memory Based RUNTIME Keys These involve passing some information in the memory of your program to ILM No files containing access keys are involved Rather you set the key in your program and pass it to ILM by calling the CPXRegisterLicense routine in C or C or IloCplex registerLicense in java Routines Used for Licensing z E E O 2 oS Us a UE Q All ILOG CPLEX applications either call the CPXopenCPLEX routine to establish the CPLEX environment or use the T1oCplex constructor to initialize LOG CPLEX for use with Concert Technology Until either CPXopenCPLEX is called or the IloCplex object exists few ILOG CPLEX routines operate In addition to allocating the environment CPXopenCPLEX performs license checks as does the constructor for the 11o0Cplex object For development licenses no additional licensing steps are required For runtime licenses your application first needs to provide some additional licensing information before the call to CPXopenCPLEX or the use of an TloCplex constructor For RTNODE RTSTOKEN and TOKEN Keys
323. har amp zmatind free and null char amp zmatval free and null char amp zlb free and null char amp zub free and null char amp zqgmatbeg free and null char amp zqmatcnt free and null char amp zqmatind free and null char amp zqmatval else numcols_p NUMCOLS numrows_p NUMROWS objsen_p CPX_MAX The problem is maximization probname_p zprobname obj p zobj rhs p zrhs sense p Zsense matbeg p zmatbeg matcnt p zmatcnt matind p zmatind matval p zmatval lb p zlb ub p zub gmatbeg p zqmatbeg gmatcnt p zqmatcnt qmatind_p zqmatind qmatval p zqmatval return status END setproblemdata This simple routine frees up the pointer ptr and sets static void free and null char ptr if ptr NULL free ptr ptr NULL TE ILOG CPLEX 8 1 USER S MANUAL ptr to NULL EXAMPLE READING A QP FROM A FILE END free_and_null Example Reading a QP from a File This example shows you how to optimize a QP with routines from the ILOG CPLEX Callable Library when the problem data is stored in a file The example derives from lpex2 c described in the ILOG CPLEX Getting Started manual The Concert versions of this example iloqpex2 cpp and QPex2 java are included online in the standard distribution Instead of calling CPX1popt to find a solution as we do for the l
324. he same search strategy as ilogoalex1 cpp implemented in goal MyBranchGoal However it applies first the IISumEvaluator to select nodes with high integer infeasibility sum to choose between nodes with the same integer infeasibility sum it applies the DepthEvaluator Applying the 118umEvaluator is done with IloCplex Goal iiSumGoal IloCplex Apply cplex MyBranchGoal env var IISumEvaluator The goal created by calling MyBranchGoal is merged with the evaluator created by calling IISumEvaluator into a new goal iiSumGoal Similarly the iiSumGoal is merged with the node evaluator created by calling DepthEvaluator into a new goal depthGoal IloCplex Goal depthGoal IloCplex Apply cplex iiSumGoal DepthEvaluator Thus depthGoal represents a goal implementing the branching strategy defined by MyBranchGoal but using I1SumEvaluator as a primary node selection strategy and DepthEvaluator as a secondary node selection strategy for breaking ties This goal is finally used for the branch amp cut search by passing it to the solve method Node evaluators are only active while the search is controlled by goals That is if the goal stack becomes empty at a node and 11oCplex continues searching with its built in search strategy that search is no longer controlled by any node evaluator In order to maintain control over the node selection strategy while using the 11oCplex branch strategy you can o use
325. his matrix is influenced by the barrier ordering parameter The ILOG CPLEX Barrier Optimizer is appropriate and often advantageous for large problems for example those with more than 1000 rows or columns It is effective on problems with staircase structures or banded structures in the constraint matrix It is also effective on problems with a small number of nonzeros per column Its performance is most dependent on these characteristics the number of floating point operations required to compute the Cholesky factor the presence of dense columns that is columns with a relatively high number of nonzero entries To decide whether to use the barrier optimizer on a given problem you should look at both these characteristics We explain how to check those characteristics later in this chapter in Cholesky Factor in the Log File on page 162 and Nonzeros in Lower Triangle of AAT in the Log File on page 162 Barrier Simplex Crossover Since many users prefer basic solutions because they can be used to restart simplex optimization the ILOG CPLEX Barrier Optimizer includes basis crossover algorithms By default the barrier optimizer automatically invokes a primal crossover when the barrier algorithm terminates unless termination occurs abnormally because of insufficient memory or numerical difficulties Optionally you can also execute barrier optimization with a dual crossover or with no crossover at all The section Controllin
326. i 10f n i slack il pilil for j 0 J lt cur numcols J printf Column d Value 10f Reduced cost 10f n j x3 833l31 Finally write a copy of the problem to a file status CPXwriteprob env lp lpex6 sav NULL if status fprintf stderr Failed to write LP to disk n goto TERMINATE TERMINATE Free up the problem as allocated by CPXcreateprob if necessary if lp NULL status CPXfreeprob env amp lp if status fprintf stderr CPXfreeprob failed error code d n status 154 ILOG CPLEX 8 1 USER S MANUAL EXAMPLE USING A STARTING BASIS IN AN LP PROBLEM Free up the CPLEX environment if necessary if env NULL status CPXcloseCPLEX amp env Note that CPXcloseCPLEX produces no output so the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines the errors will be seen if the CPX_PARAM_SCRIND indicator is set to CPX_ON if status char errmsg 1024 fprintf stderr Could not close CPLEX environment Nn CPXgeterrorstring env status errmsg fprintf stderr s errmsg return status END main This function builds by column the linear program Maximize obj xl 2 x2 3 x3 Subject To Cl xl x2 x3 lt 20 C2 xl 3 x2 x3 lt 30 Bounds 0 lt xl lt 40 End xf statie rnt populatebycolumn CPXENVptr env CPXLPptr lp
327. iately ILOG CPLEX 8 1 USER S MANUAL EXAMPLE USING THE NETWORK OPTIMIZER WITH THE CALLABLE LIBRARY Preprocessing and the Network Optimizer If your LP problem includes network structures there is a possibility that ILOG CPLEX preprocessing may eliminate those structures from your model For that reason you should consider turning off preprocessing before you invoke the network optimizer on a problem TEN OI Example Using the Network Optimizer with the Callable Library 7 E gt eQ o e T z e In the standard distribution of ILOG CPLEX the file netex1 c contains code that creates solves and displays the solution of the network flow problem illustrated in Figure 6 1 on page 178 Briefly the main function initializes the ILOG CPLEX environment and creates the problem object it also calls the optimizer to solve the problem and retrieves the solution In detail main first calls the Callable Library routine CPXopenCPLEX As we explain in Initialize the ILOG CPLEX Environment on page 85 CPXopenCPLEX must always be the first ILOG CPLEX routine called in a ILOG CPLEX Callable Library application Those routines create the ILOG CPLEX environment and return a pointer called env to it This pointer will be passed to every Callable Library routine If this initialization routine fails env will be NULL and the error code indicating the reason for the failure will be written to status
328. ient server applications within distributed computing environments multithreaded applications running on multiple processors ILOG CPLEX 8 1 USER S MANUAL 83 ARCHITECTURE OF THE ILOG CPLEX CALLABLE LIBRARY 84 applications linked to database managers or applications using flexible graphic user interface builders just to name a few The Callable Library together with the ILOG CPLEX database make up the ILOG CPLEX core as you see in Figure 3 1 The ILOG CPLEX database includes the computing environment its communication channels and your problem objects You will associate the core with your application by calling library routines User Written Application ILOG CPLEX Callable Library ILOG CPLEX database Figure 3 1 A View of the ILOG CPLEX Callable Library The ILOG CPLEX Callable Library itself contains routines organized into several categories problem modification routines let you define a problem and change it after you have created it within the ILOG CPLEX database optimization routines enable you to optimize a problem and generate results utility routines handle application programming issues problem query routines access information about a problem after you have created it 9 9 file reading and writing routines move information from the file system of your operating system into your application or from your application into the file system parameter
329. ilities or it may be necessary for you to revise the coefficients To determine which way to go we recommend these steps in such a case 1 Use the command display solution quality in the Interactive Optimizer to locate the infeasibilities 2 Examine the coefficient matrix for poorly scaled rows and columns 3 Evaluate whether you can change unnecessarily large or small coefficients 4 Consider alternate scalings You may also be able to re optimize the problem successfully after you reduce optimality tolerance as explained in Maximum Reduced Cost Infeasibility on page 142 or after you reduce feasibility tolerance as explained in Maximum Bound Infeasibility Identifying Largest Bound Violation on page 142 When you change these tolerances ILOG CPLEX may produce a better solution to your problem but lowering these tolerances sometimes produces erratic behavior or an unstable optimal basis Check the basis condition number as explained in Measuring Problem Sensitivity with Basis Condition Number on page 137 If the condition number is fairly low for example as little as Je or less then you can be confident about the solution If the condition number is high or if reducing tolerance does not help then you must revise the model because the current model may be too ill conditioned to produce a numerically reliable result Interpreting Solution Statistics By default individual infeasibilities are written to a log file but no
330. ility finder 144 parameter specification file 402 reading QP from file 215 rowwise modeling 49 100 using arrays for I O 51 exception querying 120 executing a goal 319 exportModel member function IloCplex class 138 expr 63 expression UsER S MANUAL 409 INDEX building 34 editable 62 linear 35 piecewise linear 35 expressions construct using modeling variables 61 external variables 87 extra rim vectors 293 F FailGoal 320 feasibility analysis and barrier optimizer 172 check 320 dual 133 157 network flows and 177 primal 157 progress toward 139 177 Feasible return status 67 file format converting 294 described 290 example of quadratic program 215 numerically accurate 291 file reading routine defined 84 file writing routine defined 84 flow cover cuts defined 235 flow path cuts defined 236 FORTRAN 96 121 FracCand 238 FracPass 238 fractional cuts defined 236 free row 293 G ge method 63 generalized upper bound GUB 236 410 ILOG CPLEX 8 1 see also GUB getBasisStatus 72 getBasisStatuses member function IloCplex class 43 getBoundSA 73 getBoundSA member function IloCplex class 44 getCplexStatus member function IloCplex class 43 44 getDefault member function IloCplex class 40 getDual 72 getDual member function IloCplex class 43 getDuals 72 getDuals member function IloCplex class 43 getIIS 73 getIIS member function IloCplex class 44 getMax 72 getMax member func
331. ilog concert import ilog cplex public class QPexl public static void main String args try IloCplex cplex new IloCplex IloLPMatrix lp populateByRow cplex ll if cplex solve double x cplex getValues 1p double dj cplex getReducedCosts 1p double pi cplex getDuals lp double slack cplex getSlacks 1p System out println Solution status cplex getStatus System out println Solution value cplex getObjValue int ncols lp getNcols for int j 0 J lt ncols j System out println Column j Value x j Reduced cost dj j int nrows lp getNrows for int i 0 i lt nrows i System out printlin Row OWGBR OX Slack slack i Pi pi i cplex exportModel qpexl lp cplex end catch IloException e System err println Concert exception e caught static IloLPMatrix populateByRow IloMPModeler model throws IloException IloLPMatrix lp model addLPMatrix 206 ILOG CPLEX 8 1 USER S MANUAL EXAMPLE CREATING A QP OPTIMIZING FINDING A SOLUTION double lb 0 0 0 0 0 0 double ub 40 0 Double MAX_VALUE Double MAX_VALUE IloNumVar x model numVarArray model columnArray lp 3 lb ub double lhs Double MAX_VALUE Double MAX VALUE double rhs 20 0 30 0 double val 1 0 1 0 1 0 0r S820 Led fF int
332. ime is generally much worse than with best bound node selection because each branch is searched exhaustively to its deepest level before it is fathomed in favor of better branches Another memory conserving strategy is to use strong branching VarSel parameter value 3 for variable selection Strong branching requires substantial computational effort at each node to determine the best branching variable As a result it generates fewer nodes and thus makes less overall demand on memory Often strong branching is faster as well Difficulty Solving Subproblems There are classes of MIPs that produce very difficult subproblems for example if the subproblems are dual degenerate In such a case a different optimizer such as the primal simplex or the barrier optimizer may be better suited to your problem than the default dual simplex optimizer for subproblems These alternatives are discussed in Subproblem Optimization on page 257 A stronger dual pricing algorithm such as dual steepest edge pricing the parameter DPriInd set to 2 could also be considered ILOG CPLEX 8 1 USER S MANUAL TROUBLESHOOTING MIP PERFORMANCE PROBLEMS Overcoming Degeneracy If the subproblems are dual degenerate then consider using the primal simplex optimizer for the subproblems You make this change by setting the SubAlg parameter to 1 Another effective strategy in overcoming dual degeneracy is to permanently perturb the problem For subproblems that
333. imum reduced cost infeasibility identifies a value for the optimality tolerance that would cause ILOG CPLEX to perform additional iterations It refers to the infeasibility in the dual slack associated with reduced costs Whether ILOG CPLEX terminated with an optimal or infeasible solution if the maximum reduced cost infeasibility is only slightly smaller in absolute value than the optimality tolerance then solving the problem with a smaller optimality tolerance may result in an improvement in the objective function To change the optimality tolerance set the parameter EpOpt Maximum Row Residual The maximum row residual identifies the maximum constraint violation ILOG CPLEX Simplex Optimizers control these residuals only indirectly by applying numerically sound methods to solve the given linear system When ILOG CPLEX terminates with an infeasible solution all infeasibilities will appear as bound violations on structural or slack variables not constraint violations The maximum row residual may help you determine whether a model of your problem is poorly scaled or whether the final basis whether it is optimal or infeasible is ill conditioned Maximum Dual Residual The maximum dual residual indicates whether the current optimality tolerance is set appropriately If the maximum dual residual exceeds the optimality tolerance ILOG CPLEX may stall before it reaches an optimal solution In particular if ILOG CPLEX stalls during Phase I af
334. in the actual matrix coefficients and row indices Status CPXgetcols env lp amp nzcnt cmatbeg NULL NULL O0 amp cmatsz 0 numcols 1 if status CPXERR NEGATIVE SURPLUS if status 0 CPXmsg cpxerror CPXgetcols for surplus failed status d n status goto TERMINATE CPXmsg cpxwarning All columns in range d d are empty n 0 numcols 1 cmatsz cmatsz cmatind int malloc unsigned 1 cmatsz sizeof int cmatval double malloc unsigned 1 cmatsz sizeof double if cmatind NULL cmatval NULL CPXmsg cpxerror CPXgetcol mallocs failed n status 1 goto TERMINATE status CPXgetcols env lp amp nzcnt cmatbeg cmatind cmatval cmatsz amp surplus 0 numcols 1 if status CPXmsg cpxerror CPXgetcols failed status d n status goto TERMINATE That sample code or your application does not need to determine the length of the array cmatbeg The array cmatbeg has one element for each column in the requested range Since this length is known ahead of time your application does not need to call a query routine to calculate it More generally query routines use surplus arguments in the way we just described only for the length of any array required to store problem data of unknown length Problem data in this category includes nonzero matrix entries row and column names other problem data names special ordered
335. ind 0 1 2 0 1 2 lp addRows lhs rhs ind val Q 0 5 33 x0 x0 22 xl x1l 11 x2 x2 12 x0 xl 23 xl x2 loNumExpr x00 model prod 33 model square x 0 loNumExpr x11 model prod 22 model square x 1 loNumExpr x22 model prod 11 model square x 2 1 2 loNumExpr x01 model prod 12 model prod x 0 x 1 loNumExpr x12 model prod 23 model prod x 1 x 2 loNumExpr Q model prod 0 5 model sum x00 x11 x22 x01 x12 double objvals 1 0 2 0 3 0 model add model maximize model diff model scalProd x objvals Q return lp o 5 Q 2 U Uv E O D 3 2 Example qpexl c In the routine setproblemdata there are parameters for qmatbeg qmatcnt qmatind and qmatval to fill the quadratic coefficient matrix The Callable Library routine CPXcopyquad copies this data into the problem object created by the Callable Library routine CPXcreateprob In this example the problem is a maximization so we handle that fact by specifying the objective sense of CPX MAX The off diagonal terms in the matrix Q are one half the value of the terms x x2 and x2x3 as they appear in the algebraic form of the example Instead of calling CPX1popt to find a solution as we do for the inear programming problem in 1pex1 c this time we call CPXqpopt to optimize this quadratic programming problem Complete Program qpex1 c The complete pr
336. ine CPXsetintparam env CPX PARAM CLOCKTYPE i Replace the i with the value 1 to specify CPU time or 2 to specify wall clock time Using Parallel Optimizers in the Interactive Optimizer 1 If necessary for your platform set any environment variable needed for parallel operation See Threads on page 371 for details 2 Start the parallel CPLEX Interactive Optimizer with the command cp1lex at the operating system prompt 3 Set the thread limit as explained in Threads on page 371 4 Enter and populate your problem object as usual 5 Call the parallel optimizer with the appropriate command Parallel MIP Optimizer mipopt Parallel Barrier Optimizer baropt Parallel Simplex Optimizer primopt Ortranopt Using Parallel Optimizers in the ILOG CPLEX Component Libraries 1 Link your application to the parallel implementation of the ILOG CPLEX Component Libraries 2 Create your ILOG CPLEX environment and initialize a problem object in the usual way See Initialize the ILOG CPLEX Environment on page 85 and Instantiate the Problem Object on page 86 for details 3 Within your application set the appropriate ILOG CPLEX parameter from Table 9 7 to ILOG CPLEX 8 1 USER S MANUAL USING PARALLEL OPTIMIZERS specify the number of threads 4 Enter and populate your problem object in the usual way as in Put Data in the Problem Object on page 86 5 Call the parallel optimizer with the appropriate method or routine Table
337. inear programming problem in 1peg2 c this time we call CPXqpopt to optimize this quadratic programming problem This example also differs in the available algorithms for solving the problem QP barrier with crossover sifting and concurrent are not available for QP o gt Q 2 U Uv E e D 3 2 Like other applications based on the ILOG CPLEX Callable Library this one begins with calls to CPXopenCPLEX to initialize the ILOG CPLEX environment and to CPXcreateprob to create the problem object Before it ends it frees the problem object with a call to CPX reeprob and it frees the environment with a call to CPXcloseCPLEX Complete Program qpex2 c The complete program qpex2 c appears here and online in the standard distribution pom File examples src qpex2 c Version 8 1 o M Copyright C 1997 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products rl qpex2 c Reading in and optimizing a QP problem To run this example command line arguments are required i e qpex2 filename method where filename is the name of the file with mps lp or sav extensio
338. ines the errors will be seen if the CPX PARAM SCRIND indicator is set to CPX ON i AS fe ES D di Buinjos if env NULL char errmsg 1024 fprintf stderr Could not open CPLEX environment n CPXgeterrorstring env status errmsg fprintf stderr s errmsg goto TERMINATE Turn on output to the screen status CPXsetintparam env CPX PARAM SCRIND CPX ON if status fprintf stderr Failure to turn on screen indicator error d n status goto TERMINATE Fill in the data for the problem ILOG CPLEX 8 1 USER S MANUAL 279 EXAMPLE USING SOS AND PRIORITY status setproblemdata amp probname amp numcols amp numrows amp objsen amp obj amp rhs amp sense amp matbeg amp matcnt amp matind amp matval amp lb amp ub amp ctype if status fprintf stderr Failed to build problem data arrays n goto TERMINATE Create the problem lp CPXcreateprob env amp status probname A returned pointer of NULL may mean that not enough memory was available or there was some other problem In the case of failure an error message will have been written to the error channel from inside CPLEX In this example the setting of the parameter CPX PARAM SCRIND causes the error message to appear on stdout if lp NULL fprintf stderr Failed to create LP n goto TERMINATE Now copy the problem data into the lp
339. ing but it is probably safer and easier to include the methods for querying solution within try catch statements When an LP has been proven to be infeasible ILOG CPLEX provides assistance for determining the cause of the infeasibility This is done by computing what is known as an irreducibly inconsistent set IIS which is a description of the minimal subproblem that is still infeasible Here minimality is defined as being if you remove any of the constraints including finite bounds the infeasibility vanishes An IIS is computed for an infeasible LP model by calling method cplex getIIS To compute an IIS for a QP you should change the model to an LP by removing zeroing any quadratic terms from the objective function and then compute an IIS on the LP version 44 ILOG CPLEX 8 1 USER S MANUAL MODIFYING A MODEL Solution Quality The ILOG CPLEX optimizer uses finite precision arithmetic to compute solutions To compensate for numerical errors due to this tolerances are used by which the computed solution is allowed to violate feasibility or optimality conditions Thus the solution computed by the solve method may in fact slightly violate the bounds specified in the model for example You can call IloNum violation cplex getQuality IloCplex MaxPrimalInfeas to query the maximum bound violation among all variables and slacks If you are also interested in the variable or constraint where the maximum violation occurs ca
340. ing facilities to allow the programmer to embed ILOG CPLEX optimizers in C and Java applications The library is provided in files i1ocplex lib concert lib and cplex jar on Windows platforms and in 1ibilocplex a libconcert a and cplex jar on UNIX platforms and makes use of the Callable Library described next The ILOG CPLEX Callable Library is a C library that allows the programmer to embed ILOG CPLEX optimizers in applications written in C Visual Basic Fortran or any other language that can call C functions The library is provided in files cp1ex81 1ib and cplex81 d11 on Windows platforms and in 1ibcplex a and libcplex81 so or libcplex81 s1 on UNIX platforms ILOG CPLEX 8 1 USER S MANUAL 21 WHAT IS ILOG CPLEX In this manual the phrase ILOG CPLEX Component Libraries is used when referring equally to any of these libraries While all libraries are callable the term ILOG CPLEX Callable Library as used here refers specifically to the C library This preface introduces ILOG CPLEX version 8 1 It includes the following sections What Is ILOG CPLEX What You Need to Know In This Manual Notation in This Manual Related Documentation 9 99 99 For More Information What Is ILOG CPLEX ILOG CPLEX is a tool for solving first of all linear optimization problems Such problems are conventionally written like this Minimize or maximize CIX C3X2 Cy Xp subject to j1X djoX5 t Aln ev b 5 X A2
341. ing loop creates the constraints of the problem one by one and adds them to the model First the expression L Buy j nutrPer i j is created by building a Concert Technology expression An expression variable expr of type IloExpr is created and linear terms are added to it by using operator in a loop The expression is used with the overloaded operator to construct a range constraint an I1oRange object which is added to the model mod add nutrMin i lt expr lt nutrMax il After an expression has been used for creating a constraint it is deleted by calling expr end Finally the array of modeling variables Buy is returned Building the Model by Column The function buildModelByColumn implements the creation of the model by columns It begins by creating the array of modeling variables Buy of size 0 This is later populated when the columns of the problem are created and eventually returned The statement IloObjective cost IloAdd mod IloMinimize env creates a minimization objective function object with 0 expressions and adds it to the model The objective object is created with the function IloMinimize The template function IloAdd is used to add the objective object to the model and to return an objective object with the same type so that we can store the objective in variable cost The method IloModel add returns the modeling object as an IloExtractable which cannot be assigned to a variable of a deri
342. ing the Gap for more information about how these cuts have been found Of course the best way to solve the noswot model with these cuts is to simply add the cuts to the model before calling the optimizer However for demonstration purposes we will add the cuts using a cut callback only when they are violated at a node This cut callback takes a list of cuts as parameter and adds individual cuts whenever they are violated with the current LP solution Notice that adding cuts does not change the extracted model but affects only the internal problem representation of the ILOG CPLEX object Let us first consider the C version of the callback In C the callback is implemented with the code ILOCUTCALLBACK3 CtCallback IloExprArray lhs IloNumArray rhs IloNum eps IloInt n lhs getSize for IloInt i 0 i lt n i IloNum xrhs rhs i if xrhs lt IloInfinity amp amp getValue lhs i gt xrhs eps IloRange cut try cut lhs i lt xrhs add cut end rhs i IloInfinity catch cut end throw z E 563 O 2 oS Us a UE Q This defines the class CtCallbackI as a derived class of 11o0Cplex CutCallbackI and provides the implementation for its virtual methods main and duplicateCallback It also implements a function CtCallback that creates an instance of CtCallbackI and returns an IloCplex Callback handle for it As indicated by the 3 in the macro na
343. ing the amount of food j to buy for the diet Then the objective is minimize Buy j foodCost j The nutritional requirements mean that the following conditions must be observed that is for all i nutriMin i lt nutrPerFood i j Buy j SnutriMax i e E c8 g lt cs 5 o o Q lt z Finally every food must be within its bounds that is for all j foodMin j lt Buy j s foodMax j With what we have learned so far we can implement a method that creates such a model static void buildModelByRow IloModeler model Data data IloNumVar Buy IloNumVarType type throws IloException int nFoods data nFoods int nNutrs data nNutrs for int j 0 J lt nFoods J Buy j model numVar data foodMin j data foodMax jl type model addMinimize model scalProd data foodCost Buy for int i 0 i lt nNutrs i model addRange data nutrMin i model scalProd data nutrPerFood i Buy data nutrMax i The function receives several parameters The parameter model is used for two things creating other modeling objects and representing the model being created ILOG CPLEX 8 1 USER S MANUAL 65 SOLVING THE MODEL Solving the Model 66 The parameter data contains the data for the dietary model to be built Parameter Buy is an array initialized to length data nFoods containing the model s variables Finally parameter t ype is used to
344. intf stderr goto TERMINATE printf Solution status d if solntype CPX_NO_SOLN fprintf stderr goto TERMINATE ILOG CPLEX 8 1 solution method d n LI UNBOUNDED LI INFEASIBLE e n INForUNBD le or unbounded n amp solnmethod amp solntype Solution not available n USER S MANUAL error d n status NULL NULL Failed to obtain solution info n solnstat solnmethod EXAMPLE READING A QP FROM A FILE status CPXgetobjval env lp amp objval if status fprintf stderr Failed to obtain objective value n goto TERMINATE printf Objective value 10g n objval The size of the problem should be obtained by asking CPLEX what the actual size is cur_numrows and cur_numcols store the current number of rows and columns respectively cur numcols CPXgetnumcols env 1p fprintf stderr No memory for basis statuses Wn goto TERMINATE cur numrows CPXgetnumrows env 1p 5 Retrieve basis if one is available vo if solntype CPX_BASIC_SOLN 2 cstat int malloc cur_numcols sizeof int U rstat int malloc cur numrows sizeof int v if cstat NULL rstat NULL o J 7 status CPXgetbase env lp cstat rstat if status fprintf stderr Failed to get basis error d n status goto TERMINATE
345. iority order into the problem object e It writes the SOS information to files by calling CPXsoswrite e It writes the priority order to files by calling CPXordwrite o File examples src mipex3 c vy Version 8 1 ky Q Copyright C 1997 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products lr ILOG CPLEX 8 1 USER S MANUAL 277 EXAMPLE USING SOS AND PRIORITY mipex3 c Entering and optimizing a MIP problem with SOS sets and priority orders Is a modification of mipexl c Note that the problem solved is slightly different than mipexl c so that the output is interesting Bring in the CPLEX function declarations and the C library header file stdlib h with the following single include finclude ilcplex cplex h Bring in the declarations for the string functions include lt string h gt include lt stdlib h gt Include declaration for function at end of program static int setproblemdata char probname_p int numcols_p int numrows_p int objsen_p double obj_p double rhs_p char sense_p int matbeg_p int matcnt_p int matind_p double matval_p double lb_p doubl
346. irst calling the Mixed Integer Optimizer in its most straightforward form To invoke the Mixed Integer Optimizer In the Interactive Optimizer use the mipopt command Inthe Concert Technology Library with the IloCplex method solve In the Callable Library use the CPXmipopt routine Feasibility and Optimality The following section Performance Features of the Mixed Integer Optimizer goes into great detail about the algorithmic features controlled by parameter settings that are available in ILOG CPLEX to achieve performance tuning on difficult MIP models However there is an important parameter MIPEmphasis that is oriented less toward the user understanding the algorithm being used to solve the model and more toward the user telling the algorithm something about the underlying aim of the optimization being run That parameter is discussed here v AS fej ES D 7 diN Buinjos Optimizing a MIP model involves 1 finding a succession of improving integer feasible solutions solutions satisfying the linear constraints and the integrality conditions while 2 also working toward a proof that no better feasible solution exists and is undiscovered For most models a balance between these two sometimes competing aims works well and this is another way of stating the philosophy behind the default MIPEmphasis setting balance optimality and integer feasibility At this default MIPEmphasis setting o
347. is correctly as it handles adding the same cut from different threads Function makeCuts generates the arrays rhs and 1ns to be passed to the cut callback It first declares the array of variables to be used for defining the cuts Since the environment is not passed to the constructor of that array an array of O variable handles is created In the following loop these variable handles are initialized to the correct variables in the noswot model which are passed to this function as parameter vars The identification of the variables is done by querying variables names Once all the variables have been assigned they are used to create the 1hs expressions and rhs values of the cuts z a D3 qe oS US a UE Q The cut callback is created and passed to ILOG CPLEX in the line cplex use CtCallback env lhs rhs cplex getParam IloCplex EpRHS The function CtCallback constructs an instance of our callback class CtCallbackI and returns an IloCplex Callback handle object for it This is directly passed to function cplex use The Java implementation of the callback is quite similar ILOG CPLEX 8 1 USER S MANUAL 363 USING CALLBACKS 364 public static class Callback extends IloCplex CutCallback double eps 1 0e 6 IloRange cut Callback IloRange cuts cut cuts public void main throws IloException int num cut length for int i 0 i lt num i if cut i null double val
348. is the pointer returned by CPXopenCPLEX The second argument of each of those parameter routines is the parameter number a symbolic constant defined in the header file cplex h Managing Parameters from the Callable Library on page 98 offers more details about parameter settings Null Arguments Certain ILOG CPLEX routines that accept optional arguments allow you to pass a NULL pointer in place of the optional argument The documentation of those routines in the ILOG CPLEX Reference Manual indicates explicitly whether NULL pointer arguments are acceptable Passing NULL arguments is an effective way to avoid allocating unnecessary arrays Row and Column References Consistent with standard C programming practices in ILOG CPLEX an array containing k items will contain these items in locations 0 zero through x 1 Thus a linear program with m rows and n columns will have its rows indexed from 0 to m 1 and its columns from 0 to n 1 Within the linear programming data structure the rows and columns that represent constraints and variables are referenced by an index number Each row and column may optionally have an associated name If you add or delete rows the index numbers usually change for deletions ILOG CPLEX decrements each reference index above the deletion point and for additions ILOG CPLEX makes all additions at the end of the existing range However ILOG CPLEX updates the names so that each row or colum
349. is also a tool for solving linear programming problems in which some or all of the variables must assume integer values in the solution Such problems are known as mixed integer programs or MIPs because they may combine continuous and discrete for example integer variables in the objective function and constraints MIPs with linear objectives are referred to as mixed integer linear programs or MILPs and MIPs with quadratic objective terms are referred to as mixed integer quadratic programs or MIQPs Within the category of mixed integer programs we distinguish two kinds of discrete integer variables if the integer values of the discrete variables must be either 0 zero or 1 one then we refer to them as binary if the integer values are not restricted in that way we refer to them as general integer variables This manual explains more about the mixed integer optimizer in Chapter 8 Solving Mixed Integer Programming Problems ILOG CPLEX also offers a Network Optimizer aimed at a special class of linear problem with network structures ILOG CPLEX can optimize such problems as ordinary linear programs but if ILOG CPLEX can extract all or part of the problem as a network then it will apply its more efficient Network Optimizer to that part of your problem and use the partial solution it finds there to construct an advanced starting point to optimize the rest of the problem Chapter 6 Solving Network Flow Problems offers more detail about how the IL
350. is condition number at optimality is el then a change in a single matrix coefficient in the thirteenth place may dramatically alter the solution Furthermore since many computers provide about 16 places of accuracy in double precision only three accurate places are left in such a solution Even if an answer is obtained perhaps only the first three significant digits are reliable Because of this effective loss of precision for matrices with high basis condition numbers ILOG CPLEX may be unable to select an optimal basis In other words a high basis condition number can make it impossible to find a solution In the Interactive Optimizer use the command display solution kappa in order to see the basis condition number of a resident basis matrix Inthe Concert Technology Library use the method cplex getQuality IloCplex Kappa C cplex getQuality IloCplex QualityType Kappa Java ILOG CPLEX 8 1 USER S MANUAL 137 o 2 Q T U Ru cA D 3 7 DIAGNOSING PERFORMANCE PROBLEMS 138 In the Callable Library use the routine cPXgetdblquality to access the condition number in the double precision variable dvalue like this status CPXgetdblquality env lp amp dvalue CPX_KAPPA Repeated Singularities Whenever ILOG CPLEX encounters a singularity it removes a column from the current basis and proceeds with its work ILOG CPLEX reports such actions to the log file by default and to
351. is done in the following loop for int i 0 i lt nNutrs i col col and model column constraint i data nutrPerFood i j When the full column object has been constructed it is finally used to create and install the new variable using Buy j model numVar col data foodMin j data foodMax j type Once the model is created solving it and querying the solution is straightforward What remains to be pointed out is the exception handling In case of an error ILOG CPLEX will throw an exception of type I1oException or one of its subclasses Thus the entire ILOG CPLEX program is enclosed in t ry catch statements The InputDataReader can throw exceptions of type java io IOException Or InputDataReader InputDataReaderException Since none of these three possible exceptions is handled elsewhere the main function ends by catching them and issuing appropriate error messages ILOG CPLEX 8 1 USER S MANUAL 77 SOLVING THE DIET MODEL WITH THE JAVA API Example Diet java Source Code Here is the entire source code listing for the example we have been presenting It is available in the distributed files for ILOG CPLEX Java Ye ia ER File examples src Diet java Nersion 8 1 EL I a a aa E E Copyright C 2001 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products f RR RRR RRR SSS SSS SRS SS Se
352. is optimizer is called it makes a number of copies of the problem These copies are known as clones The parallel MIP optimizer creates as many clones as there are threads available to it When the optimizer exits these clones and the memory they used are discarded If a log file is active when the clones are created then ILOG CPLEX creates a clone log file for each clone The clone log files are named c1oneK 10g where K is the index of the clone ranging from 0 zero to the number of threads minus one Since the clones are created at each call to the parallel MIP optimizer and discarded when it exits the clone logs are opened at each call and closed at each exit The clone log files are not removed when the clones themselves are discarded The clone logs contain information normally recorded in the ordinary log file by default cplex 1log but inconvenient to send through the normal log channel The information likely to be of most interest to you are special messages such as error messages that result from calls to the LP optimizers called for the subproblems Parallel Barrier Optimizer The ILOG CPLEX Parallel Barrier Optimizer achieves significant speedups over its serial counterpart the ILOG CPLEX Barrier Optimizer described in Solving LP Problems with the Barrier Optimizer on page 156 and in Chapter 7 Solving Quadratic Programming Problems on a wide variety of classes of problems Consequently the parallel barrier optimizer wi
353. is the list of arguments for CPXgetcols CPXgetcols CPXENVptr env CPXLPptr lp int nzcnt p int cmatbeg int cmatind double cmatval int cmatspace int surplus p int begin int end The arrays cmat ind and cmatval require one element for each nonzero matrix coefficient in the requested range of columns The required length of these arrays specified in cmat space remains unknown at the time of the query Your application the calling program can determine the length of these arrays by first calling CPXgetcols witha value of 0 for cmat space This call will return an error status of CPXERR NEGATIVE SURPLUS indicating a shortfall of the array length specified in cmatspace in this case 0 it will also return the actual number of matrix nonzeros in the ILOG CPLEX 8 1 USER S MANUAL USING QUERY ROUTINES IN THE CALLABLE LIBRARY requested range of columns CPXgetcols deposits this shortfall as a negative number in the integer pointed to by surplus p Your application can then negate this shortfall and allocate the arrays cmat ind and cmatval sufficiently long to contain all the requested matrix elements The following sample of code shows you what we mean The first call to CPXget cols passes a value of 0 for cmat space in order to obtain the shortfall in cmat sz The sample then uses the shortfall to allocate the arrays cmat ind and cmat val properly then it calls CPXgetcols again to obta
354. is you create the following column ILOG CPLEX 8 1 USER S MANUAL EXAMPLE DIETARY OPTIMIZATION cost foodCost j sum i rng i nutrper i j 1 mon where the notation and sum indicates that you add the new variable j to the objective cost and constraints rng i The value in parentheses is the linear coefficient that is used for the new variable Program Description All definitions needed for a ILOG CPLEX Callable Library program are imported by including file lt ilcplex cplex h gt at the beginning of the program After a number of lines that establish the calling sequences for the routines that are to be used the program s main function begins by checking for correct command line arguments printing a usage reminder and exiting in case of errors Next the data defining the problem are read from a file specified in the command line at run time The details of this are handled in the routine xeaddata In this file cost lower bound and upper bound are specified for each type of food then minimum and maximum levels of several nutrients needed in the diet are specified finally a table giving levels of each nutrient found in each unit of food is given The result of a successful call to this routine is two variables n oods and nnutr containing the number of foods and nutrients in the data file arrays cost 1b ub containing the information on the foods arrays nut rmin nutrmax containing nutri
355. ist of evaluators attached to them ILOG CPLEX 8 1 USER S MANUAL 333 z E E O 2 oS US a UE Q GOALS IN ILOCPLEX When node evaluators are used nodes are selected as follows e IloCplex starts to choose the node with the built in strategy as a first candidate e Then 11oCplex loops over all remaining active nodes and considers choosing them instead e Ifa node has the same evaluator attached to it as the current candidate the evaluator is asked if this node should take precedence over the current candidate If the response is positive the node under investigation becomes the new candidate and the test against other nodes continues If a node has multiple evaluators attached they are consulted in the order the evaluators have been applied This occurs as follows e Ifthe first evaluator prefers one node over the other the preferred node is used as candidate and the next node is considered e If the first evaluator does not give preference to one node over the other the second evaluator is considered and so on Thus by adding multiple evaluators you can build composite node selection strategies where later evaluators are used for breaking ties in previous ones Node evaluators are implemented as subclasses of class IloCplex NodeEvaluatorl Class TloCplex NodeEvaluator is the handle class for node evaluators In Java node evaluators are implemented in objects of type IloCplex NodeEvaluator and there a
356. ith the command netopt or the command optimize Understanding the Network Log File As ILOG CPLEX solves the problem it produces a log like the following lines Iteration log Iteration 0 Infeasibility 48 000000 5 15396e 13 Network Optimal Objective 2 6900000000e 02 Solution time 0 00 sec Iterations 7 7 This network log file differs slightly from the log files produced by other ILOG CPLEX optimizers it contains values enclosed in parentheses that represent modified objective function values As long as the network optimizer has not yet found a feasible solution we say that it is in Phase I In Phase I the network optimizer uses modified objective coefficients that penalize infeasibility At its default settings the ILOG CPLEX Network Optimizer displays the value of the objective function calculated in terms of these modified objective coefficients in parentheses in the network log file ILOG CPLEX 8 1 USER S MANUAL SOLVING PROBLEMS WITH THE NETWORK OPTIMIZER You can control the amount of information recorded in the network log file just as you control the amount of information in other ILOG CPLEX log files To record no information at all in the log file use the command set network display 0 To display the current objective value in parentheses relative to the actual unmodified objective coefficients use the command set network display 1 To see the display we described earlier in this section leave
357. ix coefficients indicated by the Interactive Optimizer match the ones for the intended model in your application Use the Interactive Optimizer command display problem stats to verify that the size of the problem the sense of the constraints and the types of variables match your expectations For example if your model is supposed to contain only general integer variables but the Interactive Optimizer indicates the presence of binary variables check the type variable passed to the constructor of the variable Concert Technology Library or check the specification of the ctype array and the routine CPXcopyctype Callable Library You can also examine the matrix objective and right hand side coefficients in an LP or MPS file to see if they are consistent with the values you expect in the model e 2 D Q i P e 2 7 Buruiue1DoJg 1ou1inJ Eliminating Common Programming Errors We hope this section serves as a checklist to help you eliminate common pitfalls from your application ILOG CPLEX 8 1 USER S MANUAL 119 ELIMINATING COMMON PROGRAMMING ERRORS 120 Check Your Include Files Make sure that the header file i locplex h Concert Technology Library or cplex h Callable Library is included at the top of your application source file If that file is not included then compile time linking or runtime errors may occur Clean House and Try Again Remove all object files recompile and relink
358. izer Solving the extracted model with ILOG CPLEX involves solving one or a series of LPs or QPs Only one LP or QP needs to be solved if the extracted model is continuous itself that is if it does not contain integer Boolean semi continuous or semi integer variables SOS or piecewise linear functions Chapter 5 Solving Linear Programming Problems discusses the algorithms available for solving LPs Similarly Chapter 7 Solving Quadratic Programming Problems discusses the algorithms available for solving QPs Inall other cases the extracted problem that ILOG CPLEX sees is indeed a MIP and in general a series of LPs or QPs needs to be solved Method cplex isMIP returns IloTrue in such a case Chapter 8 Solving Mixed Integer Programming Problems discusses the algorithms applied The optimizer option used for solving the first LP or QP whether it is the only one or just the first in a series of problems is controlled by setting the root algorithm parameter cplex setParam IloCplex RootAlg alg where alg is a member of the nested enumeration type enum IloCplex Algorithm Primal Dual Barrier Network Sifting Concurrent Note that the last two choices Sifting and Concurrent are not available for QP models As a nested enumeration type the fully qualified names that must be used in the program are ILOG CPLEX 8 1 USER S MANUAL 39 SOLVING CONCERT TECHNOLOGY MODELS WITH ILOCPLEX 40 IloCplex
359. jecting Sol tions i eriee he e bel oe Exe dd Vad Sider ie int ae vee dee 332 Controlling Goal Controlled Search 0 0 0 00 ccc cette 333 Search Limits 2 222 ke bes be Pi ane E qe eee SiMe CE gend made 340 Using Callbacks 22 2222 ec beens mt mmm uk x x RE ee OE ERA ee Eun 341 Diagnostic Callbacks n aana cee I I mu 341 Control Callbacks for lloCplex lslseeeseeee RII 359 A Comparison of Goals and Callbacks 0 0 cece cece eee nnn 369 Using Parallel Optimizers 2 2 ee cee ee eee eee ee eee 371 Threads x52 ee ceived eos She 24 Caa eee GR REG NE VUE eee ad eed bogus 371 Nondeterminism sse ocean ee veda ee eee raed cede Rp RW RN RU AUR RU ee 373 Clock Settings and Time Measurement 0 0000 e cence eee eee eee 373 Using Parallel Optimizers in the Interactive Optimizer 0000ee eee 374 Using Parallel Optimizers in the ILOG CPLEX Component Libraries 374 Parallel MIP Optimizer 0 0 0 0 cette I 375 Parallel Barrier Optimizer 2 2 0 eet 379 Parallel Simplex Optimizer 2 0 0 0 eee eh 379 CPLEX Runtime Development and Licensing Procedures lesus 381 Types of ILM Runtime Licenses lisse RII 381 Routines Used for Licensing lille I 381 IST PPP EPIIT 384 Appendix A ILOG CPLEX Parameter Names 0 0c cece e eee n nnn 385 Appendix B Interactive Optimizer Commands 0 000 eee e eee eee eee
360. jective value maximum bound violation variable values and basis int solnstat solnmethod solntype double objval maxviol double x NULL int cstat NULL int rstat NULL CPXENVptr env NULL CPXLPptr lp NULL int status 0 int j int cur_numrows cur_numcols z char cur colname NULL Q char cur_colnamestore NULL o D int cur_colnamespace Q E int surplus Q o int method v S ne char basismsg X 2 vo Check the command line arguments if arge 3 strchr podhbnsc argv 2 0 NULL usage argv 0 goto TERMINATE Initialize the CPLEX environment ILOG CPLEX 8 1 USER S MANUAL 311 USING QUERY ROUTINES IN THE CALLABLE LIBRARY 312 env CPXopenCPLEX amp status If an error occurs the status value indicates the reason for failure A call to CPXgeterrorstring will produce the text of the error message Note that CPXopenCPLEX produces no output so the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines the errors will be seen if the CPX PARAM SCRIND indicator is set to CPX ON if env NULL char errmsg 1024 fprintf stderr Could not open CPLEX environment n CPXgeterrorstring env status errmsg fprintf stderr s errmsg goto TERMINATE Turn on output to the screen status CPXsetintparam env CPX PARAM SCRIND CPX ON if status fprintf st
361. k problem we have measured performance 100 times faster with the network optimizer However if the network component of your problem is small relative to its other parts then using the solution of the network part of the problem as a starting point for the remainder may or may not improve performance compared to running the primal or dual simplex optimizer Only experiments with your own problem can tell Formulating a Network Problem 176 A network flow problem finds the minimal cost flow through a network where a network consists of a set N of nodes and a set A of arcs connecting the nodes An arc a in the set A is an ordered pair i j where i and j are nodes in the set N node i is called the tail or the from node and node j is called the head or the to node of the arc a Not all the pairs of nodes in a set N are necessarily connected by arcs in the set A More than one arc may connect a pair of nodes in other words a i j and a gt i j may be two different arcs in A both connecting the nodes i and j in N Each arc a may be associated with four values x isthe flow value that is the amount passing through the arc a from its tail or from node to its head or to node The flow values are the modeling variables of a network flow problem Negative values are allowed a negative flow value indicates that there is flow from the head to the tail l the lower bound determines the minimum flow allowed through the arc
362. ks vals rng env out lt lt Slacks lt lt vals lt lt endl cplex getDuals vals rng env out lt lt Duals lt lt vals lt lt endl cplex getReducedCosts vals var env out lt lt Reduced Costs lt lt vals lt lt endl cplex exportModel lpex6 1p catch IloException amp e cerr Concert exception caught e endl catch Gan 1 cerr lt lt Unknown exception caught lt lt endl env end return 0 END main static void populatebycolumn IloModel model IloNumVarArray x IloRangeArray c IloEnv env model getEnv IloObjective obj IloMaximize env c add IloRange env IloInfinity 20 0 c add IloRange env IloInfinity 30 0 x add IloNumVar obj 1 0 c 0 1 0 c 1 1 0 35 0 40 0 x add obj 2 0 c 0 1 0 c 1 3 0 x add obj 3 0 c 0 1 0 c 1 1 0 model add obj model add c END populatebycolumn Example lpex6 c The example 1pex6 c resembles one you may have studied in the ILOG CPLEX Getting Started manual 1pex1 c This example differs from that one in these ways Inthe main routine the arrays cstat and rstat set the status of the initial basis After the problem data has been copied into the problem object the basis is copied by a call to CPXcopybase After the problem has been optimized the iteration count is printed For the given data and basis the basis is optimal
363. l then a different starting point heuristic may perform better than the default To change the starting point heuristic see Table 5 12 on page 168 Difficulties during Optimization Numerical difficulties can degrade performance of the ILOG CPLEX Barrier Optimizer or even prevent convergence toward a solution There are several possible sources of numerical difficulties elimination of too many dense columns may cause numerical instability tight convergence tolerance may aggravate small numerical inconsistencies in a problem unbounded optimal faces may remain undetected and thus prevent convergence The following subsections offer guidance about overcoming those difficulties ILOG CPLEX 8 1 USER S MANUAL SOLVING LP PROBLEMS WITH THE BARRIER OPTIMIZER Numerical Instability Due to Elimination of Too Many Dense Columns Detecting and Eliminating Dense Columns on page 167 explains how to change parameters to encourage ILOG CPLEX to detect and eliminate as many dense columns as possible However in some problems if ILOG CPLEX removes too many dense columns it may cause numerical instability You can check how many dense columns ILOG CPLEX removes by looking at the preprocessing statistics at the beginning of the log file as we explained in Preprocessing in the Log File on page 161 If you observe that the removal of too many dense columns results in numerical instability in your problem then increase the column nonzeros para
364. l constructor methods come in pairs one with and one without the name parameter The Active Model Modeling objects constraints and objective functions created as described above are now added to the active model The active model is the model implemented by the IloCplex object itself In fact IloModeler is an extension of the 11oMode1 interface defining the model API Thus 11oCplex implements IloModel or in other words an 11oCplex object is a model We will refer to the model implemented by the IloCp1ex object itself as the active model of the 11oCplex object or if there is no possibility of confusion between several optimizers simply as the active model A model is just a set of modeling objects of type IloAddable such as IloObjective and IloRange Objects of classes implementing this interface can be added to an instance of IloModel Other 11o0Addable objects usable with IloCplex are I1oLPMatrix IloConversion I10S0S1 and 1105052 These will be covered in the IloMPModeler section Variables cannot be added to a model because IloNumVar is not an extension of IloAddable All variables used by other modeling objects I loAddab1e objects that have been added to a model are implicitly part of this optimization model The explicit addition of a variable to a model can thus be avoided During modeling a typical sequence of operations is to create a modeling object and immediately add it to the active model To facilitate this for most
365. l pil il for j 0 J lt cur numcols j printf Column d Value 10f Reduced cost 10f n j xl3 ajlil Finally write a copy of the problem to a file status CPXwriteprob env lp qpexl lp NULL if status fprintf stderr Failed to write LP to disk n goto TERMINATE TERMINATE o 5 Q 2 U v E O D 3 2 Free up the problem as allocated by CPXcreateprob if necessary if lp NULL status CPXfreeprob env amp lp if status fprintf stderr CPXfreeprob failed error code d n status Free up the CPLEX environment if necessary if env NULL status CPXcloseCPLEX amp env Note that CPXcloseCPLEX produces no output so the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines the errors will be seen if the CPX PARAM SCRIND indicator is set to CPX ON if status 1 char errmsg 1024 fprintf stderr Could not close CPLEX environment Nn CPXgeterrorstring env status errmsg fprintf stderr s errmsg Free up the problem data arrays if necessary free_and_null char amp probname free_and_null char amp ob3 Re cas free and null char amp rhs free and null char amp sense ILOG CPLEX 8 1 USER S MANUAL 211 EXAMPLE 212 CREATING A QP OPTIMIZING wy FINDING A SOLUTION free and null
366. l basis can be copied and used to start an optimization Bring in the CPLEX function declarations and the C library header file stdio h with the following single include finclude ilcplex cplex h Bring in the declarations for the string functions include lt string h gt Include declaration for function at end of program static int populatebycolumn CPXENVptr env CPXLPptr 1p o The problem we are optimizing will have 2 rows 3 columns E and 6 nonzeros a r define NUMROWS 2 v define NUMCOLS 3 3 define NUMNZ 6 oy 3 7 ILOG CPLEX 8 1 USER S MANUAL 151 EXAMPLE 152 USIN int mai G A STARTING BASIS IN AN LP PROBLEM n void char probname 16 Problem name is max 16 characters int cstat NUMCOLS int rstat NUMROWS Declare and allocate space for the variables and arrays where we will store the optimization results including the status objective value variable values dual values row slacks and variable reduced costs int solstat double objval double x NUMCOLS double pi NUMROWS double slack NUMROWS double dj NUMCOLS CPXENVptr env NULL CPXLPptr lp NULL int status int i dj int cur numrows cur numcols Initialize the CPLEX environment env CPXopenCPLEX amp status If an error occurs the status value indicates the reason for failure A call to CPXgeterrorstring will produce the
367. lI FailGoal IloCplex failGoal creates a goal that causes I1oCplex to prune the current node In other words it discontinues the search at the node where the goal is executed IloCplex will continue with another active node from the tree if available Class IloCplex Goal has constructors that take an IloRange object or an IloRangeArray IloRange object as parameters When one of these constructors is used a local cut goal is created Local cut goals add local cuts to the node where they are executed To create local cut goals with the Java API use method IloCplex constraintGoal orif more convenient one of the methods IloCplex leGoal IloCplex geGoal OoriloCplex eqGoal ILOG CPLEX 8 1 USER S MANUAL GOALS IN ILOCPLEX The 0 nu11 goal or empty goal that is an IloCplex Goal handle object with 0 implementation pointer can also be returned by method IloCplex GoalI execute In most cases this will instruct 11oCplex to take over control of the branch amp cut search with its built in strategies Since IloCplex GoalI OrGoal IloCplex or and IloCplex GoalI AndGoal IloCplex and take other goals as parameters goals can be combined into aggregate goals In fact this is how goals are typically used for specifying a branching strategy A typical return goal of a user written execute method for C looks like this return AndGoal OrGoal var lt IloFloor val var gt IloFloor val 1 this
368. lbacks In ILOG CPLEX with Concert Technology Callbacks are accessed via the TloCplex Callback handle class in the C version of IloCplex It points to an implementation object of a subclass of 11oCplex CallbackI In java there is no handle class and one only deals with implementation classes which are subclasses of IloCplex Callback One such implementation class is provided for each type of callback The implementation class provides the functions that can be used for the particular callback as protected member functions To reflect the fact that some callbacks share part of their protected API the callback classes are organized in a class hierarchy as shown by this diagram for C ILOG CPLEX 8 1 USER S MANUAL 341 USING CALLBACKS 342 IloCplex CallbackI IloCplex PresolveCallbackI IloCplex CrossoverCallbackI IloCplex NetworkCallbackI IloCplex ContinuousCallbackI a TloCplex BarrierCallbackI IloCplex SimplexCallbackI IloCplex MIPCallbackI A IloCplex ProbingCallback IloCplex FractionalCutCallbackI IloCplex DisjunctiveCutCallbackI The callback class hierarchy for Java is exactly the same but the class names differ in that there is no 1 at the end For example the corresponding Java implementation class for IloCplex ContinuousCallbackI is IloCplex ContinuousCallback This means that for example all functions available for the MIP callback are a
369. ld be more efficient Table 8 13 summarizes the values available for the RootAlg parameter di Buinjos To set this parameter Inthe Interactive Optimizer use the command set mip strategy startalgorithm with the value to indicate the optimizer you want Inthe Concert Technology library use the method IloCplex method setParam with the parameter RootAlg and the appropriate algorithm enumeration value In the Callable Library use the routine CPXsetintparam with the parameter CPX_PARAM_STARTALG and the appropriate symbolic constant ILOG CPLEX 8 1 USER S MANUAL 257 EXAMPLE OPTIMIZING A BASIC MIP PROBLEM Table 8 13 Values of RootAlg and NodeAlg Parameters E Eee Sonane Condant Value Calis this Optimizer Auto CPX_ALG_AUTO 0 automatic Primal CPX_ALG_PRIMAL 1 primal simplex Dual CPX_ALG_DUAL 2 dual simplex default Network CPX_ALG_HYBNETOPT 3 network simplex Barrier CPX_ALG_BARRIER 4 barrier with crossover Sifting CPX ALG SIFTING 5 sifting NodeAlg Parameter The NodeAlg parameter indicates the algorithm for ILOG CPLEX to use on node relaxations other than the root node By default ILOG CPLEX applies the dual simplex optimizer to subproblems and unlike the Root A1g parameter it is extremely unusual for this to not be the most desirable choice but again you may have information about your problem that tells you another optimizer could be more efficient The v
370. le 1b p x2 xl 2 x2 3 exl X2 x3 xl 3 x2 x3 char zprobname double zobj NULL double zrhs NULL char zsense NUL int zmatbeg NU int zmatcnt NU int zmatind NU double zmatval NU double zlb NULL double zub NULL char zctype NUL int status 0 zprobname char malloc zobj double zrhs double zsense the data structures for the mixed integer program amp matcnt amp matind amp matval amp lb amp ub amp ctype x3 x4 10x4 lt 20 lt 30 3 5x4 0 char probname_p int objsen_p NULL b LL LL LL LL Li int numcols_p int numrows_p double rhs_p int matcnt_p double obj_p int matbeg_p double matval_p double ub_p char ctype_p Problem name lt 16 characters 16 sizeof char malloc NUMCOLS sizeof double malloc NUMROWS sizeof double char malloc ILOG CPLEX 8 1 NUMROWS sizeof char USER S MANUAL EXAMPLE OPTIMIZING A BASIC MIP PROBLEM zmatbeg int malloc NUMCOLS sizeof int zmatent int malloc NUMCOLS sizeof int zmatind int malloc NUMNZ sizeof int zmatval double malloc NUMNZ sizeof double zlb double malloc NUMCOLS sizeof double zub double malloc NUMCOLS sizeof double zctype char malloc NUMCOLS sizeof char if zprobname NULL zobj
371. lem log 402 ILOG CPLEX 8 1 USER S MANUAL A absolute objective difference 252 absolute optimality tolerance 252 accessing basis information 43 current parameter value 40 98 default parameter value 98 dual values 43 maximum parameter value 98 minimum parameter value 98 objective function value 43 parameters in Interactive Optimizer 400 reduced costs 43 slack values 43 solution quality 45 solution values 43 active model 64 MIP 69 active node 319 add member function IloModel class 36 45 addMinimize 66 advanced basis in networks 126 reading 130 saving 130 starting from 129 starting parameter 130 advanced starting basis 148 ILOG CPLEX 8 1 AggCut Lim 238 aggregator barrier preprocessing 167 alg 69 algorithm choosing in LP 39 controlling in IloCplex 40 pricing 130 type 70 Algorithm Barrier 72 application creating with Concert Technology 33 development steps 33 arc 176 architecture 83 arguments null pointers 92 optional 92 array constructing 76 creating multi dimensional 50 extensible 36 using for I O 51 aspect ratio 379 barrier 72 barrier optimizer algorithm 157 USER S MANUAL Index 403 INDEX algorithms and infeasibility 172 barrier display parameter 170 centering corrections 170 column nonzeros parameter 167 171 corrections limit 170 growth parameter 171 infeasibility analysis 172 linear 156 to 173 log file 160 numerical difficulties and 170 out of core barrier 166
372. les and Expressions The lloNumVar Object Probably the first modeling class you will need is IloNumVar Objects of this class represent modeling variables They are described by the lower and upper bound for the variable and a type which can be one of ILOFLOAT ILOINT or ILOBOOL for continuous integer or Boolean variables respectively The following constructor creates an integer variable with bounds 1 and 10 IloNumVar myIntVar env 1 10 ILOINT The r1oNumVar class provides methods that allow querying of the data needed to specify a variable However only bounds can be modified Concert Technology provides a modeling object class IloConversion to change the type of a variable This allows you to use the same variable with different types in different models Variables are usually used to build up expressions which in turn are used to define the objective or constraints of the optimization problem An expression can be explicitly written as in 1 x 1 2 x 2 3 x 3 where x is assumed to be an array of variables IloNumVarArray Expressions can also be created piece by piece with a loop IloExpr expr env ILOG CPLEX 8 1 USER S MANUAL MODELING AN OPTIMIZATION PROBLEM WITH CONCERT TECHNOLOGY for int i 0 i lt x getSize i expr data i x i Whenever possible build your expressions in terms of data that is either integer or double precision 64 bit floating point Single precision 32 bit f
373. les src ilolpex6 cpp Version 8 1 Copyright C 1999 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products ilolpex6 cpp Illustrates that optimal basis can be copied and used to start an optimization finclude lt ilcplex ilocplex h gt ILOSTLBEGIN static void populatebycolumn IloModel model IloNumVarArray var IloRangeArray rng int main int argc char argv IloEnv env try loModel model env example loNumVarArray var env loRangeArray rng env populatebycolumn model var rng loCplex cplex model loCplex BasisStatusArray cstat env rstat env cstat add IloCplex AtUpper cstat add IloCplex Basic cstat add IloCplex Basic rstat add IloCplex AtLower rstat add IloCplex AtLower cplex setBasisStatuses cstat var rstat rng cplex solve cplex out lt lt Solution status lt lt cplex getStatus lt lt endl cplex out lt lt Solution value lt lt cplex getObjValue lt lt endl cplex out lt lt Iteration count lt lt cplex getNiterations lt lt endl IloNumArray vals env cplex getValues vals var env out Values lt lt vals lt lt endl ILOG CPLEX 8 1 USER S MANUAL 149 o 2 Q T U Uv E e D 3 EXAMPLE USING A STARTING BASIS IN AN LP PROBLEM cplex getSlac
374. lete program 1pex5 c appears here and online in the standard distribution o o OF Besa Sass Sas Se SS SS SSS SSS SSS SS SS SS SSS SE SSS SS SSE SSS SSS ny OO File examples src lpex5 c uS Version 8 1 r Ba M UE Copyright C 1997 2002 by ILOG 5 All Rights Reserved A e Permission is expressly granted to use this example in the course of developing applications that use ILOG products LO LO ee lpex5 c Illustrating the CPLEX message handler This is a modification of lpexl c We ll label each channels output with its name and also put our own output into a file Note that the labels may cause the output to go past 80 characters per line ILOG CPLEX 8 1 USER S MANUAL 299 MANAGING 300 INPUT amp OUTPUT Bring in the CPLEX function declarations and the C library header file stdio h with the following single include finclude lt ilcplex cplex h gt Bring in the declarations for the string functions include lt string h gt Include declaration for function at end of program static int populatebycolumn CPXENVptr env CPXLPptr 1p Static void CPXPUBLIC ourmsgfunc void handle const char message The problem we are optimizing will have 2 rows 3 columns and 6 nonzeros define NUMROWS 2 define NUMCOLS 3 define NUMNZ 6 int main void
375. lication Use that call to create a file whether an LP SAV or MPS formatted problem file Understanding File Formats on page 290 briefly describes these file formats Then read that file into the Interactive Optimizer and optimize the problem there Note that MPS LP and SAV files have differences that influence how to interpret the results of the Interactive Optimizer for debugging SAV files contain the exact binary representation of the problem as it appears in your program while MPS and LP files are text files containing possibly less precision for numeric data And unless every variable appears on the objective function ILOG CPLEX will probably order the variables differently when it reads the problem from an LP file than from an MPS or SAV file With this in mind SAV files are the most useful for debugging using the Interactive Optimizer followed by MPS files then finally LP files in terms of the change in behavior you might see by use of explicit files On the other hand LP files are often quite helpful when you want to examine the problem more so than as input for the Interactive Optimizer Furthermore try solving ILOG CPLEX 8 1 USER S MANUAL ELIMINATING COMMON PROGRAMMING ERRORS both the SAV and MPS files of the same problem using the Interactive Optimizer Different results may provide additional insight into the source of the difficulty In particular use the following guidelines with respect to reproducing your progr
376. lity barrier optimizer and 172 diagnosing in network flows 190 diagnosing in QPs 202 displaying on screen 141 dual 169 172 during preprocessing 143 maximum bound 144 142 maximum reduced cost 141 142 network flow 177 network optimizer and 190 norms 163 primal 163 169 172 ratio in barrier log file 163 reports 139 scaling and 140 UsER S MANUAL unscaled 140 infeasibility finder 143 172 multiple IISs 144 network flows and 190 preprocessing and 148 sample output 144 setting time limit on 147 Infeasible return status 67 infeasible problem analyzing 44 infeasible solution information 73 InfeasibleOrUnbounded return status 67 initializing CPLEX environment 181 problem object 86 181 input operator 36 instantiating CPLEX environment 181 problem object 86 181 int 70 integer variables single LP 69 integrality constraints 319 Interactive Optimizer accessing parameters in 400 commands 385 to 393 to 400 customized parameter settings 400 debugging and 118 description 21 experimenting with optimizers 116 improving application performance 118 setting parameters 400 testing code in 114 Interactive Optimizer parameter names 386 IntParam 69 intVar 62 irreducibly inconsistent constraints 143 irreducibly inconsistent set 73 irreducibly inconsistent set IIS 144 algorithms 147 example cumulative constraint 146 example network 190 ILOG CPLEX 8 1 INDEX file format for 290 network flows and 190 s
377. ll 41 99 using status variables 352 changing limit on barrier corrections 170 maximization to minimization 182 pricing algorithm 179 problem type network to LP 189 qp 200 USER S MANUAL zeroed_qp 200 quadratic coefficients 199 200 variable type 47 channel example 298 character string length requirements 93 check c CPLEX file 94 Cholesky factor 166 barrier iteration 158 barrier log file and 162 choosing algorithm in LP 39 clique cuts defined 235 cloneK log 379 clones 379 log files 379 threads and 379 closing application 87 182 environment 87 182 log files 295 col and 77 column dense 171 density 167 growth parameter 182 index number 92 modeling by 75 name 92 nonzeros parameter 167 171 referencing 92 columnwise modeling 50 61 75 100 complementarity 157 158 172 convergence tolerance 171 Component Libraries defined 22 Concert Technology Library accessing parameter values 40 application development steps 33 creating application 33 description 21 design 31 error handling 47 ILOG CPLEX 8 1 INDEX solving problem with 31 using 31 to 58 writing programs with 31 see also individual Iloxxx routines constraint accessing slack values 43 cumulative 146 147 cuts as 235 modeling linear 37 removing from basis 46 representing with IloRange 35 violation 142 constraints create ranged 61 ranged 63 constructing arrays of variables 76 continuous relaxation 231 continuous relaxa
378. ll Cuts under emphasis 3 but the user has the option if that is what is desired Performance Features of the Mixed Integer Optimizer The ILOG CPLEX Mixed Integer Optimizer contains a wealth of features intended to aid in the solution of challenging MIP models While default strategies are provided that solve the majority of models without user involvement there exist difficult models that benefit from attention to performance tuning This section discusses the ILOG CPLEX parameters that are the most likely to offer help on such models Because many of these parameter settings directly affect the branch amp cut algorithm we first give a description of how that algorithm is implemented within ILOG CPLEX Branch amp Cut In the branch amp cut algorithm ILOG CPLEX solves a series of continuous subproblems To manage those subproblems efficiently ILOG CPLEX builds a tree in which each subproblem is a node The root of the tree is the continuous relaxation of the original MIP problem If the solution to the relaxation has one or more fractional variables ILOG CPLEX will try to find cuts Cuts are constraints that cut away areas of the feasible region of the relaxation that contain fractional solutions ILOG CPLEX can generate several types of cuts Cuts on page 235 tells you more about that topic If the solution to the relaxation still has one or more fractional valued integer variables after ILOG CPLEX tries to add cuts
379. ll be the best LP choice on a parallel computer more frequently than on a single processor For that reason you should be careful not to apply performance data or experience based on serial optimizers when you are choosing which optimizer to use on a parallel platform If you decide to use the parallel barrier optimizer on the subproblems of a MIP see also other special considerations about nested parallelism in Nested Parallel Processing on page 376 z EN E Qe oS US a UE Q Parallel Simplex Optimizer In the ILOG CPLEX implementation of the Parallel Simplex Optimizer the column based work occurs in parallel Consequently a significant gain in speed may occur in the dual simplex optimization t ranopt IloCplex Dual CPXdualopt Occasionally in the primal simplex optimizer if the primal gradient parameter is set to steepest edge pricing and the aspect ratio that is the number of columns divided by the number of rows is relatively large for example 70 or more then good speedups may ILOG CPLEX 8 1 USER S MANUAL 379 USING PARALLEL OPTIMIZERS 380 occur with the parallel optimizer here too Larger problems with a somewhat smaller aspect ratio may also benefit from parallel simplex optimization Since it is difficult to predict where the breakpoint will be we encourage you to experiment If you decide to use the parallel simplex optimizer on the subproblems of a MIP see other special consideratio
380. ll instead Q e O D e m ES 7 ey i ES Q lt IloRange maxrange IloNumVar maxvar IloNum violation cplex getQuality IloCplex MaxPrimalInfeas amp maxrange amp maxvar ILOG CPLEX will copy the variable or constraint handle in which the maximum violation occurs to maxvar or maxrange and make the other handle an empty one The maximum primal infeasibility is only one example of a wealth of quality measures The full list is defined by the nested enumeration type I1oCplex Quality All of these can be used as a parameter for the getQuality methods though some measures are not available for all optimizer option choices A list of solution qualities is given in Appendix D of the ILOG CPLEX 6 1 Reference Manual Modifying a Model In some applications you may want to solve the modification of another model in order for example to do scenario analysis or to make adaptations based on the solution of the first model To do this you do not have to start a new model from scratch but instead you can take an existing model and change it to your needs This is done by calling the modification methods of the individual modeling objects When an extracted model is modified the modification is tracked in the cplex object This is done through notification Whenever a modification method is called cp1ex objects that have extracted the model are notified about it The cplex objects then track the modification in
381. loModeler IloModeler defines an interface for building optimization models This interface defines methods for constructing variable constraint and objective function objects Modeling Variables A modeling variable in Concert Technology is represented by an object of type IloNumVar or one of its extensions You can choose from a variety of methods defined in 11oModeler and IloMPModeler to create one or multiple modeling variable objects An example of the method is IloNumVar x cplex numVar lb ub IloNumVarType Float xname This constructor method allows you to set all the attributes of a variable its lower and upper bounds its type and its name Names are optional in the sense that nu11 strings are considered to be valid as well ILOG CPLEX 8 1 USER S MANUAL 61 O E c8 g lt cs 5 o o Q lt z fa MODELING WITH CONCERT TECHNOLOGY 62 The other constructor methods for variables are provided mainly for ease of use For example because names are not frequently assigned to variables all variable constructors come in pairs where one variant requires a name string as the last parameter and the other one does not defaulting to a nu11 string Integer variables can be created using the int Var methods and do not require the type IloNumVarType Int to be passed as this is implied by the method name The bound parameters are also specified more consistently as integers These method
382. loating point data should be avoided as it can result in unnecessarily ill conditioned problems For more information refer to Numerical Difficulties on page 135 While Concert Technology supports very general expressions only linear piecewise linear and quadratic expressions can be used in models to be solved with IloCplex When you are done using an expression object that is you created a constraint with it you need to delete it by calling its method end for example Q e O D m ES 7 ey i ES ite lt expr end Declaring the Objective The lloObjective Object Objects of class 1100b jective represent objective functions of optimization models IloCplex may only handle models with at most one objective function though the modeling API provided by Concert Technology does not impose this restriction An objective function is specified by creating an instance of 1100bjective For example IloObjective obj env L x 1 2 x 2 3 x 3 IloObjective Minimize defines the objective to minimize the expression 1 x 1 2 x 2 3 x 3 Adding Constraints The lloRange Object Similarly objects of class IloRange represent constraints of the form lower bound Sexpression Supper bound Any floating point value or IloInfinity can be used for the bounds For example IloRange rl env 3 0 x 1 x 2 3 0 defines the constraint x 1 x 2 3 0 Formulating a Problem The lloModel Object
383. lso available for the probing fractional cut and disjunctive cut callbacks In particular the function to abort the current optimization is provided by the class 110Cplex CallbackI IloCplex Callback and is thus available to all callbacks There are two ways of implementing callbacks for IloCplex a more complex way that exposes all the C implementation details and a simplified way that uses macros to handle the C technicalities Since the Java programing language does not provide macros only the more complex way is available for Java We will first explain the more complex way and discuss the underlying design To quickly implement your callback without details about the internal design proceed directly to Writing Callbacks with Macros on page 343 Writing Callback Classes by Hand To implement your own callback for IloCp1lex first select the callback class corresponding to the callback you want implemented From it derive your own implementation class and overwrite the virtual method main This is where you implement the callback actions using the protected member functions of the callback class from which you derived your callback or one of its base classes ILOG CPLEX 8 1 USER S MANUAL USING CALLBACKS Next write a function that creates a new object of your implementation class using the environment operator new and returning it as an I1oCplex Callback handle object Here is an example implementation of such a function
384. lution quality 165 solution quality 141 solutions on screen 299 variables 292 DPE file format 257 290 DUA file format 290 dual feasibility 157 dual residual 141 dual simplex optimizer perturbing objective function 138 selecting 125 stalling 138 see also simplex dual variable solution data 43 duality gap 157 E elapsed time for the MIP optimizer 377 EMB file format 290 empty goal 321 326 end member function IloEnv class 34 enter Interactive Optimizer command 225 entering 225 LPs for barrier optimizer 159 mixed integer programs MIPs 225 network arcs 181 network data 181 network data from file 189 network nodes 181 enumeration Algorithm 39 BasisStatus 44 BoolParam 40 IntParam 40 NumParam 40 Quality 45 Status 42 ILOG CPLEX 8 1 INDEX String Param40 environment initializing 85 multithreaded 85 parameter specification file 401 releasing 87 variable 401 environment object constructing 34 EpAGap 252 EpGap 252 eq method 63 Error return status 67 error checking diagnostic routines for 94 MPS file format 293 problem dimensions 121 error handling in Concert Technology Library 47 example columnwise modeling 50 100 contents of IIS file 145 creating multi dimensional arrays 50 FORTRAN 96 message handler 298 MIP node log file 247 MIP optimization 258 MIP problem from file 269 MIP with SOS and priority orders 275 network optimization 177 optimizing QP 203 output channels 298 output from infeasib
385. lver and Aggregator When you invoke the MIP optimizer whether through the Interactive Optimizer command mipopt through a call to the Concert Technology IloCplex method solve or through the Callable Library routine CPXmipopt ILOG CPLEX by default automatically preprocesses your problem Table 8 8 summarizes the preprocessing parameters In preprocessing ILOG CPLEX applies its presolver and aggregator one or more times to reduce the size of the integer program in order to strengthen the initial linear relaxation and to decrease the overall size of the mixed integer program Table 8 8 Parameters for Controlling MIP Preprocessing Concert Technology Callable Library Interactive Command Comment Library Parameter Parameter set preprocessing aggregator AggInd CPX PARAM AGGIND on by default set preprocessing presolve PreInd CPX PARAM PREIND on by default set preprocessing boundstrength BndStrenInd CPX PARAM BNDSTRENIND presolve must be on set preprocessing coeffreduce CoeRedInd CPX PARAM COEREDIND presolve must be on set preprocessing relax RelaxPreInd CPX PARAM RELAXPREIND applies to relaxation wo uo set preprocessing reduce Reduce CPX PARAM REDUCE all on by default G oA set preprocessing numpass PrePass CPX_PARAM_PREPASS automatic by default S dE U The parameters Reduce and Numpass have the same meanings for LP QP and MIP Preprocessing on page 127 explains the meanings and
386. ly handles memory allocations to accommodate the changing size of a problem object as you modify it And it manages using a cache most changes to prevent inefficiency when the changes will require memory re allocations If an application builds a large problem in small increments you may be able to improve performance by increasing the growth parameters RowGrowth ColGrowth and NzGrowth In particular if you know reasonably accurate upper bounds on the number of rows columns and nonzeros and you are building a large problem in very small pieces with many calls to the problem modification routines then setting the growth parameters to the known upper bounds will ILOG CPLEX 8 1 USER S MANUAL 133 o 2 Q T me Uv al e D 3 7 DIAGNOSING PERFORMANCE PROBLEMS make ILOG CPLEX perform the fewest allocations and may thus improve performance of the problem modification routines However overly generous upper bounds may result in excessive memory use Diagnosing Performance Problems 134 While some linear programming models offer opportunities for performance tuning others unfortunately entail outright performance problems that require diagnosis and correction This section indicates how to diagnose and correct such performance problems as lack of memory or numerical difficulties Lack of Memory To sustain computational speed ILOG CPLEX should use only available physical memory rather than virtual mem
387. m has large objective values consider increasing BarObjRng Also if you know that your problem has large objective values consider changing the barrier algorithm by resetting the BarAlg parameter Diagnosing Barrier Optimizer Infeasibility When the ILOG CPLEX Barrier Optimizer terminates and reports an infeasible solution all the usual solution information is available However the solution values reduced costs and dual variables reported then do not correspond to a basis hence that information does not have the same meaning as the corresponding output from the ILOG CPLEX simplex optimizers Actually since the ILOG CPLEX Barrier Optimizer works in a single phase all reduced costs and dual variables are calculated in terms of the original objective function If the ILOG CPLEX Barrier Optimizer reports to you that a problem is infeasible but you still need a basic solution for the problem use the primal simplex optimizer ILOG CPLEX will then use the solution provided by the barrier optimizer to determine a starting basis for the primal simplex optimizer When the primal simplex optimizer finishes its work you will have an infeasible basic solution for further infeasibility analysis If the default algorithm in the ILOG CPLEX Barrier Optimizer determines that your problem is primal infeasible or dual infeasible then try the alternate algorithms in the barrier optimizer These algorithms though slower than the default are better a
388. m of parallelism at the root by selecting a specific optimizer with the starting algorithm parameter RootAlg in Concert CPX PARAM STARTALG in the Callable Library set mip strategy startalgorithm in the Interactive Optimizer The parallel threads will all be applied to the selected starting algorithm to the extent that the algorithm supports parallelism Parallel Barrier in particular is a frequent choice for this purpose Later sections contain information on the Parallel Barrier Optimizer and the Parallel Simplex Optimizer Note that if you use the barrier optimizer at the root of an MIQP problem you must also use it for the nodes This restriction does not apply in the case of MILP Individual Optimizer Parallel Processing Parallelism in either barrier or simplex is ordinarily controlled by the global thread count parameter but this default behavior can be overridden by the individual optimizer thread limit parameters BarThreads and SimThreads respectively The degree of parallelism within the branch amp cut tree likewise can be controlled by the MIP thread limit MipThreads which overrides the global thread limit This capability to set any or all of MipThreads BarThreads and SimThreads permits great flexibility in the use of parallel resources during the solution of a MIP model For example on a model where only a small number of nodes is active at any one time the benefit of parallel solution of these nodes is limited If the in
389. matically In this context numerical difficulties mean such phenomena as repeated occurrence of singularities little or no progress toward reaching the optimal objective function value little or no progress in scaled infeasibility repeated problem perturbations and repeated occurrences of the solution becoming infeasible While ILOG CPLEX will usually achieve an optimal solution in spite of these difficulties you can help it do so more efficiently This section describes situations in which you can help Some problems will not be solvable even after you take the measures we suggest Problems can be so poorly conditioned that their optimal solutions are beyond the numerical precision of your computer Numerically Sensitive Data There is no absolute link between the form of data in a model and the numerical difficulty the problem poses Nevertheless certain choices in how you present the data to ILOG CPLEX can have an adverse effect ILOG CPLEX 8 1 USER S MANUAL 135 o 2 Q T U Uv al D 3 7 DIAGNOSING PERFORMANCE PROBLEMS 136 Placing large upper bounds say in the neighborhood of 7 e to 1e on individual variables can cause difficulty during Presolve If you intend for such large bounds to mean no bound is really in effect it is better to simply not include such bounds in the first place Large coefficients anywhere in the model can likewise cause trouble at various poin
390. me the constructor of CtCallbackI takes three parameters called 1hs rhs and eps The constructor stores them as private members to have direct access to them in the callback function implemented as method main Notice i http w ww ilog com products optimization tech researchpapers cfm MIPTheory ILOG CPLEX 8 1 USER S MANUAL 361 USING CALLBACKS 362 the comma between the type and the argument object in the macro invocation Here is how the macro expands class CtCallbackI public IloCplex CutCallbackI IloExprArray lhs IloNumArray rhs IloNum eps public IloCplex CallbackI duplicateCallback const return new getEnv CtCallbackI this CtCallbackI IloExprArray xlhs IloNumArray xrhs IloNum xeps lhs xlhs rhs xrhs eps xeps void main IloCplex Callback CtCallback IloEnv env IloExprArray lhs IloNumArray rhs IloNum eps return IloCplex Callback new env CtCallbackI lhs rhs eps void CtCallbackI main where the actual implementation code has been substituted with Similar macros are provided for other numbers of parameters ranging from 0 through 7 for all callback classes The first parameter lhs is an array of expressions and the parameter rhs is an array of values These parameters are the left hand side and right hand side values of cuts of the form lhs amp rhs to be tested for violation and potentially added The third parameter
391. me models might also be solved by using other algorithms such as the class IloSolver for constraint programming or by using a hybrid algorithm consisting of both IloSolver and ILOG CPLEX Some models on the other hand cannot be solved with ILOG CPLEX The makeup of the model determines whether or not ILOG CPLEX can be used to solve it More precisely in order to be handled by 11oCplex objects a model may only consist of modeling objects of the following classes Table 1 1 Concert Technology Modeling Objects To model Use numerical variables objects of class 11oNumVar as long as they are not constructed with a list of feasible values semi continuous variable objects of class 11o0SemiContVar linear objective functions objects of class IloOb jective with linear or piecewise linear expressions quadratic objective functions objects of class IloObjective with quadratic expressions linear constraints objects of class 11oRange with linear or piecewise linear expressions variable type conversions objects of class IloConversion special ordered sets of type 1 objects of class I1oSOS1 special ordered sets of type 2 objects of class IloSOS2 and constraints objects of class 11oAnd ILOG CPLEX 8 1 USER S MANUAL 37 SOLVING CONCERT TECHNOLOGY MODELS WITH ILOCPLEX 38 For a description of special ordered sets see Using Special Ordered Sets on page 244 The last class 110And is listed for completeness only and is generally not us
392. meter BarColNz The default value of the column nonzeros parameter is 0 zero that value tells ILOG CPLEX to calculate the parameter automatically To see the current value of the column nonzeros parameter either one you have set or one ILOG CPLEX has automatically calculated you need to look at the level two display by setting the BarDisplay parameter to 2 If you determine that the current value of the column nonzeros parameter is inappropriate for your problem and thus tells ILOG CPLEX to remove too many dense columns then you can increase the parameter BarCo1Nz to keep the number of dense columns removed low Small Numerical Inconsistencies and Tight Convergence Tolerance If your problem contains small numerical inconsistencies it may be difficult for the ILOG CPLEX Barrier Optimizer to achieve a satisfactory solution at the default setting of the complementarity convergence tolerance In such a case you should increase the BarEpComp parameter to a value greater than its default e Unbounded Variables and Unbounded Optimal Faces An unbounded optimal face occurs in an LP or QP that contains a sequence of optimal solutions all with the same value for the objective function and unbounded variable values The ILOG CPLEX Barrier Optimizer will fail to terminate normally if an undetected unbounded optimal face exists Normally the ILOG CPLEX Barrier Optimizer uses its barrier growth parameter BarGrowth to detect such condi
393. mize MIP n goto TERMINATE solstat CPXgetstat env 1p Write the output to the screen printf nSolution status d n solstat status CPXgetmipobjval env lp amp objval if status 4 fprintf stderr No MIP objective value available Exiting n goto TERMINATE printf Solution value f n n objval The size of the problem should be obtained by asking CPLEX what the actual size is rather than using what was passed to CPXcopylp cur numrows and cur numcols store the current number of rows and columns respectively cur numrows CPXgetnumrows env 1p cur numcols CPXgetnumcols env 1p status CPXgetmipx env lp x 0 cur numcols 1 if status fprintf stderr Failed to get optimal integer x n goto TERMINATE status CPXgetmipslack env lp slack 0 cur numrows 1 if status fprintf stderr Failed to get optimal slack values n goto TERMINATE for i 0 i lt cur numrows i ILOG CPLEX 8 1 USER S MANUAL EXAMPLE OPTIMIZING A BASIC MIP PROBLEM printf Row d Slack 10f n i slack i for j 0 J lt cur numcols J printf Column d Value 10f n j x j 1 Finally write a copy of the problem to a file status CPXwriteprob env lp mipexl lp NULL if status fprintf stderr Failed to write LP to disk n goto TERMINATE TERMINATE Free up the problem as allocated b
394. mmarizes display options in the Interactive Optimizer that are specific to MIP problems Table 8 1 Interactive Optimizer Display Options for MIP Problems Interactive command Purpose display problem binaries lists variables restricted to binary values display problem generals lists variables restricted to integer values display problem semi continuous lists variables of type semi continuous and semi integer display problem integers lists all of the above display problem sos lists the names of variables in one or more Special Ordered Sets display problem stats lists LP statistics plus binary variable types if present general variable types if present and number of SOS if present In the Concert Technology Library use one of the accessor methods supplied with the appropriate object class such as 1108082 getVariables Refer to the ILOG Concert Technology Reference Manual for more information From the Callable Library use the routines CPXgetctype and CPXgetsos to access this information Changing Problem Type in MIPs 226 Concert Technology 11oCplex programs treat all models as capable of containing integer variables and thus these variable declarations may be added or deleted at will When extracting a model with integer variables it will automatically detect it as a MIP and make the required adjustments to data structures However the other ways of using ILOG
395. mmunication channels and your problem objects For users familiar with object oriented design patterns this design is that of a factory where IloCplex is a factory for modeling objects The advantage of such a design is that code which creates a model using the Concert Technology modeling interface can be used not ILOG CPLEX 8 1 USER S MANUAL 59 O fe 3 c8 go lt cs 5 9 0 o e lt fe MODELING WITH CONCERT TECHNOLOGY only with IloCplex but also with any other factory class for instance IloSolver This allows you to try different ILOG optimization technologies for solving your model User Written Application Concert Technology modeling interfaces lloCplex ILOG CPLEX database Figure 2 1 A View of Concert Technology for Java Users Modeling with Concert Technology 60 An optimization problem is represented by a set of interconnected modeling objects in an IloCplex object Modeling objects in Concert Technology are objects of type 11oNumVar and its extensions or Il1oAddable and its extensions Since these are Java interfaces and not classes objects of these types cannot be created explicitly Rather modeling objects are created using methods of an 11oModeler or one of its extensions such as IloMPModeler or IloCPModeler For this discussion we will concentrate on TloModeler and IloMPModeler because the class IloCplex implements these interf
396. mn ILOG CPLEX either records the objective value at the node or a reason to fathom the node A node is fathomed if the solution of a subproblem at the node is infeasible or if the value of objective function at the node is worse than the cutoff value for branch amp cut or if the node supplies an integer solution In the column labeled TInf ILOG CPLEX records the number of integer infeasible variables and special ordered sets If no solution has been found the next column is left blank otherwise it records the best integer solution found so far ILOG CPLEX 8 1 USER S MANUAL 247 PROGRESS REPORTS INTERPRETING THE NODE LOG The column labeled Cuts Best Node records the best objective function value of all the unexplored nodes If the word Cuts appears in this column it means various cuts were generated if a particular name of a cut appears then only that kind of cut was generated The column labeled It Cnt records the cumulative iteration count of the algorithm solving the subproblems Until a solution has been found the column labeled Gap is blank If a solution has been found the relative gap value is printed when it is less than 999 99 otherwise hyphens are printed The gap is computed as abs best integer best node 1e 10 abs best integer Consequently the printed gap value may not always move smoothly In particular there may be sharp improvements whenever a new best integer solution is found ILOG CPLEX also l
397. mple Dietary Optimization The optimization problem solved in this example is to compose a diet from a set of foods so that the nutritional requirements are satisfied and the total cost is minimized Example diet cpp illustrates Q e 3 iv e m E o ig zz i ES e Ko lt Creating a Model Row by Row Creating a Model Column by Column Creating Multi Dimensional Arrays with IloArray Using Arrays for Input Output 9 Solving the Model with IloCplex Problem Representation The problem contains a set of foods which are the modeling variables a set of nutritional requirements to be satisfied which are the constraints and an objective of minimizing the total cost of the food There are two ways of looking at this problem The problem can be modeled by rows by entering the variables first and then adding the constraints on the variables and the objective function The problem can be modeled by columns by constructing a series of empty constraints and then inserting the variables into the constraints and the objective function Concert Technology is equally suited for both kinds of modeling in fact you can even mix both approaches in the same program If a new food product is created you can create a new variable for it regardless of how the model was originally built Similarly if a new nutrient is discovered you can add a new constraint for it Creating a Model Row by Row You walk int
398. ms 3 Scaling Poorly conditioned problems that is problems in which even minor changes in data result in major changes in solutions may benefit from an alternative scaling method Scaling attempts to rectify poorly conditioned problems by multiplying rows or columns by constants without changing the fundamental sense of the problem If you observe that your problem has difficulty staying feasible during its solution then you should consider an alternative scaling method Scaling is determined by the parameter ScaInd and may be set to any of the following values Table 5 5 ScalndParameter Values for Scaling Methods Scalnd Value Meaning 1 no scaling 0 equilibration scaling default 1 aggressive scaling Refactorization Frequency ILOG CPLEX dynamically determines the frequency at which the basis of a problem is refactorized in order to maximize iteration speed On very large problems ILOG CPLEX refactorizes the basis matrix infrequently Very rarely should you consider increasing the number of iterations between refactorizing The refactorization interval is controlled by the ReInv parameter The default value of 0 means ILOG CPLEX will decide dynamically any positive integer specifies the user s chosen factorization frequency ILOG CPLEX 8 1 USER S MANUAL TUNING LP PERFORMANCE Crash It is possible to control the way ILOG CPLEX builds an initial crash basis through the CraInd param
399. ms x zobj 0 1 0 zobj 1 2 0 zobj 2 3 0 zobj 3 1 0 zmatbeg 0 0 zmatbeg 1 2 zmatbeg 2 5 zmatbeg 3 zmatcnt 0 2 zmatcnt 1 3 zmatcnt 2 2 zmatcnt 3 2 zmatind 0 0 zmatind 2 0 zmatind 5 0 zmatind 7 0 zmatval 0 1 0 zmatval 2 1 0 zmatval 5 1 0 zmatval 7 10 0 zmatind 1 1 zmatind 3 1 zmatind 6 1 zmatval 1 1 0 zmatval 3 3 0 zmatval 6 1 0 zmatind 4 2 zmatind 8 2 zmatval 4 1 0 zmatval 8 3 5 zlb 0 0 0 zlb 1 0 0 zlb 2 0 0 zlb 3 2 0 zub 0 40 0 zub 1 CPX INFBOUND zub 2 CPX INFBOUND zub 3 3 0 zctype 0 C zctype 1 I zctype 2 I zctype 3 I The right hand side values don t fit nicely on a line above So put them here zsense 0 zrhs 0 Il zsense 1 zrhs 1 ll ILOG CPLEX 8 1 y UBUS 20 0 L 30 0 USER S MANUAL EXAMPLE USING SOS AND PRIORITY zsense 2 E zrhs 2 0 0 TERMINATE if status free and null char amp zprobname free and null char amp zobj free and null char amp zrhs free and null char amp zsense free and null char amp zmatbeg free and null char amp zmatcnt free and null char amp zmatind free and null char amp zmatval free and null char amp zlb free and null char amp zub free and null char amp zctype else numcols_p N
400. n can only specify a type for a variable that is in a model Converting the type more than once is an error because there is no rule about which would have precedence However this is not a restriction since you can remove the conversion from a model and add a new one In Concert Technology two kinds of errors are distinguished 1 Programming errors such as e accessing empty handle objects e mixing modeling objects from different environments e accessing Concert Technology array elements beyond an array s size and e passing arrays of incompatible size to functions Such errors are usually an oversight of the programmer Once they are recognized and fixed there is usually no danger of corrupting an application In a production version it is not necessary to handle these kinds of errors In Concert Technology such error conditions are handled using assert statements If compiled without DNDEBUG the error check is performed and the code aborts with an error message indicating which assertion failed A production version should then be compiled with the DNDEBUG compiler option which removes all the checking In other words no CPU cycles are consumed for checking the assertions 2 Runtime errors such as memory exhaustion A correct program assumes that such failures can occur and therefore must be treated even in a production version In Concert Technology if such an error condition occurs an exception is thrown ILOG
401. n method is the optimization method o default p primal simplex d dual simplex n network with dual simplex cleanup ILOG CPLEX 8 1 USER S MANUAL 215 EXAMPLE 216 READING A QP FROM A FILE b barrier without crossover Example qpex2 example mps xf Bring in the CPLEX function declarations and the C library header file stdio h with the following single include finclude ilcplex cplex h Bring in the declarations for the string and character functions and malloc include lt ctype h gt include lt stdlib h gt include lt string h gt Include declarations for functions in this program static void free_and_null char ptr usage char progname irit main int argc char argv Declare and allocate space for the variables and arrays where we will store the optimization results including the status objective value maximum bound violation variable values and basis int solnstat solnmethod solntype double objval maxviol double x NULL int cstat NULL int rstat NULL CPXENVptr env NULL CPXLPptr lp NULL int status 0 int ae int cur_numrows cur_numcols int method char basismsg Check the command line arguments if arge 3 E strchr podbn argv 2 0 NULL usage argv 0 goto TERMINATE Initialize the CPLEX environment env CPXopenCPLEX amp status ILOG CPLEX 8 1 USER S
402. n index will correspond to the correct row or column name Double checking names against index numbers is the only sure way to determine which changes may have been made to matrix ILOG CPLEX 8 1 USER S MANUAL ILOG CPLEX PROGRAMMING PRACTICES indices in such a context The routines CPXget rowindex and CPXgetcolindex translate names to indices Character Strings You can pass character strings as parameters to various ILOG CPLEX routines for example as row or column names The Interactive Optimizer truncates output strings usually at 18 characters Routines from the Callable Library truncate strings at 255 characters in output text files such as MPS LP and SOS text files but not in binary SAV files Routines from the Callable Library also truncate strings at 255 characters in names that occur in messages Routines of the Callable Library that produce log files such as the simplex iteration log file or the MIP node log file truncate at 16 characters The Callable Library routine CPXwritesol truncates character strings in binary solution files at 8 characters and in text solution files at 16 characters Input such as names read from LP and MPS files or typed interactively by the enter command are truncated to 255 characters However we do not recommend that you rely on this truncation because unexpected behavior may result Checking Problem Data If you inadvertently make an error entering problem data the problem o
403. n the source of an anomaly in the heap try making certain local variables temporarily global This debugging trick may prove useful after your ILOG CPLEX 8 1 USER S MANUAL TELL US application reads in a problem file or modifies a problem object If application behavior changes when you change a local variable to global then you may get from it a better idea of the source of the anomaly Solve the Problem You Intended Your application may inadvertently alter the problem and thus produce unexpected results To check whether your application is solving the problem you intended use the Interactive Optimizer as we suggest on page 118 and the diagnostic routines as described on page 94 You should not ignore any ILOG CPLEX warning message in this situation either so read your messages as we suggest on page 120 If you are working in the Interactive Optimizer we also suggest that you use the command display problem stats to check the problem dimensions Special Considerations for Fortran Check row and column indices Fortran conventionally numbers from one 1 whereas C and C number from zero 0 This difference in numbering conventions can lead to unexpected results with regard to row and column indices when your application modifies a problem or exercises query routines We strongly recommend that you use the Fortran declaration IMPLICIT NONE to help you detect any unintended type conversions as such inadvertent
404. n this problem and its 1p counterpart is somewhat arbitrary in terms of the steps that will be taken to solve it v A fej ES D 7 di Bulnjos Thus when using the Interactive Optimizer you use the command change problem with one of the following options milpormiqp indicating that you want ILOG CPLEX to treat the problem as an MILP or MIQP respectively This change in Problem Type makes the model ready for declaration of the integer variables via subsequent change type commands If you change the problem to be an MIQP and there are not already quadratic terms in the objective function an empty quadratic matrix is created ready for populating via the change qpterm command 9 lporgp indicating that you want all integer declarations removed from the variables in the problem If you choose the qp problem type and there are not already quadratic terms in ILOG CPLEX 8 1 USER S MANUAL 227 CHANGING PROBLEM TYPE IN MIPS 228 the objective function an empty quadratic matrix is created ready for populating via the change qpterm command From the Callable Library use the routine CPXchgprobt ype to change the Problem Type to CPXPROB MILP or CPXPROB MIQP for the MILP and MIQP case respectively and then assign integer declarations to the variables through the CPXcopyctype function Conversely remove all integer declarations from the problem by using CPXchgprobtype with Problem Type CPXPROB LP or CPXPROB
405. n this manual doing this carries the risk that this will make the model harder to solve and only delay the eventual exhaustion of available memory during branching Certainly if you increase the amount of available memory you extend the problem solving capability of ILOG CPLEX Unfortunately when a problem fails because of insufficient memory it is difficult to project how much further the process needed to go and how much ILOG CPLEX 8 1 USER S MANUAL 253 D A fej ES D 7 di Bulnjos TROUBLESHOOTING MIP PERFORMANCE PROBLEMS 254 more memory is needed to solve the problem For these reasons the following suggestions aim at avoiding memory failure whenever possible and recovering gracefully otherwise Reset the Tree Memory Parameter To avoid a failure due to running out of memory we recommend setting the working memory parameter WorkMen to a value significantly lower than the available memory on your computer in megabytes to instruct ILOG CPLEX to begin compressing the storage of nodes before it consumes all of available memory See the related topic Use Node Files for Storage on page 254 for other choices of what should happen when WorkMenm is exceeded Because the storage of nodes can require a lot of space it may also be advisable to set a tree limit on the size of the entire tree being stored so that not all of your disk will be filled up with working storage The call to the MIP optimizer will be stoppe
406. name option value Use the command display settings in the Interactive Optimizer to generate a list of current parameter settings Those settings will be recorded in the log file You can then edit the log file to create your parameter specification file display settings changed lists parameters different from the default display settings all lists all parameters Each entry on a line must be separated by at least one space or tab Blank lines in a parameter specification file are acceptable there are no provisions for comments in the file You may abbreviate parameter names to unique character sequences as you do in the set command As ILOG CPLEX reads a parameter specification file if the parameter name and value are valid ILOG CPLEX sets the parameter and writes a message about it to the screen and to the log file If ILOG CPLEX encounters a repeated parameter it uses the last value specified ILOG CPLEX terminates under the following conditions ifit encounters a parameter that is unknown ifit encounters a parameter that is not unique if the parameter is correctly specified but the value is missing invalid or out of range ILOG CPLEX 8 1 USER S MANUAL 401 Interactive Optimizer Commands Here is an example of a parameter specification file that resets the limits on the size of problem reads and opens a log file named problem log read constraints 50 read variables 100 read nonzeros 500 logfile prob
407. nd 137 complementarity 171 convergence tolerance 171 dense columns removed 171 infeasibility and 139 sensitivity 137 unbounded optimal face 171 numerical variable 37 numVarArray 62 O ObjDif 232 objective coefficients crash parameter and 133 modified in log file 178 network flows and 178 priority and 241 objective difference absolute 252 relative 252 objective function 63 accessing value 43 changing sense 182 constructor 63 create 61 free row as 293 in log file 178 in MPS file format 294 maximization 294 maximize 36 minimize 36 network flows and 176 quadratic terms in a single LP 69 representing with I100bjective 35 sign reversal in 294 objective value in log file 178 network flows and 176 object range parameter 172 unbounded 172 operator lt lt 36 operator gt gt 36 416 ILOG CPLEX 8 1 Optimal return status 67 optimality basis condition number and 137 cutoff parameters 253 duality and 257 infeasibility ration 163 normalized error and 165 singularities and 138 tolerance 141 142 252 relative 252 tolerance absolute 252 tolerance relative 252 optimization interrupting 352 stopping 241 352 optimization problem defining with modeling objects 32 representing with IloModel 35 optimization routine 84 optimizer barrier linear 156 to 173 barrier quadratic 195 to 221 differences between Barrier simplex 158 dual simplex 125 MIP 223 network 126 175 to 181 parallel 371 to primal simplex 125
408. nd it is rare that it offers any advantage over other settings In instances where Best Estimate node selection NodeSel 2 or 3 is in effect the BBInterval parameter determines the frequency at which backtracking is done by Best Bound anyway The default value of 7 works well but you can set it to 0 to assure that Best Estimate is used every time backtracking occurs ILOG CPLEX 8 1 USER S MANUAL 233 USING THE MIXED INTEGER OPTIMIZER 234 Once a node has been selected the variable selection parameter VarSe1 influences which variable is chosen for branching at that node Table 8 5 VarSel Parameter Values for Branching Variable Choice VarSel r Symbolic Value Branching Variable Choice Value 1 CPX VARSEL MININFEAS Branch strictly at the nearest integer value which is closest to the fractional variable 1 CPX_VARSEL_MAXINFEAS Branch strictly at the nearest integer value which is furthest from the fractional variable 0 CPX_VARSEL_DEFAULT ILOG CPLEX makes the determination of Default each branch direction 2 CPX_VARSEL_PSEUDO Use pseudo costs which derives an estimate about the effect of each proposed branch from duality information 3 CPX_VARSEL_STRONG Use Strong Branching which invests considerable effort in analyzing potential branches in the hope of drastically reducing the number of nodes that will be explored
409. nd parameters in the ILOG CPLEX Callable Library begin with CPX the names of C and Java classes in the ILOG CPLEX Concert Technology Library begin with 110 and both appear in this typeface for example CPXcopyobjnames or IloCplex Where specific language usage C Java C and so on is unimportant and the effect on the optimization algorithms is to be emphasized the names of ILOG CPLEX parameters are given as their Concert Technology variant Appendix A ILOG CPLEX Parameter Names contains a table showing the correspondence of these names to the 26 ILOG CPLEX 8 1 USER S MANUAL RELATED DOCUMENTATION Callable Library and the Interactive Optimizer Full information about CPLEX parameters is found in the LOG CPLEX Reference Manual Appendix A Text that is entered at the keyboard or displayed on the screen and commands and their options available through the Interactive Optimizer appear in this typeface for example set preprocessing aggregator n Values that you must fill in for example the value to set a parameter also appear in the same typeface as the command but slanted to indicate you must supply an appropriate value for example set simplex refactor i indicates that you must fill in a value for i Matrices are denoted in two ways e In printed material where superscripts and bold type are available we denote the product of A and its transpose like this AAT The superscript T indicates the matrix tr
410. nds on 725 and T35 combine with the row NODES to imply that T57 T58 20 However row D7 and the bound on 747 imply that T57 2 18 Since row D8 requires T58 2 30 we see that T57 T58 gt 48 so the constraints and bounds are infeasible Notice that every constraint and bound contributes to this infeasibility according to the definition of an IIS There are in consequence many different ways to modify such a problem to make it feasible The right change will depend on your knowledge of the problem When ILOG CPLEX records the constraints and bounds of an IIS it also lists as free all columns that intersect one or more rows in the IIS but do not have bounds in the IIS This portion of the file ensures that when you read the file into ILOG CPLEX the resulting problem satisfies the definition of an IIS After you read in such a file you can perform additional problem analysis within your ILOG CPLEX session ILOG CPLEX 8 1 USER S MANUAL 145 o J Q T U Uv E e D 3 7 DIAGNOSING LP INFEASIBILITY 146 Example Interpreting a Cumulative Constraint In the example that we have been looking at there were sufficiently few row and column bounds in the IIS for us to see the cause of infeasibility at a glance In contrast other IIS files may contain so many rows and columns that it becomes difficult to see the cause of infeasibility When an IIS contains many equality constraints and only a few bounds for example
411. ned when calling method get Status In contrast to most other Concert Technology classes exception classes are not handle classes Thus the correct type of an exception is lost if it is caught by value rather than by reference that is using catch IloException amp e This is one reason that we suggest catching I loException objects by reference as demonstrated in all examples See for example ilodiet cpp Some derived exceptions may carry information that would be lost if caught by value So if you output an exception caught by reference you may get a more precise message than when outputting the same exception caught by value There is a second reason for catching exceptions by reference Some exceptions contain arrays to communicate the reason for the failure to the calling function If this information were lost by calling the exception by value method end could not be called for such arrays and their memory would be leaked until env end is called After catching an exception by reference calling the exception s method end will free all the memory that may be used by arrays or expressions of the actual exception that was thrown In summary the preferred way of catching an exception is catch IloException amp e e end 48 ILOG CPLEX 8 1 USER S MANUAL EXAMPLE DIETARY OPTIMIZATION where IloException may be substituted for the desired Concert Technology exception class Exa
412. ng branching 252 StrongThreadLim 375 sum 62 surplus argument 308 symbolic constants 91 98 T tail 176 terminating because of singularities 138 because of stalling 139 because of time limit 147 MIP optimization 241 network optimizer iterations 179 Threads 375 threads 371 USER S MANUAL clones 379 parallel optimizers 371 performance and 372 thread safe 87 tolerance feasibility 179 Markowitz 138 139 optimality 142 relative optimality 252 tolerance parameters 232 TRE file format 242 254 292 TreLim 254 TXT file format 292 type conversion 82 variable change 61 U Unbounded return status 67 unbounded optimal face 159 171 Unknown return status 67 upper bound values choosing 63 utility routine defined 84 V variable accessing dual 43 cannot be added to a model 64 changing type 34 47 constructing an array 76 deleting 82 external 87 global 87 in expressions 34 modeling 61 numerical 37 order 292 removing from basis 46 ILOG CPLEX 8 1 INDEX representing with I1oNumVar 34 semi continuous 37 246 static 87 type 225 variable selection strategy strong branching 251 256 variable type change 61 variables create modeling 61 semi continuous 61 VarSel 375 VEC file format 160 292 vectors rim 293 violation bound 142 constraint 142 W WorkDir 166 255 working memory 166 WorkMem 166 242 254 USER S MANUAL 421 INDEX 422 ILOG CPLEX 8 1 USER S MANUAL
413. nnnn 118 Eliminating Common Programming Errors 0 00 e cece eee eee nnn 119 Check Your Include Files 2 0 0 0 0c cece Ih 120 Clean House and Try Again 0 2 eect rn 120 Read Your Messages ssa sse eX GU RR Re EROR HEURE EROR STR eae ee ee ee 120 Check Return Values lssseeseseeeeeeee hh hn 120 Beware of Numbering Conventions 00 cece eee eee tees 120 Make Local Variables Temporarily Global 0 000 c cece eee eee 120 ILOG CPLEX 8 1 USER S MANUAL TABLE OF CONTENTS Solve the Problem You Intended 00 e eee eet eee 121 Special Considerations for Fortran 2 0 0 cette eee 121 IH ee eee 121 Chapter 5 Solving Linear Programming Problems 20000see cece eeeeeee 123 Choosing an Optimizer for Your LP Problem 00 0c eee ee ee ee eee eee 124 Automatic Selection of Optimizer n sssaaa aaua aeaaee 125 Dual Simplex Optimizer 0 2 0 0 eet ee 125 Primal Simplex Optimizer 22x uie ERE Ep ed Rae en ERE ae ee ROGER Es 125 Network Optimizer oce gosig era cated a e hh rns 126 Barrier Optimizer llsleeleeeeee eee mcer 126 Sifting Optimizet sc bas eee re Re mma repe AU ERE AFER ATE RES 126 Concurrent Optimizer 2n Been Pea Rau Eee y rx Rer wed aw pu eres 127 Tuning LP Performances ice csc an dete aie eed ee ee ee ee 127 PreprocessifIg vrs veers uet dee eee ves APRA Fae Pd edi eate a ER RE RR 127 Starting from an Advanced Basis ee 129 Simplex Par
414. not be the optimal one for example the optimization may have terminated prematurely because it ran into an iteration limit ILOG CPLEX 8 1 USER S MANUAL SOLVING THE MODEL Additional information about a possible solution available in the IloCplex object can be queried with the method get Status returning an IloCplex Status object Possible statuses include Table 2 2 Solution Status Return Status Active Model Error It has not been possible to process the active model or an error occurred during the optimization Unknown It has not been possible to process the active model far enough to prove anything about it A common reason may be that a time limit was reached Feasible A feasible solution for the model has been proven to exist S o Bounded It has been proven that the active model has a finite bound in S oO 7 the direction of optimization However this does not imply the existence of a feasible solution 10 ABojouyda 39u09 Optimal The active model has been solved to optimality The optimal solution can be queried Infeasible The active model has been proven to possess no feasible solution Unbounded The active model has been proven to be unbounded The notion of unboundedness adopted by 11oCplex is technically that of dual infeasibility this does not include the notion that the model has been proven to be feasible Instead what has been proven is that if there is a feasibl
415. ns about nested parallelism in Using Parallel Optimizers on page 371 Platform Considerations The parallel simplex optimizer is only available in the OpenMP version of ILOG CPLEX which is not available on all platforms ILOG CPLEX 8 1 USER S MANUAL CPLEX RUNTIME DEVELOPMENT AND LICENSING PROCEDURES CPLEX Runtime Development and Licensing Procedures ILOG CPLEX uses the standard ILOG License Manager ILM The JLOG License Manager online documentation which comes with your software distribution describes ILM access keys or keys for short in more detail This section describes how to write applications that use ILM runtime access keys An ILOG CPLEX runtime license costs significantly less money than a regular development license However its usage is restricted to applications created by a particular developer or company In order to distinguish runtime access keys from development keys as well as runtime keys for applications created by other companies you need to call an additional routine in your source code before initializing the CPLEX environment Types of ILM Runtime Licenses ILM runtime licenses come in two forms file based and memory based File Based RTNODE RTSTOKEN or TOKEN Keys These are a file based access key that is tied to a particular computer or server Refer to the ILOG License Manager online documentation which can be found in your distribution source for information regarding how to establis
416. nsistency of the mapping of rows to constraints and columns to variables For example if a ranged constraint that uses variables not yet part of the IloLPMatrix is added to the IloLPMatrix new columns will automatically be added and associated to those variables See the online ILOG CPLEX Java Reference Manual for more information about IloLPMatrix methods O o E c8 go lt cs 5 o o Q lt z Modeling by Column The concept of modeling by column modeling comes from the matrix view of mathematical programming problems Starting from a degenerate constraint matrix with all its rows but no columns you populate it by adding columns to it The columns of the constraint matrix correspond to variables Modeling by column in ILOG CPLEX is not limited to IloLPMat rix but can be used with IloObjective and IloRange objects as well So for ILOG CPLEX modeling by column can be more generally described as creating new variables and immediately installing them in existing modeling objects Procedure for Modeling by Column Start by creating a description of how to install a new variable into existing modeling objects Such a description is represented by 11oColumn objects Individual 11o0Column objects describe how to install a new variable in one existing modeling object and are created with one of the 11oMPModeler column methods Several 11oColumn objects can be linked together with the 11oCplex add method
417. nt nNutr nutrMin getSize if foodMin getSize nFoods foodMax getSize nFoods nutrPer getSize nNutr nutrMax getSize nNutr cerr ERROR Data file filename lt lt contains inconsistent data lt lt endl throw 1 for i 0 i lt nNutr i if nutrPer i getSize nFoods cerr lt lt ERROR Data file lt lt argv 0 lt lt contains inconsistent data lt lt endl throw 1 Build model IloModel mod env IloNumVarArray Buy env if byColumn buildModelByColumn mod Buy foodMin foodMax foodCost nutrMin nutrMax nutrPer varType else buildModelByRow mod Buy foodMin foodMax foodCost ILOG CPLEX 8 1 USER S MANUAL 57 EXAMPLE DIETARY OPTIMIZATION nutrMin nutrMax nutrPer varType Solve model IloCplex cplex mod cplex exportModel diet sav cplex solve cplex out lt lt solution status lt lt cplex getStatus lt lt endl cplex out lt lt endl cplex out lt lt cost lt lt cplex getObjValue lt lt endl for i 0 i lt foodCost getSize i cplex out lt lt Buy lt lt i lt lt lt lt cplex getValue Buy i lt lt endl catch IloException amp ex cerr Error ex endl catch cerr lt lt Error lt lt endl env end return 0 cost 14 8557 BuyO 4 38525 Buyl 0 Buy2 0
418. nted sum of infeasibilities may be a symptom of this case If so it may be worthwhile to set a higher Markowitz tolerance just as in the more obvious case of numerical difficulties in Phase II Diagnosing LP Infeasibility ILOG CPLEX reports statistics about any problem that it optimizes For infeasible solutions it reports values that you can analyze to determine where your problem formulation proved infeasible In certain situations you can then alter your problem formulation or change ILOG CPLEX parameters to achieve a satisfactory solution When the ILOG CPLEX primal simplex optimizer terminates with an infeasible basic solution it calculates dual variables and reduced costs relative to the Phase I objective that is relative to the infeasibility function The Phase I objective function depends on the current basis Consequently if you use the primal simplex optimizer with various parameter settings an infeasible problem will produce different objective values and different solutions o gt Q T U Uv al D 3 7 ILOG CPLEX 8 1 USER S MANUAL 139 DIAGNOSING LP INFEASIBILITY 140 Inthe case of the dual simplex optimizer termination with a status of infeasibility occurs only during Phase II Therefore all solution values are relative to the problem s natural primal formulation including the values related to the objective function such as the dual variables and reduced costs As with the primal
419. number of rows You can check column density as we suggest in Nonzeros in Lower Triangle of AAT in the Log File on page 162 We also say more about column density in Detecting and Eliminating Dense Columns on page 167 In adjusting parameters you may need to experiment to find beneficial settings because the precise effect of parametric changes will depend on the nature of your LP problem as well as your platform hardware operating system compiler etc Once you have found satisfactory parametric settings keep them in a parameter specification file for re use as explained in Saving a Parameter Specification File on page 400 Out of Core Barrier Letting the Optimizer Use Disk for Storage Under default settings the ILOG CPLEX Barrier Optimizer will do all of its work using central memory variously referred to also as RAM core or physical memory For models too large to solve in the central memory on your computer or in cases where it is simply not desired to use this much memory it is possible to instruct the barrier optimizer to use disk for part of the working storage it needs specifically the Cholesky factorization Since disk is slower than central memory there may be some lost performance by making this choice on models that could be solved entirely in central memory but the out of core feature in the ILOG CPLEX Barrier Optimizer is designed to make this as efficient as possible It generally will be far more effective than relyin
420. nutrients are known and relevant for you For each nutrient you note the minimum and maximum amount that should be found in your diet Also you go through the list of foods and determine how much a food item will contribute for each nutrient This gives you one constraint per nutrient which can naturally be represented as a range constraint nutrmin i nutrper i j buy j nutrmax i where i represents the number of the nutrient under consideration nut zmin i and nutrmax i the minimum and maximum amount of nutrient i and nutrper i j the amount of nutrient i in food j Finally you specify your objective function sense L cost jJ buy 31 This way to create the model is shown in function populatebyrow in example diet c Creating a Model Column by Column You start with the medical book where you compile the list of nutrients that you want to ensure are properly represented in your diet For each of the nutrients you create an empty constraint nutrmin i lt lt nutrmax i where is left to be filled once you walk into your store You also set up the objective function to minimize the cost We will refer to constraint i as rng i and to the objective as Cost Now you walk into the store and for each food you check its price and nutritional content With this data you create a variable representing the amount you want to buy of the food type and install it in the objective function and constraints That
421. o better than the incumbent You control the path that CPLEX traverses in the tree through several parameters as summarized in Table 8 3 Table 8 3 Parameters for Controlling Branch amp Cut Strategy Interactive Optimizer Concert Technology Callable Library Routine Command lloCplex Method set mip strategy backtrack setParam BtTol n CPXsetdblparam env CPX PARAM BTTOL n set mip strategy nodeselect setParam NodeSel i CPXsetintparam env CPX PARAM NODESEL i set mip strategy variableselect setParam VarSel i CPXsetintparam env CPX PARAM VARSEL i set mip strategy bbinterval setParam BBInterval i CPXsetintparam env CPX PARAM BBINTERVAL i set mip strategy branch setParam BrDir i CPXsetintparam env CPX PARAM BRDIR i 232 During the branch amp cut algorithm ILOG CPLEX may choose to continue from the present node and dive deeper into the tree or it may backtrack that is begin a new dive from elsewhere in the tree The value of the backtrack parameter Bt To1 influences this ILOG CPLEX 8 1 USER S MANUAL USING THE MIXED INTEGER OPTIMIZER decision in terms of the relative degradation of the objective function caused by the branches taken so far in this dive Setting Bt Tol to a value near 0 0 increases the likelihood that a backtrack will occur while the default value near 1 0 makes it more likely that the present dive will continue to a resolution fathoming either via
422. o the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines the errors will be seen if the CPX PARAM SCRIND indicator is set to CPX ON if env NULL char errmsg 1024 fprintf stderr Could not open CPLEX environment Mn CPXgeterrorstring env status errmsg fprintf stderr s errmsg goto TERMINATE ILOG CPLEX 8 1 USER S MANUAL 183 EXAMPLE USING THE NETWORK OPTIMIZER WITH THE CALLABLE LIBRARY Turn on output to the screen status CPXsetintparam env CPX PARAM SCRIND CPX ON if status fprintf stderr Failure to turn on screen indicator error d n status goto TERMINATE Create the problem net CPXNETcreateprob env amp status netex1 A returned pointer of NULL may mean that not enough memory was available or there was some other problem In the case of failure an error message will have been written to the error channel from inside CPLEX In this example the setting of the parameter CPX PARAM SCRIND causes the error message to appear on stdout if net NULL fprintf stderr Failed to create network object Wn goto TERMINATE Fill in the data for the problem Note that since the space for the data already exists in local variables we pass the arrays directly to the routine to fill in the data structures status buildNetwork env net if status fprintf stderr Failed to b
423. o the store and compile a list of foods that are offered For each food you store the price per unit and the amount in stock For some foods that you particularly like you also set a minimum amount you would like to use in your diet Then for each of the foods you create a modeling variable to represent the quantity to be purchased for your diet Now you get a medical book and look up which nutrients are known and relevant for you For each nutrient you note the minimum and maximum amounts that should be found in your diet Also you go through the list of foods and determine how much a food item will contribute for each nutrient This gives you one constraint per nutrient which can naturally be represented as a range constraint ILOG CPLEX 8 1 USER S MANUAL 49 EXAMPLE 50 DIETARY OPTIMIZATION nutrMin i lt sum_j nutrPer i j Buy j lt nutrMax i where i represents the number of the nutrient under consideration nut rMin i and nutrMax i the minimum and maximum amount of nutrient i and nutrPer i j the amount of nutrient i in food j Finally you specify your objective function minimize sum_j cost j Buy jl This way of creating the model is shown in the function buildModelByRow in example ilodiet cpp Creating a Model Column by Column You start with the medical book where you compile the list of nutrients that you want to ensure are properly represented in your diet For each of the nutrients you create
424. obal cuts e With goals you can add global and local cuts by using global and local cut goals respectively e With callbacks you need to implement either a cut callback for global and local cuts or a branch callback for branching on local cuts Injecting solution candidates e With goals you inject solutions by using a solution goal z a E O 2 oS Us a UE Q e With callbacks you need to implement a heuristic callback to inject solutions Controlling the node selection strategy e With goals you control node selection by applying node evaluators to your search goal e With callbacks you control node selection by using a node callback ILOG CPLEX 8 1 USER S MANUAL 369 A COMPARISON OF GOALS AND CALLBACKS 370 Thus one of the main differences between goals and callbacks is that with goals all functionality is available from the execute method of the goal whereas with callbacks you must implement different callbacks to access different functionality As an example suppose you want to extend a search to satisfy additional constraints that could not conveniently be added as linear constraints to the model With callbacks you need to use an incumbent callback and a branch callback The incumbent callback has to reject an otherwise integer feasible solution if it violates such an additional constraint In this case the branch callback has to follow up with an appropriate branch to enforce the
425. oblem as its starting point when applicable After it finishes using ILOG CPLEX your application must free the problem object and release the ILOG CPLEX environment it has been using The following sections explain these steps in greater detail 2 D ie D D D o A 0 E lt Initialize the ILOG CPLEX Environment ILOG CPLEX needs certain internal data structures to operate In your own application you use a routine from the Callable Library to initialize these data structures You must initialize these data structures before your application calls any other routine in the ILOG CPLEX Callable Library To initialize a ILOG CPLEX environment you must use the routine CPXopenCPLEX This routine checks for a valid ILOG CPLEX license and then returns a C pointer to the ILOG CPLEX environment that is creates Your application then passes this C pointer to other ILOG CPLEX routines except CPXmsg As a developer you decide for yourself whether the variable containing this pointer should be global or local in your application Because the operation of checking the license can be relatively time consuming it is strongly recommended that you call the CPXopenCPLEX routine only once or as infrequently as possible in a program that solves a sequence of problems A multithreaded application needs multiple ILOG CPLEX environments Consequently ILOG CPLEX allows more than one environment to exist at a time I
426. oblem modification routines For example let s say a user has already solved a given problem and then changes the upper bound on a variable by means of an appropriate call to the Callable Library ILOG CPLEX will then begin any further optimization from the previous optimal basis If that basis is still optimal with respect to the new bound then ILOG CPLEX will return that information without even needing to refactor the basis Destroy the Problem Object Use the routine CPX reeprob to destroy a problem object when your application no longer needs it Release the ILOG CPLEX Environment After all the calls from your application to the ILOG CPLEX Callable Library are complete you must release the ILOG CPLEX environment by calling the routine CPXcloseCPLEX This routine tells ILOG CPLEX that E 2 D ie D D o A 5 lt all application calls to the Callable Library are complete ILOG CPLEX should release any memory allocated by ILOG CPLEX for this environment the application has relinquished the ILOG CPLEX license for this run thus making the license available to the next user ILOG CPLEX Programming Practices This section lists the programming practices we observe in developing and maintaining the ILOG CPLEX Callable Library The ILOG CPLEX Callable Library supports modern programming practices It uses no external variables Indeed no global nor static variables are used in the li
427. oblems but not valid for the feasible region of LP relaxation of the MIP problem Flow Cover Cuts Flow covers are generated from constraints that contain continuous variables where the continuous variables have variable upper bounds that are zero or positive depending on the setting of associated binary variables The idea of a flow cover comes from considering the constraint containing the continuous variables as describing a single node in a network where the continuous variables are in flows and out flows The flows will be on or off depending on the settings of the associated binary variables for the variable upper bounds The flows and the demand at the single node imply a knapsack constraint That knapsack ILOG CPLEX 8 1 USER S MANUAL 235 USING THE MIXED INTEGER OPTIMIZER constraint is then used to generate a cover cut on the flows that is on the continuous variables and their variable upper bounds Flow Path Cuts Flow path cuts are generated by considering a set of constraints containing the continuous variables that describe a path structure in a network where the constraints are nodes and the continuous variables are in flows and out flows The flows will be on or off depending on the settings of the associated binary variables Gomory Fractional Cuts Gomory fractional cuts are generated by applying integer rounding on a pivot row in the optimal LP tableau for a basic integer variable with a fractional solution value
428. of its default setting of 0 To reduce memory usage presolve may compress the arrays used for storage of the original model This can make more memory available for the use of the optimizer that the user has called Under default settings ILOG CPLEX will only perform this compression when using the out of core variant of the barrier optimizer discussed in Solving LP Problems with the Barrier Optimizer on page 156 You can explicitly turn this feature on or off by setting the presolve compression parameter PreCompress to 1 for off or 1 for on the default of 0 specifies the automatic setting In rare instances a user may wish to specify the number of analysis passes that the presolver or the aggregator makes through the problem The parameters PrePass and AggInd respectively control these two preprocessing features the default automat ic setting of 1 lets ILOG CPLEX determine the number of passes to make while a setting of 0 directs ILOG CPLEX to not use that preprocessing feature and a positive integer limits the number of passes to that value Under the automatic setting ILOG CPLEX applies the aggregator just once when it is solving an LP model for some problems it may be worthwhile to increase the Agg Ind setting The behavior under the PrePass default is less easy to predict but if the output log indicates it is performing excessive analysis you may wish to try a limit of five passes or some other modest value Another parameter
429. og file as it does for other LP optimizers Because barrier solutions prior to crossover are not basic solutions certain solution statistics associated with basic solutions are not available for a strictly barrier solution For example reduced costs and dual values are available for strictly barrier LP solutions but range information about them is not To help you evaluate the quality of a barrier solution more readily ILOG CPLEX offers a special display of information about barrier solution quality To display this information in the Interactive Optimizer use the command display solution quality after optimization When using the Component Libraries use the method ILOG CPLEX 8 1 USER S MANUAL 163 o 2 Q T U Ru cA e D 3 7 SOLVING LP PROBLEMS WITH THE BARRIER OPTIMIZER cplex getQuality or use the routines CPXgetintquality for integer information and CPXgetdblquality for double valued information Table 5 11 Barrier Solution Quality Display Item Meaning primal objective primal objective value cx dual objective dual objective value bly u w Iz duality gap difference between primal and dual objectives complementarity sum of column and row complementarity column complementarity total sum of x lj zi uj Xj wil column complementarity max maximum of x Ij zj and u x wj over all variables row complement
430. ogram qpex1 c appears here and online in the standard distribution VE File examples src qpexl c f Version 8 1 Do Copyright C 1997 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products y Jine ee ee ee ee ee ILOG CPLEX 8 1 USER S MANUAL 207 EXAMPLE CREATING A QP OPTIMIZING FINDING A SOLUTION qpexl c Entering and optimizing a quadratic programming problem Bring in the CPLEX function declarations and the C library header file stdio h with include of cplex h finclude lt ilcplex cplex h gt include lt stdlib h gt Bring in the declarations for the string functions include lt string h gt Include declaration for function at end of program static int setproblemdata char probname_p int numcols_p int numrows_p int objsen_p double obj_p double rhs_p char sense_p int matbeg_p int matcnt_p int matind p double matval p double lb p double ub p int qmatbeg p int qmatcnt p int gmatind p double qgmatval p static void free and null char ptr The problem we are optimizing will have 2 rows 3 columns 6 nonzeros and 7 nonzeros in the quadratic coefficient matrix define NUMRO
431. ogs its addition of cuts to a model Here is an example of a node log file from a problem where ILOG CPLEX added several cover cuts MIP Presolve eliminated 0 rows and 1 columns MIP Presolve modified 12 coefficients Reduced MIP has 15 rows 32 columns and 97 nonzeros Presolve time 0 00 sec Nodes Cuts Node Left Objective IInf Best Integer Best Node ItCnt Gap 0 0 2819 3574 7 2819 3574 35 2881 8340 8 Covers 4 44 2881 8340 12 Covers 3 48 3 6 3089 0000 0 3089 0000 2904 0815 62 5 99 Cover cuts applied 30 Integer optimal solution Objective 3 0890000000e 003 Solution time 0 10 sec Iterations 192 Nodes 44 ILOG CPLEX also logs the number of clique inequalities in the clique table at the beginning of optimization Cuts generated at intermediate nodes are not logged individually unless they happen to be generated at a node logged for other reasons ILOG CPLEX logs the number of applied cuts of all classes at the end ILOG CPLEX also indicates in the node log file each instance of a successful application of the node heuristic The following example shows a node log file for a problem where the heuristic found a solution at node 0 The denotes a node generated by the heuristic 248 Nodes Cuts Node Left Objective IInf Best Integer Best Node ItCnt Gap 0 0 403 8465 640 403 8465 4037 405 2839 609 Cliques 10 5208 405 2891 612 Cliques 2 5288 Heuristic feasible at 437 000 still looking Heuristic feasible at 437 000
432. olution of x1 1 0 and x2 1 0 giving an objective function value of 2 0 Now see what happens when using slightly more accurate data in terms of the fractional values that are clearly intended to be expressed Maximize obj xl x2 Subject To cl 0 333333333 x1 0 666666667 x2 1 c2 xl 2 x2 3 End The solution to this problem has x1 3 0 and x2 0 0 giving an optimal objective function value of 3 0 a result qualitatively different from that of the first model Since this latter result is the same as would be obtained by removing constraint c1 from the model entirely this is a more satisfactory result Moreover the numerical stability of the optimal basis as indicated by the condition number discussed in the next section is vastly improved ILOG CPLEX 8 1 USER S MANUAL DIAGNOSING PERFORMANCE PROBLEMS The result of the extra precision of the input data is a model that is less likely to be sensitive to rounding error or other effects of solving problems on finite precision computers or in extreme cases will be more likely to produce an answer in keeping with the intended model The first example above is an instance where the data truncation has fundamentally distorted the problem being solved Even if the exact integer data version of the constraint is not present with the decimal version the truncated decimal version no longer exactly represents the intended meaning and in conjunction with other constraints in your mo
433. on procedure for your particular application From what you learn by experimenting with commands in the Interactive Optimizer you can more readily choose which method or routine from the Component Libraries to call in your application Program with a View toward Maintenance and Modifications Good programming practices save development time and make an application easier to understand and modify Tips for Successful Application Development on page 113 describes our programming conventions in developing ILOG CPLEX In addition we recommend the following programming practices Comment Your Code Comments written in mixed upper and lower case will prove useful to you at a later date when you stare at code written months ago and try to figure out what it does They will also prove useful to our staff should you need to send us your application for technical support Write Readable Code Follow conventional formatting practices so that your code will be easier to read both for you and for others Use fewer than 80 characters per line Put each statement on a separate line Use white space for example space blank lines tabs to distinguish logical blocks of code Display compound loops with clearly indented bodies Display i statements like combs that is we recommend that you align if and else in the same column and then indent the corresponding block Likewise we recommend that you indent the body of compound statements loops and o
434. on reports it removes these temporary range variables from the constraint matrix Extra Rim Vectors in MPS Files The MPS format allows multiple right hand sides RHSs multiple bounds and multiple range vectors It also allows extra free rows Together these features are known as extra rim vectors By default the ILOG CPLEX MPS reader selects the first RHS bound and range definitions that it finds The first free row that is N type row becomes the objective function and the remaining free rows are discarded The extra rim data are also discarded z a D3 qe oS Us a UE Q Naming Conventions in MPS Files ILOG CPLEX accepts any noncontrol character within a name However ILOG CPLEX recognizes blanks that is spaces as delimiters so you must avoid them in names You should also avoid dollar sign and asterisk as characters in names because they normally indicate a comment within a data record Error Checking in MPS Files Fairly common problems in MPS files include split vectors unnamed columns and duplicated names ILOG CPLEX checks for these conditions and reports them If repeated ILOG CPLEX 8 1 USER S MANUAL 293 MANAGING 294 INPUT amp OUTPUT rows or columns occur in an MPS file ILOG CPLEX reports an error and stops reading the file You can then edit the MPS file to correct the source of the problem Saving Modified MPS Files You may often want to save a modified MPS file for late
435. oncurrent Optimizer On a multiprocessor computer the concurrent optimizer launches distinct LP optimizers on multiple threads terminating as soon as the first optimizer finishes The first thread uses the same strategy as the single processor automatic LPMethod setting 0 If a second thread is available the concurrent optimizer runs the barrier optimizer on it If a third processor is available dual simplex primal simplex and barrier are all run All further available threads are devoted to parallelizing the barrier optimization It should be noted that the barrier optimization is not considered complete until the crossover step has been performed and simplex reoptimization has converged in other words regardless of which optimizer turns out to be the fastest the concurrent optimizer always returns a basic solution at optimality The concurrent optimizer requires more memory than any individual optimizer and of course it adds system load by consuming more aggregate CPU time than the fastest individual optimizer would alone But the advantages offered in terms of robust solution of models and assurance in most cases of the minimum solution time will make it attractive in many situations Tuning LP Performance Each of the optimizers available in ILOG CPLEX is designed to solve most linear programming problems under its default parameter settings However characteristics of your particular problem may make performance tuning advantageou
436. onventionally denoted y z w from the corresponding dual formulation T Maximize bly ulw Iz subject to Aly Wtz c with these bounds w 2 0 and z 20 All possible solutions maintain strictly positive primal solutions x l s and strictly positive reduced costs z w so that the value 0 zero forms a barrier for primal and dual variables within the algorithm ILOG CPLEX measures progress by considering the primal feasibility dual feasibility and duality gap at each iteration To measure feasibility ILOG CPLEX considers the accuracy with which the primal constraints Ax b x s u and dual constraints Aly Z w c are satisfied The optimizer stops when it finds feasible primal and dual solutions that are complementary A complementary solution is one where the sums of the products x z and uj Xi are within some tolerance of 0 zero Since each x L uj Xj and Zj is ILOG CPLEX 8 1 USER S MANUAL 157 o 2 Q T U Uv al D 3 7 SOLVING LP PROBLEMS WITH THE BARRIER OPTIMIZER 158 strictly positive the sum can be near zero only if each of the individual products is near zero The sum of these products is known as the complementarity of the problem On each iteration of the barrier optimizer ILOG CPLEX computes a matrix based on AAT and then computes a Cholesky factor of it This factored matrix has the same number of nonzeros on each iteration The number of nonzeros in t
437. ood understanding of what it is doing Then once it works correctly look for opportunities to improve performance e 2 D Q i P e 2 7 Debug Effectively BuruiuejDoJg 1ou1inJ Using Diagnostic Routines for Debugging on page 94 contains tips and guidelines for debugging an application that uses the ILOG CPLEX Callable Library In that context we recommend using a symbolic debugger as well as other widely available development tools to produce error free code Test Correctness Test Performance Even a program that has been carefully debugged so that it runs correctly may still contain errors or features that inhibit its performance with respect to execution speed memory ILOG CPLEX 8 1 USER S MANUAL 117 USING THE INTERACTIVE OPTIMIZER FOR DEBUGGING use and so forth Just as the ILOG CPLEX Interactive Optimizer can aid in your tests for correctness it can also help you improve performance It uses the same routines as the Component Libraries consequently it requires the same amount of time to solve a problem created by a callable library application We recommend that you use CPXwriteprob specifying a file type of SAV to create a binary representation of the problem object of your application Then read that representation into the Interactive Optimizer and solve it there If your application sets parameters use the same settings in the Interactive Optimizer If you find that your applic
438. oolParam enumeration 40 IloCplex Exception class 48 120 getStatus member function 120 IloCplex IntParam enumeration 40 IloCplex Kappa 137 IloCplex NumParam enumeration 40 IloCplex Quality enumeration 45 IloCplex Reduce 140 IloCplex StringParam enumeration 40 IloCPModeler 60 IloEnv class 34 end member function 34 IloException class getMessage member function 120 IloExpr class 34 ILOG License Manager ILM CPLEX and 32 IloMaximize function 36 IloMinimize function 36 52 IloModel class 35 36 add member function 36 45 remove member function 36 45 IloModel add 82 IloModel delete 82 IloModel remove 82 IloModeler 60 61 basic modeling 61 IloMPModeler 60 61 74 IloNumArray class 36 IloNumExpr 62 63 IloNumVar 60 extension of IloNumExpr 62 IloNumVar class 34 37 IloNumVarArray class 34 412 ILOG CPLEX 8 1 IloObjective 64 75 IloObjective class 35 37 52 setExpr member function 200 IloObjectiveSense 63 IloObjectiveSense Maximize 68 IloObjectiveSense Minimize 68 iloqpexl cpp example example iloqpexl cpp 203 IloRange 64 75 IloRange class 35 37 IloSemiContVar class 37 IloSolution class 38 IloSolver 60 I10SOS1 class 37 I10SOS2 class 37 implied bound cuts defined 236 importModel member function IloCplex class 130 include file 120 inconsistent constraints 143 incumbent node 232 solution 232 index number 92 Individual optimizer parallel processing 376 inf getNumVar 74 inf getRange 74 infeasibi
439. orithm Barrier Concert for Java users CPX_ALG_BARRIER Callable Library 4 Interactive Optimizer And then you call the solution routine just as for any other ILOG CPLEX optimizer cplex solve Concert for C or Java users CPXlpopt Callable Library optimize Interactive Optimizer Special Options In addition to the parameters available for other ILOG CPLEX LP optimizers there are also parameters to control the ILOG CPLEX Barrier Optimizer In the Interactive Optimizer to ILOG CPLEX 8 1 USER S MANUAL 159 o 2 2 Q T U Uv cA D 3 7 SOLVING LP PROBLEMS WITH THE BARRIER OPTIMIZER 160 see a list of the parameters specific to the ILOG CPLEX Barrier Optimizer use the command set barrier Controlling Crossover The nature of the crossover step that follows barrier is controlled by the parameter BarCrossAlg Under the default Aut omat ic setting an appropriate crossover step will be invoked Possible settings for the parameter are Table 5 8 BarCrossAlg Parameter Values BarCrossAlg Meaning Values 1 no crossover 0 automatic default 1 primal crossover e dual crossover Using VEC File Format When you use the ILOG CPLEX Barrier Optimizer with no crossover you can save the primal and dual variable values and their associated reduced cost and dual values in a VEC format file You can then read that VEC file into ILOG CPLEX before you initiate a
440. ortantly optimization commands in the Interactive Optimizer perform exactly like optimization routines in the Component Libraries For an LP the opt imize command in the Interactive Optimizer works the same way as the cplex solve and CPXlpopt routines in the ILOG CPLEX Component Libraries Consequently any discrepancy between the Interactive Optimizer and the Component Libraries routines with respect to the solutions found memory used or time taken indicates a problem in the logic of the application calling the routines Assemble Data Efficiently As we indicated in previous chapters ILOG CPLEX offers several ways of putting data into your problem or more formally populating the problem object You must decide which approach is best adapted to your application based on your knowledge of the problem data and application specifications These considerations may enter into your decision If your Callable Library application builds the arrays of the problem in memory and then calls CPXcopylp it avoids time consuming reads from disk files In the Callable Library using the routines CPXnewcols CPXnewrows CPXaddcols CPXaddrows and CPXchgcoeflist may help you build modular code that will be more easily modified and maintained than code that assembles all problem data in one step ILOG CPLEX 8 1 USER S MANUAL TIPS FOR SUCCESSFUL APPLICATION DEVELOPMENT An application that reads an MPS or LP file may
441. ory or paged memory Even if your problem data fit in memory ILOG CPLEX will need still more memory to optimize the problem When ILOG CPLEX recognizes that only limited memory is available it automatically makes algorithmic adjustments to compensate These adjustments almost always reduce optimization speed If you detect when these automatic adjustments occur then you can determine when you need to add additional memory to your computer to sustain computational speed for your particular problem The following sections offer guidance for you to detect these automatic adjustments Warning Messages In certain cases ILOG CPLEX issues a warning message when it cannot perform an operation but it continues to work on the problem Other ILOG CPLEX messages indicate that ILOG CPLEX is compressing the problem to conserve memory These warnings mean that ILOG CPLEX finds insufficient memory available so it is following an alternate less desirable path to a solution If you provide more memory ILOG CPLEX will return to the best path toward a solution Paging Virtual Memory If you observe paging of memory to disk then your application is incurring a performance penalty If you increase available memory in such a case performance will speed up dramatically Refactorization Frequency and Memory Requirements The ILOG CPLEX primal and dual simplex optimizers refactorize the problem basis at a rate determined by the ReInv parameter The longer
442. ove all the quadratic coefficients and thus convert the model to an LP you can change the Problem Type to 1p Note that deleting each of the quadratic coefficients individually still leaves the Problem Type as qp although in most instances the distinction between this problem and its 1p or qp counterpart is somewhat arbitrary in terms of the steps to solve it When using the Interactive Optimizer you use the command change problem with one of the following options o gt Q 2 U Ru Al e D 3 1p indicates that you want ILOG CPLEX to treat the problem as an LP This change in Problem Type removes from your problem all the quadratic information if there is any present qp indicates that you want ILOG CPLEX to treat the problem as a QP This change in Problem Type creates in your problem an empty quadratic matrix if there is not one already present for the objective function ready for populating via the change qpterm command From the Callable Library use the routine CPXchgprobt ype to change the Problem Type to either CPXPROB_LP or CPXPROB QP for the LP and QP case respectively for the same purposes Changing Quadratic Terms ILOG CPLEX distinguishes between a quadratic algebraic term and a quadratic matrix coefficient The quadratic algebraic terms are the coefficients that appear in the algebraic expression defined as part of the ILOG CPLEX LP format The quadratic matrix coefficients appear in Q
443. parameter to direct output to the screen and calls CPXcreateprob to create a problem object Before it ends it calls CPX reeprob to free the space allocated to the problem object and CPXcloseCPLEX to free the environment OL A OOO File examples src mipex2 c 7 Version 8 1 Ey p a a oe a a Copyright C 1997 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products w duc nin aaa ee pal RD le a aa ia i cl Raa ra aes a al ca a sien re Ce acl ia acl ae ae alia EL c ee U o os mipex2 c Reading in and optimizing a MIP problem os o o To run this example command line arguments are required a ices mipex2 filename o UU where filename is the name of the file with mps lp or sav extension Example mipex2 mexample mps Bring in the CPLEX function declarations and the C library header file stdio h with the following single include finclude ilcplex cplex h Bring in the declarations for the string and character functions and malloc finclude ctype h include lt stdlib h gt include lt string h gt Include declarations for functions in this program static void free_and_null char ptr usage char progname ILOG CPLEX 8 1 USER S MANUAL 271 EXAMPLE 272 READING A MI
444. per function for creating an instance of that class as the macro does in the case of C The goal is then used for solving the extracted node by calling cplex solve MyBranchGoal env var for C or for Java cplex solve new MyBranchGoal var instead of the usual cplex solve The rest of the main function contains nothing new and will not be discussed any further In the implementation of the goal or more precisely its method execute we start by declaring and initializing some arrays These arrays are then used by methods of class IloCplex GoalI IloCplex Goal to query information about the node subproblem and the solution of its relaxation Method get Values is used to query the solution values for the variables in vars method getob jCoe s is used to query the linear objective function coefficients for these variables and method getFeasibilities is used to query feasibility statuses for them The feasibility status of a variable indicates whether IloCplex considers the current solution value of the variable to be integer feasible or not IloCplex GoalI IloCplex Goal provides a wealth of other query methods For details see the ILOG CPLEX Reference Manual ILOG CPLEX 8 1 USER S MANUAL GOALS IN ILOCPLEX Once we have gathered information about the variables their objective coefficients and their current feasibility statuses we compute the index of an integer infeasible variable in vars that has th
445. plex NodeEvaluator Finally for C method IloCplex NodeEvaluatorI IloCplex NodeEvaluatorI duplicateEvaluator must be implemented by the user to return a copy of the invoking node evaluator object This method is called by 11oCplex to create copies of the evaluator for parallel branch amp cut search Example ilogoalex3 cpp shows how to use node evaluators to implement a node selection strategy that chooses the deepest active node in tree among those with maximal sum of integer infeasibilities Example ilogoalex3 cpp can be found in the examples src directory of your distribution The equivalent Java version can be found as file Goalex3 java at the same location z a D3 O 2 oS US a UE Q d e Que File examples src ilogoalex3 cpp Nersion 8 1 A Copyright C 1999 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products jj PERERA Se a ilogoalex3 cpp Node selectors in goal search ILOG CPLEX 8 1 USER S MANUAL 335 GOALS IN ILOCPLEX This is an extension of example ilogoalexl cpp It adds node evaluators to further control the goal based search The node evaluator chooses the node that is deepest in the tree among those with maximum sum of integer infeasibilities finclude ilcplex ilocplex h ILOSTLBEGIN static void usage const char
446. plex getStatus lt lt endl env out lt lt Solution value lt lt cplex getObjValue lt lt endl IloNumArray vals env cplex getValues vals var env out Values lt lt vals lt lt endl catch IloException amp e cerr Concert exception caught e endl catei i c 4 cerr lt lt Unknown exception caught lt lt endl env end return 0 END main static void usage const char progname cerr lt lt Usage lt lt progname lt lt filename lt lt endl cerr lt lt where filename is a file with extension lt lt endl cerr lt lt MPS SAV or LP lower case is allowed lt lt endl cerr lt lt Exiting lt lt endl END usage 270 ILOG CPLEX 8 1 USER S MANUAL EXAMPLE READING A MIP PROBLEM FROM A FILE Complete Program mipex2 c The example derives from 1pex2 c an LP example explained in the ILOG CPLEX Getting Started manual That LP example differs from this MIP example in these ways This example solves only MIPs so it calls only CPXmipopt and its command line does not require the user to indicate an optimizer This example calls CPXgetstat CPXgetmipobjval and CPXgetmipx to get a solution It doesn t generate or print a basis Like other applications based on the ILOG CPLEX Callable Library this one calls CPXopenCPLEX to initialize the ILOG CPLEX environment it sets the screen indicator
447. presolved model if the presolver is active Thus a Cut sFactor of 1 0 would mean that no cuts will be generated which may be a more convenient way of turning off all cuts than setting them individually The default Cut sFactor value of 4 0 works well in most cases as it allows a generous number of cuts while in rare instances it also serves to limit unchecked growth in the problem size ILOG CPLEX 8 1 USER S MANUAL 237 USING THE MIXED INTEGER OPTIMIZER 238 The AggCut Lim parameter controls the number of constraints allowed to be aggregated for generating MIR and flow cover cuts The FracPass parameter controls the number of passes for generating Gomory fractional cuts This parameter will not have any effect if the parameter for set mip cuts gomory has a non default value The FracCand parameter controls the number of variable candidates to be considered for generating Gomory fractional cuts Heuristics ILOG CPLEX provides a heuristic to find integer solutions at nodes during the branch amp cut procedure This feature is controlled by the parameter HeurFreq At its default value of 0 ILOG CPLEX dynamically determines the frequency with which the heuristic is invoked The value of 1 turns the feature off A positive value specifies the frequency in node count with which the heuristic will be called For example if the HeurF req parameter is set to 20 then the node heuristic will be applied at node 0 node 20 node
448. pressions of the objective or any constraint of the model contains IloPiecewiseLinear then when a quadratic objective is specified the model becomes an MIQP problem Complete Program iloqpex1 cpp The complete program iloqpex1 cpp appears here and online in the standard distribution FM se pe tS He ee eee e Que File examples src iloqpexl cpp Nersion 8 1 jj aa E Copyright C 1999 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products ILOG CPLEX 8 1 USER S MANUAL 203 EXAMPLE CREATING A QP OPTIMIZING FINDING A SOLUTION iloqpexl cpp Entering and optimizing a quadratic problem finclude ilcplex ilocplex h ILOSTLBEGIN static void populatebyrow IloModel model IloNumVarArray var IloRangeArray con int main int argc char argv IloEnv env try IloModel model env IloNumVarArray var env IloRangeArray con env populatebyrow model var con IloCplex cplex model Optimize the problem and obtain solution if cplex solve env error Failed to optimize LP endl throw 1 IloNumArray vals env env out lt lt Solution status lt lt cplex getStatus lt lt endl env out lt lt Solution value lt lt cplex getObjValue lt lt endl cplex getValues vals var env out Values lt lt vals l
449. pressly granted to use this example in the course of developing applications that use ILOG products c P mipexl c Entering and optimizing a MIP problem Bring in the CPLEX function declarations and the C library header file stdio h with the include of cplex h finclude ilcplex cplex h Bring in the declarations for the string functions i AS fe ES D di Buinjos include lt string h gt include lt stdlib h gt Include declaration for function at end of program static int setproblemdata char probname_p int numcols_p int numrows_p int objsen_p double obj_p double rhs_p char sense_p int matbeg_p int matcnt_p int matind_p double matval_p double lb_p double ub p char ctype_p static void free and null char ptr The problem we are optimizing will have 2 rows 3 columns and 6 nonzeros define NUMROWS 3 define NUMCOLS 4 ILOG CPLEX 8 1 USER S MANUAL 261 EXAMPLE OPTIMIZING define NUMN int main void A BASIC MIP PROBLEM Z 9 Declare pointers for the variables and arrays that will contain the data which define the LP problem The setproblemdata routine allocates space for the problem data char probname NULL int numcols int numrows int objsen double obj NULL double rhs NULL char sense NULL int matbeg NULL int mat
450. primal dual barrier 126 selecting 69 optimizing cuts 236 ORD file format 245 291 OrGoal 325 out of core barrier 166 output channel parameter 296 debugging and 120 redirecting 296 output operator 36 P parallel USER S MANUAL license 371 optimizers 371 to threads 371 Parallel Barrier Optimizer 376 parallel MIP optimizer output log file 377 parallel processing branch amp cut 375 individual optimizer 376 nested 376 root relaxation 376 selected starting algorithm 376 Parallel Simplex Optimizer 376 parameter accessing current value 40 98 accessing default value 98 accessing maximum value 98 accessing minimum value 98 advanced starting 130 algorithmic 165 barrier corrections 170 Callable Library and 98 controlling branch amp cut strategy 232 customized 400 gradient 130 iisfind 147 log file 295 netfind 180 object range 172 optimality cutoff 253 output channel 296 perturbation limit 139 preprocessing dependency 167 screen indicator 181 setting 41 98 400 setting all defaults 41 99 specification file 401 symbolic constants as 98 tree memory 254 Parameter names C 385 Callable Library 385 Interactive Optimizer 386 Java 385 parameter routine ILOG CPLEX 8 1 INDEX defined 84 parameter specification file 400 401 402 creating 401 example 402 syntax in 401 Parameters 70 parameters customized 400 max and min values for 71 query 71 perturbing file format to save perturbed problem 290
451. program For Interactive Optimizer usage or as an alternative approach in a Callable Library program you can establish MIP starting values from a file MST format described briefly in Understanding File Formats on page 290 or documented in the ILOG CPLEX Reference Manual is used for this purpose Use CPXreadcopymipstart in the Callable Library or the read command in the Interactive optimizer for this purpose At the end of a MIP optimization call when a feasible not necessarily optimal solution is still in memory you can create an MST file from the Callable Library using CPXmstwrite orfrom the Interactive Optimizer using the write command for later use as starting values to another MIP problem Care should be taken to assure that the naming convention for the variables is consistent between models when this approach is used Priority Orders In branch amp cut ILOG CPLEX makes decisions about which variable to branch on at a node You can control the order in which ILOG CPLEX branches on variables by issuing a priority order A priority order assigns a branching priority to some or all of the integer variables in a model ILOG CPLEX performs branches on variables with a higher assigned priority number before variables with a lower priority variables not assigned an explicit ILOG CPLEX 8 1 USER S MANUAL USING THE MIXED INTEGER OPTIMIZER priority value by the user are treated as having a priority value of 0 Note
452. ptimizing a MIP problem finclude ilcplex ilocplex h ILOSTLBEGIN static void populatebyrow IloModel model IloNumVarArray var IloRangeArray con i AS fe ES D di Buinjos irit main void IloEnv env try H loModel model env El loNumVarArray var env H loRangeArray con env populatebyrow model var con IloCplex cplex model cplex solve env out lt lt Solution status lt lt cplex getStatus lt lt endl env out lt lt Solution value lt lt cplex getObjValue lt lt endl IloNumArray vals env cplex getValues vals var env out Values lt lt vals lt lt endl cplex getSlacks vals con env out lt lt Slacks lt lt vals lt lt endl ILOG CPLEX 8 1 USER S MANUAL 259 EXAMPLE 260 OPTIMIZING A BASIC MIP PROBLEM cplex exportModel mipexl 1lp catch IloException amp e cerr Concert exception caught e endl catch cerr lt lt Unknown exception caught lt lt endl env end return 0 END main static void populatebyrow IloModel model IloNumVarArray x IloRangeArray c IloEnv env model getEnv add IloNumVar env 0 0 40 0 add IloNumVar env add IloNumVar env add IloNumVar env 2 0 3 0 ILOINT model add IloMaximize env x 0 2 x 1 3 x 2 x 3 X X XX c add x 0 x 1 x 2 10 x 3
453. public IloCplex NodeEvaluatorI public IloNum evaluate const return getInfeasibilitySum IloCplex NodeEvaluatorl duplicateEvaluator return new IISumEvaluatorI IloCplex NodeEvaluator IISumEvaluator return new IISumEvaluatorI z TENE o 563 O 2 oS Us a UE Q int main int argc char argv IloEnv env try IloModel model env IloCplex cplex env if arge 2 usage argv 0 throw 1 ILOG CPLEX 8 1 USER S MANUAL 337 GOALS 338 IN ILOCPLEX IloObjective obj IloNumVarArray var env IloRangeArray rng env cplex importModel model argv 1 obj var rng cplex extract model IloCplex Goal iiSumGoal IloCplex Apply cplex MyBranchGoal env var IISumEvaluator IloCplex Goal depthGoal IloCplex Apply cplex iiSumGoal DepthEvaluator cplex solve depthGoal IloNumArray vals env cplex getValues vals var cout lt lt Solution status lt lt cplex getStatus lt lt endl cout lt lt Solution value lt lt cplex getObjValue lt lt endl cout lt lt Values lt lt vals lt lt endl catch IloException amp e cerr Concert exception caught e endl env end return 0 static void usage const char progname cerr lt lt Usage lt lt progname lt lt filename lt lt endl cerr lt lt where filename is a file with extension lt lt
454. r and aggregator After those preprocessing statistics the next line records the number of nonzeros in the lower triangle of a particular matrix AAT denoted A A in the log file ILOG CPLEX 8 1 USER S MANUAL 161 o J Q T ge Uv E e D 3 7 SOLVING LP PROBLEMS WITH THE BARRIER OPTIMIZER 162 Nonzeros in Lower Triangle of AAlin the Log File The number of nonzeros in the lower triangle of AAT gives an early indication of how long each barrier iteration will take The larger this number the more time each barrier iteration requires If this number is close to 50 of the square of the number of rows then the problem may contain dense columns that are not being detected In that case examine the histogram of column counts then consider setting the barrier column nonzeros parameter to a value that enables ILOG CPLEX to treat more columns as being dense Ordering Algorithm Time in the Log File After the number of nonzeros in the lower triangle of AAT ILOG CPLEX records the time required by the ordering algorithm The ILOG CPLEX Barrier Optimizer offers you a choice of four ordering algorithms explained in Choosing an Ordering Algorithm on page 167 This section in the log file indicates which ordering algorithm the default Automatic setting chose Cholesky Factor in the Log File After the time required by the ordering algorithm ILOG CPLEX records information about the Cholesky factor ILOG CPLEX compute
455. r of rows in the partial iis 101 Number of columns in the partial iis 99 Tactics for Interpreting IIS Output The size of the IIS reported by ILOG CPLEX depends on many factors in the model If an IIS contains hundreds of rows and columns you may find it hard to determine the cause of the infeasibility Fortunately there are tactics to help you interpret IIS output Consider selecting an alternative IIS algorithm The default algorithm emphasizes computation speed and it may give rise to a relatively large IIS If so try setting the IISInd parameter to 1 one to invoke the alternative algorithm and then run the infeasibility finder again Normally the resulting IIS is smaller because the alternative algorithm emphasizes finding a minimal IIS at the expense of computation speed Ifthe problem contains equality constraints examine the cumulative constraint consisting of the sum of the equality rows As we illustrated in one of the examples the cumulative constraint can simplify your interpretation of the IIS output More generally if you take other linear combinations of rows in the IIS that may also help For example if you add an equality row to an inequality row the result may yield a simpler inequality TOW Try preprocessing with the ILOG CPLEX presolver and aggregator The presolver may even detect infeasibility by itself If not running the infeasibility finder on the presolved problem may help by reducing the problem
456. r use To that end ILOG CPLEX will write out a problem exactly as it appears in memory All your revisions of that problem will appear in the new file One potential area for confusion occurs when a maximization problem is saved Since MPS conventionally represents all problems as minimizations ILOG CPLEX reverses the sign of the objective function coefficients when it writes a maximization problem to an MPS file When you read and optimize this new problem the values of the variables will be valid for the original model However since the problem has been converted from a maximization to the equivalent minimization the objective dual and reduced cost values will have reversed signs Converting File Formats MPS Mathematical Programming System an industry standard format based on ASCII text has historically been restricted to a fixed format in which data fields were limited to eight characters and specific fields had to appear in specific columns on specific lines ILOG CPLEX supports extensions to MPS that allow more descriptive names that is more than eight characters greater accuracy for numerical data and greater flexibility in data positions Most MPS files in fixed format conform to the ILOG CPLEX extensions and thus can be read by the ILOG CPLEX MPS reader without error However the ILOG CPLEX MPS reader will not accept the following conventions blank space within a name blank lines missing fields such as bound names an
457. ram ILOG CPLEX 8 1 USER S MANUAL 385 ILOG CPLEX Parameter Names CPXsetdblparam and CPXsetstrparam Boolean parameters are treated the same as integer parameters in the Callable Library Example usage status CPXsetintparam env CPX PARAM ADVIND CPX OFF Interactive Optimizer The Interactive Optimizer user sets parameters via a menu or submenu usually with a similar but not identical name to the Concert name Example usage CPLEX SET ADVANCE NO Exceptions Exceptions are marked in the manual with an asterisk They are e PreLinear is not available in Concert as its functionality is handled by other means such as callbacks e RootAlg in Concert has multiple meanings in the other two interfaces e ScrIndis available only in the Callable Library as its functionality is limited to this interface Table A 1 Parameter Name Equivalents Concert Type Callable Library Interactive Optimizer AdvInd Bool CPX_PARAM_ADVIND ADVANCE AggCutLim Int CPX PARAM AGGCUTLIM MIP LIMITS AGGFORCUT AggFill Int CPX PARAM AGGFILL PREPROCESSING FILL AggInd Int CPX PARAM AGGIND PREPROCESSING AGGREGATOR BarAlg Int CPX PARAM BARALG BARRIER ALGORITHM BarColNz Int CPX PARAM BARCOLNZ BARRIER COLNONZEROS BarCrossAlg Int CPX PARAM BARCROSSALG BARRIER CROSSOVER BarDisplay Int CPX PARAM BARDISPLAY BARRI
458. rcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars strcmp vars i lt num i B H H H H H H He He He H H H He He H He H H H He H He H H H He H He H He H H H H He He He H H H He H He H H H H H i getName X11 getName X12 getName X13 getName X14 getName X15 getName X21 getName X22 getName X23 getName X24 getName X25 getName X31 getName X32 getName X33 getName X34 getName X35 getName X41 getName X42 getName X43 getName X44 getName X45 getName X51 getName X52 getName X53 getName X54 getName X55 getName W11 getName W12 getName W13 getName W14 getName W15 getName W21 getName W22 getName W23 getName W24 getName W25 getName W31 getName W32 getName W33 getName W34 getName W35 getName W4 getName W42 getName W43 getName W44 getName W45 getName W
459. rder of the variables could result in a change in the solution path of the algorithm and there may be noticeable variation in the solution values of the individual variables Working with MPS Files The ILOG CPLEX MPS file reader is highly compatible with existing modeling systems There is generally no need to modify existing problem files to use them with ILOG CPLEX However there are ILOG CPLEX specific conventions that may be useful for you to know This section explains those conventions and the LOG CPLEX Reference Manual documents MPS format more fully Free Rows in MPS Files In an MPS file ILOG CPLEX selects the first free row or N type row as the objective function and it discards all subsequent free rows unless it is instructed otherwise by an OBJNAME section in the file To retain free rows in an MPS file reformulate them as equality rows with an additional free variable For example replace the free row x y by the equality row x y s 0 where s is free Generally the ILOG CPLEX presolver will remove rows like that before optimization so they will have no impact on performance Ranged Rows in MPS Files To handle ranged rows ILOG CPLEX introduces a temporary range variable creates appropriate bounds for this variable and changes the sense of the row to an equality that is MPS type EQ The added range variables will have the same name as the ranged row with the characters Rg prefixed When ILOG CPLEX generates soluti
460. re no handle classes Like goals node evaluators use reference counting for memory management As a result you should always use the handle objects when dealing with node evaluators and there is no method end to be called Node evaluators use a two step process to decide whether one node should take precedence over another First the evaluator computes a value for every node to which it is attached This is done by calling method IloNum IloCplex NodeEvaluatorI evaluate in the case of C and for Java by calling method double IloCplex NodeEvaluator evaluate This method must be implemented by users who write their own node evaluators In method evaluate the protected member functions of class 11o0Cplex NodeEvaluatorI I1loCplex NodeEvaluator can be called to query information about the node being evaluated The method evaluate must compute and return an evaluation value that is used later on in the second step to compare two nodes and select one of them The evaluate method is called only once for every node and the result is cached and reused whenever the node is compared against another node with the evaluator The second step consists of comparing the current candidate to another node This only happens for evaluators that are shared by the current candidate and the other node By 334 ILOG CPLEX 8 1 USER S MANUAL GOALS IN ILOCPLEX default the candidate is replaced by the other node if
461. re frequently represented as min max f x s t L Ax U L lt xU where A isa sparse matrix A sparse matrix is one in which a significant portion of the coefficients are zero so algorithms and data structures can be designed to take advantage of it by storing and working with the substantially smaller subset of non zero coefficients Objects of type IloLPMat rix are provided for use with IloCplex to express constraint matrices rather than individual constraints An 11oLPMatrix object allows you to view a set of ranged constraints and the variables used by them as a matrix that is as L SAx SU Every row of an 11oLPMatrix object corresponds to an 11oRange constraint and every column of an IloLPMat rix object corresponds to a modeling variable an instance of IloNumVar ILOG CPLEX 8 1 UsER S MANUAL ADVANCED MODELING WITH ILOMPMODELER An IloLPMatrix object is created with method LPMatrix defined in 11oMPModeler by calling TloLPMatrix lp cplex LPMatrix or cplex addLPMatrix to immediately add it to the active model The rows and columns are then added to it by specifying the non zero matrix coefficients Alternatively you can add complete IloRange and IloNumVar objects to it to create new rows and columns When adding ranged constraints columns will be implicitly added for all the variables in the constraint expression that do not already correspond to a column of the IloLPMatrix The rl1oLPMatrix object will ensure co
462. reduce the coding effort but on the other hand may increase runtime and disk space requirements Keep in mind that if an application using the ILOG CPLEX Component Libraries reads an MPS or LP file then some other program must generate that formatted file The data structures used to generate the file can almost certainly be used directly to build the problem populating arrays for CPXcopylp or CPXaddrows a choice resulting in less coding and a faster more efficient application In short formatted files are useful for prototyping your application For production purposes assembly of data arrays in memory may be a better enhancement Test Data ILOG CPLEX provides the Dat aCheck parameter to check the correctness of data used in problem creation and problem modification methods When this parameter is set ILOG CPLEX will perform extra checks to determine that array arguments contain valid values such as indices within range no duplicate entries valid row sense indicators and valid numerical values These checks can be very useful during development but are probably too costly for deployed applications The checks are similar to but not as extensive as those performed by the CPXcheck functions provided for the C API When the parameter is not set the default only simple error checks are performed for example checking for the existence of the environment Choose an Optimizer After you have instantiated and popula
463. removed variable are not managed by Concert Technology Instead it is up to the user to make sure that these handles are not used after the deletion of the modeling object The only operation allowed then is the assignment operator Concert Technology also provides a way to remove a modeling object from all other modeling objects and algorithms exactly the same way as when deleting it yet without deleting the modeling object This is done by calling the method remover romAll This may be helpful to temporarily remove a variable from your model while keeping the option to add it back later on It is important to understand the difference between the above and calling model remove obj for an object obj In this case it does not necessarily mean that obj is removed from the problem ILOG CPLEX maintains Whether or not this happens depends on the removed object being referenced by yet another extracted modeling object Usually when a constraint is removed from the extracted model the constraint is also removed from ILOG CPLEX as well unless it was added to the model more than once Consider the case where a variable is removed from ILOG CPLEX after one of the delete or remove operations discussed above If the cp1ex object contains a simplex basis by default the status for that variable is removed from the basis as well If the variable happens to be basic the operation corrupts the basis If this is not desired ILOG CPLEX provides a delete mo
464. rent number of rows and columns respectively ILOG CPLEX 8 1 USER S MANUAL 355 z EN D3 Qe oS Us a UE Q USING CALLBACKS 356 cur numrows CPXgetnumrows env 1p cur numcols CPXgetnumcols env 1p for i 0 i lt cur numrows i printf Row d Slack 10f Pi 10f n i slack il pilil for j 0 j lt cur numcols j printf Column d Value 10f Reduced cost 10f n j xl 31 3303 Finally write a copy of the problem to a file status CPXwriteprob env lp lpex4 lp NULL if status fprintf stderr Failed to write LP to disk n goto TERMINATE TERMINATE Free up the problem as allocated by CPXcreateprob if necessary if lp NULL int frstatus frstatus CPXfreeprob env amp lp if frstatus f fprintf stderr CPXfreeprob failed error code d n frstatus if status amp amp frstatus status frstatus Free up the CPLEX environment if necessary if env NULL int clstatus clstatus CPXcloseCPLEX amp env if elstatus fprintf stderr CPXcloseCPLEX failed error code d n clstatus if status amp amp clstatus status clstatus if status char errmsg 1024 Note that since we have turned off the CPLEX screen indicator we ll need to print the error message ourselves CPXgeterrorstring env status errmsg ILOG CPLEX 8 1
465. reprocessing when the model is large enough that the root solution is itself a time consuming step ILOG CPLEX preprocesses a MIP by default However if you use a basis to start LP optimization of the root relaxation ILOG CPLEX will proceed with that starting basis without preprocessing it Frequently the strategic benefits of MIP presolve outweigh the tactical advantage of using a starting basis for the root node so use caution when considering the advantages of a starting basis Starting from a Solution You can provide a known solution for example from a MIP problem previously solved or from your knowledge of the problem to serve as the first integer solution In such a start you must specify values for all integer variables for all semi continuous variables and for all members of special ordered sets Optionally you may also specify values for continuous variables ILOG CPLEX evaluates that start solution for integrality and feasibility If it is integer feasible it will become an integer solution of the current problem Once a MIP Start has been established for your model its use is controlled by the MIPStart parameter At its default setting of 0 the MIP Start values are not used but you can direct ILOG CPLEX to evaluate the MIP Start values by setting the MIPStart parameter to 1 You can establish MIP starting values by using the method setvectors in a Concert program or by using CPXcopymipstart in a Callable Library
466. rintf stderr Failed to populate problem data n goto TERMINATE ILOG CPLEX 8 1 USER S MANUAL USING CALLBACKS status CPXsetlpcallbackfunc env mycallback NULL if status fprintf stderr Failed to set callback function n goto TERMINATE Optimize the problem and obtain solution status CPXsetintparam env CPX_PARAM_LPMETHOD CPX_ALG_PRIMAL if status fprintf stderr Failed to set the optimization method error d n status goto TERMINATE status CPXlpopt env lp if status fprintf stderr Failed to optimize LP n goto TERMINATE Turn off the callback function This isn t strictly necessary but is good practice Note that the cast in front of NULL is only necessary for some compilers status CPXsetlpcallbackfunc env int CPXPUBLIC CPXCENVptr void int void NULL NULL if status fprintf stderr Failed to turn off callback function Wn goto TERMINATE status CPXsolution env lp amp solstat amp objval x pi slack dj if status fprintf stderr Failed to obtain solution n goto TERMINATE Write the output to the screen printf nSolution status d n solstat printf Solution value f n n objval The size of the problem should be obtained by asking CPLEX what the actual size is rather than using sizes from when the problem was built cur_numrows and cur_numcols store the cur
467. riority Orders cus phu pb e eat aE ce had Pag ew a gee ee 240 Termination zl he ee PREX RE ee be qon Russ Dare ed 241 Post Solution Information in a MIP llseeeseeeee II 243 Using Sensitivity Information in a MIP 0 0 cece Ki 243 Using Special Ordered Sets 02 ccc cece eee eee 244 Example SOS Type 1 for Sizing a Warehouse 0 cece eee eee ees 244 Declaring SOS Members 00 0 c eee ete ene 245 Setting Branching Priority for an SOS 00 0 cee 245 Assigning SOS Weights 0 00 teeta 246 Using Semi Continuous Variables llle 246 Progress Reports Interpreting the Node Log lllessllesseses 246 Troubleshooting MIP Performance Problems seeesseeeeesese 250 Too Much Time at Node 0 2 22 22 c 400 sns eem ke x Rx eee Rn n En 250 ILOG CPLEX 8 1 USER S MANUAL 11 TABLE OF CONTENTS Chapter 9 Trouble Finding More than One Feasible Solution 00 cece eee eae 251 Large Number of Unhelpful Cuts 0 0 cee 251 Lack of Movement in the Best Node 0 0 0 cece eect tee 251 Time Wasted on Overly Tight Optimality Criteria llle 252 Running Out of Memory hm 253 Difficulty Solving Subproblems ssssseeeeeeeee I 256 Subproblem Optimization lille n 257 Example Optimizing a Basic MIP Problem seseeeeennn B 258 Complete Program ilomipext cpp
468. rities Priority orders and branch directions allow you to control the branching performed during branch amp cut in a static way Dynamic control of the solution process of MIPs is provided through goals or control callbacks Goals and control callbacks are discussed for C in Chapter 9 More About Using ILOG CPLEX The Java goals and callbacks are similar to the C versions Goals and callbacks allow you to control the solution process when solving MIPs based on information generated during the solution process itself More Solution Information 72 Depending on the model being solved and the algorithm being used more solution information is generated in addition to the objective value and solution values for variables and slacks Dual Solution Information When solving an LP or QP all the algorithms also compute dual solution information that can be queried Reduced costs can be accessed by calling the method IloCplex getReducedCost or IloCplex getReducedCosts Similarly dual solution values for the ranged constraints of the active model can be queried using methods IloCplex getDual or IloCplex getDuals Basis Information When solving an LP using all but 110Cplex Algorithm Barrier without crossover or when solving a QP with a Simplex optimizer basis information is available as well Basis information can be queried for the variables and ranged constraints of the active model using method I1oCplex getBasisStatu
469. rminism about many other quantities that control the optimization This nondeterminism is unavoidable in such a context and its effects can result in some cases in very different solution paths Clock Settings and Time Measurement The clock type parameter determines how ILOG CPLEX measures computation time CPU time the default is most appropriate when only one processor is used It reports the amount of time the CPU spent performing computation on behalf of your application For parallel ILOG CPLEX 8 1 USER S MANUAL 373 z a E O 2 oS Us a UE Q USING PARALLEL OPTIMIZERS 374 execution CPU time is system dependent and generally will not reflect the desired metric On some parallel systems it may measure aggregate CPU time that is the sum of time used by all processors On others it may report the CPU time of only one process In short it may give you a misleading indication of parallel speed The alternative type wall clock time is usually more appropriate for parallel computing because it measures the total physical time elapsed after an operation begins When multiple processes are active and when parallel optimizers are active wall clock time can be much different from CPU time You can choose the type of clock setting in the Interactive Optimizer with the command set clocktype i Concert Technology Library use the 11oCplex method setParam ClockType i Callable Library use the rout
470. ror ex i o Co catch java io IOException ex 7 System out println IO Error ex a static void usage System out println System out println usage java Diet options data file gt System out println options c build model by column System out println i use integer variables System out println Sample output Solution status Optimal cost 14 8557 BuyO 4 38525 Buyl 0 Buy2 0 Buy3 0 Buy4 0 Buy5 6 14754 Buy6 0 Buy7 3 42213 Buy8 0 xf ILOG CPLEX 8 1 USER S MANUAL 81 SOLVING THE DIET MODEL WITH THE JAVA API 82 Modifying the Model An important feature of ILOG CPLEX is that you can modify a previously created model to consider different scenarios Furthermore depending on the optimization model and algorithm used ILOG CPLEX will save as much information from a previous solution as possible when optimizing a modified model The most important modification method is IloModel add for adding modeling objects to the active model Conversely I1loModel remove can be used to remove a previously added modeling object from a model When adding a modeling object such as a ranged constraint to a model all the variables used by that modeling object implicitly become part of the model as well However when removing a modeling object no variables are implicitly removed from the model Instead variables can only be explicitly removed from a model
471. ror code d n status Free up the problem as allocated by CPXcreateprob if necessary lp NULL CPXfreeprob env amp lp if status fprintf stderr CPXfreeprob failed error code d n status Free up the CPLEX environment if necessary env NULL status CPXcloseCPLEX amp env Note that CPXcloseCPLEX produces no output so the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines the errors will be seen if the CPX_PARAM_SCRIND indicator is set to CPX_ON if status char errmsg 1024 fprintf stderr Could not close CPLEX environment Nn CPXgeterrorstring env status errmsg fprintf stderr s errmsg return status END main ILOG CPLEX 8 1 USER S MANUAL 193 v fa TEXT Bley NET NB UIAJOS EXAMPLE NETWORK TO LP TRANSFORMATION 194 ILOG CPLEX 8 1 USER S MANUAL Solving Quadratic Programming Problems o gt Q 2 ge Uv a e D 3 This chapter tells you about solving convex quadratic programming problems QPs with ILOG CPLEX This chapter contains sections on Identifying Convex Quadratic Programming Problems Entering QPs Saving QP Problems Changing Problem Type in QPs Changing Quadratic Terms Optimizing QPs Example Creating a QP Optimizing Finding a Solution 9 9 9 9 9 9 Example Reading a QP from a File Id
472. routines enable you to query set or modify parameter values maintained by ILOG CPLEX Licenses ILOG CPLEX runs under the control of the ILOG License Manager ILM Before you can run any application program that calls ILOG CPLEX you must have established a valid ILOG CPLEX 8 1 USER S MANUAL USING THE CALLABLE LIBRARY IN AN APPLICATION license that it can read Licensing instructions are provided to you separately when you buy or upgrade ILOG CPLEX Contact your local ILOG support department if this information has not been communicated to you or if you find that you need help in establishing your ILOG CPLEX license Compiling and Linking Compilation and linking instructions are provided with the files that come in the standard distribution of ILOG CPLEX for your computer platform Check the readme htm1 file for details Using the Callable Library in an Application This section tells you how to use the Callable Library in your own applications Briefly you must initialize the ILOG CPLEX environment instantiate a problem object and fill it with data Then your application calls one of the ILOG CPLEX optimizers to optimize your problem Optionally your application can also modify the problem object and re optimize it ILOG CPLEX is designed to support this sequence of operations modification and re optimization of linear or quadratic programming problems LPs or QPs efficiently by reusing the current basis of a pr
473. rsion of the model for your problem There are modeling languages such as ILOG OPL that may be helpful to ILOG CPLEX 8 1 USER S MANUAL 113 TIPS FOR SUCCESSFUL APPLICATION DEVELOPMENT 114 you for this task This prototype model can serve as a test bed for your application and a point of reference during development Identify Routines to Use If you decompose your application into manageable components you can more easily identify the tools you will need to complete the application Part of this decomposition consists of determining which methods or routines from the ILOG CPLEX Component Libraries your application will call Such a decomposition will assist you in testing for completeness it may also help you isolate troublesome areas of the application during development and it will aid you in measuring how much work is already done and how much remains Test Interactively The Interactive Optimizer in ILOG CPLEX introduced in the manual ILOG CPLEX Getting Started offers a reliable means to test the ILOG CPLEX component of your application interactively particularly if you have prototyped your model Interactive testing through the Interactive Optimizer can also help you identify precisely which methods or routines from the Component Libraries your application needs Additionally interactive testing early in development may also uncover any flaws in procedural logic before they entail costly coding efforts Most imp
474. rst goal from the node s goal stack and calls method execute If a nonempty goal is returned it is simply pushed back on the stack IloCplex keeps doing this until the node becomes inactive or the node s goal stack becomes empty When the node stack is empty IloCplex continues with its built in search strategy for the subtree rooted at this node z a 563 O 2 oS uvg UE Q Let us now review the different types of goals in light of the goal stack 1 As we already discussed the Or goal creates child nodes 11oCplex first initializes the goal stack of every child node with a copy of the remaining goal stack of the current node Then it pushes the goal passed as the parameter to the Or goal on the goal stack of the corresponding node Finally the current node is deactivated and IloCplex continues search by picking a new active node from the tree to process 2 The And goal simply pushes the goals passed as parameters onto the goal stack in reverse ILOG CPLEX 8 1 USER S MANUAL 325 GOALS 326 IN ILOCPLEX order Thus when popping the goals from the stack for execution they will be executed in the same order as they were passed as parameters to method And goal 3 When a Fail goal executes the current node is simply deactivated and IloCplex continues on another active node from the tree In other words 11oCplex discontinues its search below the current node 4 When a local cut goal is executed its con
475. rt Technology Library use the method getParam To access the default value of a parameter use the method getDefault Use the methods getMin and getMax to access the minimum and maximum values of num and int type parameters Some integer parameters are tied to nested enumerations that define symbolic constants for the values the parameter may assume In particular these enumeration types are IloCplex MIPEmphasisType IloCplex VariableSelect IloCplex NodeSelect IloCplex PrimalPricing IloCplex DualPricing and IloCplex BranchDirection They are used for parameters IloCplex MIPEmphasis IloCplex VarSel IloCplex NodeSel IloCplex PPriInd IloCplex DPriInd and IloCplex BrDir respectively Only the parameter IloCplex MIPEmphasis may be of importance for general use ILOG CPLEX 8 1 USER S MANUAL ACCESSING SOLUTION INFORMATION There are of course routines in the Concert Technology Library to set these parameters Use the following methods to set the values of ILOG CPLEX parameters IloCplex setParam BoolParam value IloCplex setParam IntParam value IloCplex setParam NumParam value IloCplex setParam StringParam value For example the numerical parameter IloCplex EpOpt controlling the optimality tolerance for the simplex algorithms can be set to 0 0001 by calling cplex setParam IloCplex EpOpt 0 0001 Q e O D e m E 7 zz i ES Q lt
476. s As a first step in tuning performance try the different ILOG CPLEX optimizers as we suggested in Choosing an Optimizer for Your LP Problem on page 124 The following sections describe other features of ILOG CPLEX to consider in tuning the performance of your application Preprocessing Starting from an Advanced Basis Simplex Parameters Preprocessing Under default settings ILOG CPLEX preprocesses problems by simplifying constraints reducing problem size and eliminating redundancy Its presolver tries to reduce the size of a problem by making inferences about the nature of any optimal solution to the problem Its aggregator tries to eliminate variables and rows through substitution For most models o 2 Q T U Uv al D 3 7 ILOG CPLEX 8 1 USER S MANUAL 127 TUNING LP PERFORMANCE 128 preprocessing is beneficial to the total solution speed and ILOG CPLEX reports the model s solution in terms of the user s original formulation making the exact nature of any reductions immaterial In cases where your model may be primal infeasible or unbounded dual infeasible it may be desirable to control the kinds of presolve reductions which ILOG CPLEX makes in order to make your analysis of the outcome of optimization more certain These reductions can be divided into two types primal reductions and dual reductions A reduction is primal if it does not depend on the objective function A reduc
477. s This method returns basis statuses for the variables or constraints using objects of type IloCplex BasisStatus with possible values ILOG CPLEX 8 1 USER S MANUAL MORE SOLUTION INFORMATION IloCplex BasisStatus Basic IloCplex BasisStatus AtLower IloCplex BasisStatus AtUpper and IloCplex BasisStatus FreeOrSuperbasic The availability of a basis for an LP allows you to perform sensitivity analysis for your model Such analysis tells you by how much you can modify your model without affecting the solution you found The modifications supported by the sensitivity analysis function include variable bound changes changes to the bounds of ranged constraints and changes to the objective function They are analyzed by methods 11oCplex getBoundSA IloCplex getRangeSA IloCplex getRHSSA and IloCplex getObjSA respectively Infeasible Solution Information An important feature of ILOG CPLEX is that even if no feasible solution has been found that is if cplex solve returns false some information about the problem can be queried when solving LPs or QPs All the methods discussed so far may successfully return information about the current infeasible solution ILOG CPLEX maintains O re E c8 g lt cs 05 a o o Q lt z Unfortunately there is no simple comprehensive rule about whether or not current solution information can be queried This is because by default ILOG CPLEX uses a presol
478. s that could not reasonably be expressed using linear constraints through cuts or branching In other words this allows you to use goals in a way that makes them part of the model to be solved Such a use is common in Constraint Programming but it is less frequently used in Mathematical Programming Optionally find local or global cuts to be added Local cuts will be respected only for the subtree below the current node whereas global cuts will be enforced for all nodes from then on Optionally construct a solution and pass it to 11oCplex Instruct IloCplex how to proceed Instructing 11oCplex how to proceed is done through the return value of method execute which is another goal IloCplex simply continues by executing this goal IloCplex provides a selection of special goals that can be used to specify how to proceed Method 11oCplex GoalI OrGoal IloCplex or returns a goal that creates subnodes of the current node This function takes at least 2 and up to 6 goals as parameters For each of its parameters the Or goal will create a subnode in such a way that when processing that subnode the corresponding goal will be executed Once the goal has been executed the current node is immediately deactivated Method 11oCplex GoalI AndGoal IloCplex and also takes goals as parameters It returns a goal that will cause I1oCplex to execute the goals passed as parameters in the order of the parameters Method r1oCplex Goa
479. s Int CPX PARAM CLIQUES IP CUTS CLIQUES ClockType Int CPX PARAM CLOCKTYPE CLOCKTYPE CoeRedInd Int CPX PARAM COEREDIND PREPROCESSING COEFFREDUCE ColGrowth Int CPX PARAM COLGROWTH READ VARIABLES Covers Int CPX PARAM COVERS IP CUTS COVERS CraInd Int CPX PARAM CRAIND SIMPLEX CRASH CutLo um CPX PARAM CUTLO IP TOLERANCES LOWERCUTOFF CutPass Int CPX PARAM CUTPASS IP LIMITS CUTPASSES CutsFactor um CPX PARAM CUTSFACTOR IP LIMITS CUTSFACTOR CutUp um CPX PARAM CUTUP IP TOLERANCES UPPERCUTOFF DataCheck Bool CPX PARAM DATACHECK READ DATACHECK DepInd Bool CPX_PARAM_DEPIND PREPROCESSING DEPENDENCY DisjCuts Int CPX PARAM DISJCUTS MIP CUTS DISJUNCTIVE DiveType Int CPX PARAM DIVETYPE MIP STRATEGY DIVE DPrilInd Int CPX PARAM DPRIIND SIMPLEX DGRADIEN ILOG CPLEX 8 1 USER S MANUAL 387 ILOG CPLEX Parameter Names Table A 1 Parameter Name Equivalents Concert Type Callable Library Interactive Optimizer EpAGap um CPX PARAM EPAGAP MIP TOLERANCES ABSMIPGAP EpGap um CPX PARAM EPGAP MIP TOLERANCES MIPGAP EpInt um CPX PARAM EPI MIP TOLERANCES INTEGRALITY EpMrk um CPX PARAM E
480. s an irreducibly inconsistent set IIS To work the infeasibility finder must have a problem that satisfies two conditions the problem has been optimized using the primal simplex optimizer or barrier with primal crossover and the problem has terminated with an infeasible basic solution to the primal problem When the ILOG CPLEX presolver detects infeasibility during preprocessing no optimization has yet taken place Furthermore since the presolver may perform many passes on a problem the reason that it identifies a row as infeasible may not be obvious To run the infeasibility finder and to see solution statistics in such a case you should first turn off ILOG CPLEX preprocessing before you optimize as explained in Preprocessing on page 127 before you invoke the infeasibility finder The barrier optimizer may be called with primal crossover dual crossover or no crossover Only the primal crossover options will allow you to subsequently run the infeasibility finder The parameter IISInd controls the method used for determining the IIS Its default value of 0 zero invokes an algorithm that requires minimal computation time but may generate a large set of inconsistent constraints Infeasibility Finder in the Interactive Optimizer To invoke the infeasibility finder and to display part of its findings in the Interactive Optimizer use the command display iis By default ILOG CPLEX records all its findings in a log file To s
481. s return objects of type IloIntVar an extension of interface 11oNumVar that allows you to query and set bounds consistently using integers rather than doubles as used for 11oNumvar Frequently integer variables with 0 1 bounds are used as decision variables To help create such variables the boolVar methods are provided In the Boolean type 0 and 1 are implied so these methods do not need to accept any bound values For all these constructor methods there are also equivalent methods for creating a complete array of modeling variables at one time These methods are called numvarArray intVarArray and boolVarArray Building Expressions Modeling variables are typically used in expressions that define constraints or objective functions Expressions are represented by objects of type 11oNumExpr They are built using methods such as sum prod diff negative and square For example the expression xl 2 x2 where x1 and x2 are 11oNumVar objects is constructed by calling IloNumExpr expr cplex sum xl cplex prod 2 0 x2 It follows that a single variable is a special case of an expression since 11oNumVar is an extension of T1oNumExpr The special case of linear expressions is represented by objects of type IloLinearNumExpr Such expressions are editable which is especially convenient when building up linear expressions in a loop such as IloLinearNumExpr lin cplex linearNumExpr
482. s this matrix on each iteration The number of rows in the Cholesky factor represents the number after preprocessing The next line of information about the Cholesky factor integer space required indicates the amount of memory needed to store the sparsity pattern of the factored matrix If this number is low then the factor can be computed more quickly than when the number is high Information about the Cholesky factor continues with the number of nonzeros in the factored matrix The difference between this number and the number of nonzeros in AAT indicates the fill level of the Cholesky factor If the fill level is large consider an alternate ordering algorithm The final line of information indicates how many floating point operations are required to compute the Cholesky factor This number is the best predictor of the time that will be required to perform each iteration of the barrier method Iteration Progress in the Log File After the information about the Cholesky factor the log file records progress at each iteration It records both primal and dual objectives as Primal Obj and Dual Obj per iteration It also records absolute infeasibilities per iteration Internally the ILOG CPLEX Barrier Optimizer treats inequality constraints as equality constraints with added slack and surplus variables Consequently primal constraints in a problem are written as Ax b and x s u ILOG CPLEX 8 1 USER S MANUAL SOLVING LP PROBLEM
483. s to dual solution values that is the y values in the conventional barrier problem formulation The term rc refers to reduced cost that is the difference z w in the conventional barrier problem formulation Other terms are best understood in the context of primal and dual LP formulations Normalized errors for example represent the accuracy of satisfying the constraints while considering the quantities used to compute Ax on each row and ylA on each column In the primal case for each row we consider the nonzero coefficients and the xj values used to compute Ax If these numbers are large in absolute value then it is acceptable to have a larger absolute error in the primal constraint Similar reasoning applies to the dual constraint If ILOG CPLEX returned an optimal solution but the primal error seems high to you the primal normalized error should be low since it takes into account the scaling of the problem and solution After a simplex optimization whether primal dual or network or after a crossover the display command will display information related to the quality of the simplex solution Tuning Barrier Optimizer Performance Naturally the default parameter settings for the ILOG CPLEX Barrier Optimizer work best on most problems However you can tune several algorithmic parameters to improve performance or to overcome numerical difficulties These parameters are described in the sections Out of Core Barrier L
484. se To speed up the proof of optimality you can set objective difference parameters both relative and absolute Setting these parameters helps when there are many integer solutions ILOG CPLEX 8 1 USER S MANUAL TROUBLESHOOTING MIP PERFORMANCE PROBLEMS with similar objective values For example setting the Ob jDif parameter to 100 0 makes ILOG CPLEX skip any potential solution with its objective value within 100 0 units of the best integer solution so far Or setting the Re10bjDif to 0 01 would mean that ILOG CPLEX would skip any potential new solution that is not at least 1 better than the incumbent solution Naturally since this objective difference setting may make ILOG CPLEX skip an interval where the true integer optimum may be found the objective difference setting weakens the guarantee of optimality Cutoff parameters can also be helpful in restricting the search for optimality If you know that there are solutions within a certain distance of the initial relaxation of your problem then you can readily set the upper cutoff parameter for minimization problems and the lower cutoff parameter for maximization problems Set the parameters CutUp and Cut Lo respectively to establish a cutoff value When you set a MIP cutoff value ILOG CPLEX searches with the same solution strategy as though it had already found an integer solution using a node selection strategy that differs from the one it uses before a first solution has
485. se this option in any file that calls ILOG CPLEX Callable Library routines On some operating systems such as DEC Alpha running Digital Unix certain intrinsic FORTRAN functions must be in all upper case that is capital letters for the compiler to accept those functions Underscore On some systems all FORTRAN external symbols are created with an underscore character that is added to the end of the symbol name Some systems have an option to turn off this feature for example on DEC Alpha running Digital Unix the option assume nounderscore turns off the postpended underscore If you are able to turn off those postpended underscores you may not need other glue routines ILOG CPLEX 8 1 USER S MANUAL ILOG CPLEX PROGRAMMING PRACTICES Six Character Identifiers FORTRAN 77 allows identifiers that are unique only up to six characters However in practice most FORTRAN compilers allow you to exceed this limit Since routines in the Callable Library have names greater than six characters you need to verify whether your FORTRAN compiler enforces this limit or allows longer identifiers Call by Reference By default FORTRAN passes arguments by reference that is the address of a variable is passed to a routine not its value In contrast many routines of the Callable Library require arguments passed by value To accommodate those routines most FORTRAN compilers have the VMS FORTRAN extension VAL This operator use
486. search which is described in more detail in Chapter 8 Solving Mixed Integer Programming Problems Solving a Single LP or QP To solve a single LP or QP or the first LP or QP in a series use IloCplex setParam IloCplex IntParam RootAlg alg where alg is an integer ILOG CPLEX 8 1 USER S MANUAL 69 CONTROLLING ILOG CPLEX OPTIMIZERS specifying the algorithm type The following constants are defined for identifying the available algorithm types Table 2 3 Algorithm Types alg Algorithm Type 0 TloCplex Algorithm Auto 1 IloCplex Algorithm Primal 2 IloCplex Algorithm Dual 3 IloCplex Algorithm Network 4 IloCplex Algorithm Barrier 5 IloCplex Algorithm Sifting If IloCplex setParam IloCplex IntParam RootAlg alg is not called the default I1o0Cplex Algorithm Auto will be used The IloCplex Algorithm Sifting algorithm is not available for QP IloCplex will default to the ILloCplex Algorithm Auto setting when parameter IloCplex IntParam RootAlg is set to IloCplex Algorithm Sifting for a QP Solving Subsequent LPs or QPs in a MIP Parameter IloCplex IntParam RootAlg also controls the algorithm used for solving the first LP or QP when solving a MIP The algorithm for solving all subsequent LPs or QPs is then controlled by parameter I1oCplex IntParam NodeAlg The same set of algorithm choices is available with the exception of 11o0Cplex Algorithm Sifting and IloCplex Algorithm
487. simplex optimizer the basis at which the determination of infeasibility is made may not be unique The Effect of Preprocessing on Feasibility ILOG CPLEX preprocessing may declare a model infeasible before the selected optimization algorithm begins This saves considerable execution time in most cases It is important when this is the outcome to understand that there are two classes of reductions performed by the preprocessor Reductions that are independent of the objective function are called primal reductions those that are independent of the right hand side are called dual reductions Preprocessing operates on the assumption that the model being solved is expected by the user to be feasible and that a finite optimal solution exists If this assumption is false then the model is either infeasible or no bounded optimal solutions exist i e unbounded Since primal reductions are independent of the objective function they cannot detect unboundedness they can only detect infeasibility Similarly dual reductions can only detect unboundedness Thus to aid analysis of an infeasible or unbounded declaration by the preprocessor a parameter is provided that the user can set so that the optimization can be rerun to assure that the results reported by the preprocessor can be interpreted If a model is declared by the preprocessor to be infeasible or unbounded and the user believes that it might be infeasible the parameter Reduce can be set to 1
488. sisting only of 128 variables This model is very hard to solve by itself in fact until the release of ILOG CPLEX 6 5 it appeared to be unsolvable even after days of computation While it is now solvable directly the computation time is in the order of several hours on state of the art computers However cuts can be derived the addition of which make the problem solvable in a matter of minutes or seconds These cuts are x21 x22 lt 0 x22 x23 lt 0 x23 x24 lt 0 2 08 x11 2 98 x21 3 47 x31 2 24 x41 2 08 x51 0 25 w11 0 25 w21 0 25 w31 0 25 w41 0 25 w51 lt 20 25 2 08 x12 2 98 x22 3 47 x32 2 24 x42 2 08 x52 0 25 w12 0 25 w22 0 25 w32 0 25 w42 0 25 w52 lt 20 25 2 08 x13 2 98 x23 3 47 x33 2 24 x43 2 08 x53 0 25 w13 0 25 w23 0 25 w33 0 25 w43 0 25 w53 lt 20 25 ILOG CPLEX 8 1 USER S MANUAL USING CALLBACKS 2 08 x14 2 98 x24 3 47 x34 2 24 x44 2 08 x54 0 25 w14 0 25 w24 0 25 w34 0 25 w44 0 25 w54 lt 20 25 2 08 x15 2 98 x25 3 47 35 2 24 x45 2 08 x55 0 25 wl15 0 25 w25 0 25 w35 0 25 w45 0 25 w55 lt 16 25 These cuts have been derived after interpreting the model as a resource allocation model on five machines with scheduling horizon constraints and transaction times The first three cuts break symmetries among the machines while the others capture minimum bounds on transaction costs See MIP Theory and Practice Clos
489. slightly different than mipexl c so that the output is interesting finclude ilcplex ilocplex h ILOG CPLEX 8 1 USER S MANUAL 275 EXAMPLE USING SOS AND PRIORITY ILOSTLBEGIN static void populatebyrow IloModel model IloNumVarArray var IloRangeArray con int main void IloEnv env try loModel model env loNumVarArray var env loRangeArray con env populatebyrow model var con loCplex cplex model loNumVarArray ordvar env 2 var 1 var 3 loNumArray ordpri env 2 8 0 7 0 cplex setPriorities ordvar ordpri cplex setDirection var 1 IloCplex BranchUp cplex setDirection var 3 IloCplex BranchDown cplex solve env out lt lt Solution status lt lt cplex getStatus lt lt endl env out lt lt Solution value lt lt cplex getObjValue lt lt endl IloNumArray vals env cplex getValues vals var env out Values lt lt vals lt lt endl cplex getSlacks vals con env out lt lt Slacks lt lt vals lt lt endl cplex exportModel mipex3 1lp catch IloException amp e cerr Concert exception caught e endl catch cerr lt lt Unknown exception caught lt lt endl env end return 0 END main static void populatebyrow IloModel model IloNumVarArray x IloRangeArray c IloEnv env model getEnv x add IloNumVar env 0 0 40 0 276 ILOG
490. solution then you can invoke the ILOG CPLEX infeasibility finder on this optimized problem and its infeasible basic solution The ILOG CPLEX infeasibility finder will compute an IIS of constraints and column bounds from your problem and record this IIS in a log file along with other useful information to help you locate the source of infeasibility and aid in revising or reformulating your model If you want ILOG CPLEX to display this additional information on your screen in the Interactive Optimizer use the command set output logonly yes Afterthat command invoke the infeasibility finder with the command display iis ILOG CPLEX will respond like this Starting Infeasibility Finder Algorithm Performing row sensitivity filter Performing column sensitivity filter Number of rows in the iis 3 Number of columns in the iis 3 Names of rows in the iis NODE5 fixed D7 lower bound D8 lower bound Names of columns in the iis T25 upper bound T35 upper bound T47 upper bound Iis Computation Time 0 01 sec As you can see ILOG CPLEX states how many rows and columns comprise the HS It also displays the row and column names and it identifies the bound causing the infeasibility In this example all the columns in the IIS are limited by their upper bound If you remove any of the upper bounds on those columns then the IIS becomes feasible The bound information about rows is really needed only for ranged rows In the case o
491. status CPXgetcallbackinfo env cbdata wherefrom CPX_CALLBACK_INFO_PRIMAL_OBJ amp suminf or objective if status goto TERMINATE printf Iteration d Objective f n itcnt suminf or objective TERMINATE return status END mycallback Control Callbacks for lloCplex Control callbacks allow you to control the branch amp cut search during the optimization of MIP problems The following control callbacks are available for 11oCplex The node callback allows you to query and optionally overwrite the next node ILOG CPLEX will process during a branch amp cut search The solve callback allows you to specify and configure the optimizer option to be used for solving the LP at each individual node The cut callback allows you to add problem specific cuts at each node z a D3 qe oS US a UE Q The heuristic callback allows you to implement a heuristic that tries to generate a new incumbent from the solution of the LP relaxation at each node The branch callback allows you to query and optionally overwrite the way ILOG CPLEX will branch at each node The incumbent callback allows you to check and optionally reject incumbents found by ILOG CPLEX during the search These callbacks are implemented as an extension of the diagnostic callback class hierarchy This extension is shown below along with the macro names for each of the control callbacks ILOG CPLEX 8 1 USER S
492. straints are added to the node problem as local cuts and the relaxation is re solved 5 Anempty goal cannot be executed Thus empty goals are not pushed on the goal stack If the goal stack is empty IloCp1lex continues with the built in branching strategy With this understanding let us revisit what really goes on when a goal returns return AndGoal OrGoal var lt IloFloor val var gt IloFloor val 1 this The And goal is pushed onto the current node s goal stack only to be immediately popped back off of it When it is executed it will push this on the goal stack and then the Or goal Thus the Or goal is the next goal that 11oCplex pops and executes The Or goal creates two subnodes and initializes their goal stacks with copies of the goal stack of the current node At this point both subnodes will have this on top of their goal stacks Next the or goal will push a local cut goal for var 3 val where va1 denotes the floor of val on the goal stack of the first subnode Similarly it pushes a local cut goal for var 2 val 1 on the goal stack of the second subnode Finally the current node is deactivated and IloCplex continues its search with a new active node from the tree When 110oCplex processes one of the subnodes that have been created by the Or goal it will pop and execute the first goal from the node s goal stack As we just saw this will be a local cut goal Thus 11oCplex adds the constraint to the node problem and
493. t lt endl cplex getSlacks vals con env out lt lt Slacks lt lt vals lt lt endl cplex getDuals vals con env out lt lt Duals lt lt vals lt lt endl cplex getReducedCosts vals var env out lt lt Reduced Costs lt lt vals lt lt endl cplex exportModel qpexl lp catch IloException amp e cerr Concert exception caught e endl catch cerr lt lt Unknown exception caught lt lt endl env end return 0 END main To populate by row we first create the variables and then use them to create the range constraints and objective The model we create is 204 ILOG CPLEX 8 1 USER S MANUAL EXAMPLE CREATING A QP OPTIMIZING FINDING A SOLUTION Maximize obj xl 2 x2 3 x3 fi 0 5 33 x14 x1 4 22 XxX2 x2 11 x3 x3 12 xl x2 22 x2 x3 Subject To Cl xl x2 x3 lt 20 iy C2 xl 3 x2 x3 lt 30 Bounds 0 lt x1 lt 40 End static void populatebyrow IloModel model IloNumVarArray x IloRangeArray c IloEnv env model getEnv 5 x add IloNumVar env 0 0 40 0 x add IloNumVar env Ce x add IloNumVar env oO model add IloMaximize env x 0 2 x 1 3 x 2 U 0 5 33 x 0 x 0 22 x 1 x 1 U 11 x 2 x 2 12 x 0 x 1 e 23 x 1 x 2 D c add x 0 x 1 x 2 lt 20 3 c add x 0 3 x 1
494. t detecting primal and dual infeasibility To select one of the barrier infeasibility algorithms set the BarA1g parameter to either 1 or 2 In Finding a Set of Irreducibly Inconsistent Constraints on page 143 we explained how to invoke the infeasibility finder on a solution basis found by one of the simplex optimizers If you are using the pure barrier optimizer that is with no crossover to a simplex optimizer ILOG CPLEX 8 1 USER S MANUAL SOLVING LP PROBLEMS WITH THE BARRIER OPTIMIZER then it will not generate a basis on which you can call the infeasibility finder to analyze your constraints and locate an ITS Consequently if you are interested in finding an IIS for your problem you should invoke the ILOG CPLEX Barrier Optimizer with crossover as explained in Controlling Crossover on page 160 ILOG CPLEX 8 1 USER S MANUAL o 2 Q T U Uv x D 3 7 SOLVING LP PROBLEMS WITH THE BARRIER OPTIMIZER 174 ILOG CPLEX 8 1 USER S MANUAL i e ES D M0 J 4J0M 9N BulAjos Solving Network Flow Problems This chapter tells you more about the ILOG CPLEX Network Optimizer It includes sections on Choosing an Optimizer Network Considerations Formulating a Network Problem Example Network Optimizer in the Interactive Optimizer Example Using the Network Optimizer with the Callable Library Solving Network Flow Problems as LP Problems Example Network to LP Transforma
495. t displayed on the screen To display the infeasibilities on your screen use the command set output logonly y cplex log Regardless of whether a solution is infeasible or optimal the command display solution quality in the Interactive Optimizer displays the bound and reduced cost infeasibilities for both the scaled and unscaled problem In fact it displays the following summary statistics for both the scaled and unscaled problem maximum bound infeasibility that is the largest bound violation maximum reduced cost infeasibility maximum row residual maximum dual residual 9 maximum absolute value of a variable a slack variable a dual variable and a reduced cost The following sections discuss these summary statistics in greater detail ILOG CPLEX 8 1 USER S MANUAL 141 o gt Q T ge Uv al D 3 7 DIAGNOSING LP INFEASIBILITY 142 Maximum Bound Infeasibility Identifying Largest Bound Violation The maximum bound infeasibility identifies the largest bound violation This information may help you determine the cause of infeasibility in your problem If the largest bound violation exceeds the feasibility tolerance of your problem by only a small amount then you may be able to get a feasible solution to the problem by increasing the feasibility tolerance parameter EpRHS Its range is between e and 0 1 Its default value is Je Maximum Reduced Cost Infeasibility The max
496. t each time a thread finishes one node it is assigned to solving another s 2 E O 2 oS Us a UE Q Branch amp Cut Parallel Processing A contrasting and specialized approach to obtaining speed increases by parallel processing within the branch amp cut tree is to 1 choose strong branching varsel parameter setting 3 as the variable selection strategy 2 apply multiple processors to the strong branching variable selection computation by setting the strong branching thread limit st rongThreadLin to a value greater than 1 and ILOG CPLEX 8 1 USER S MANUAL 375 USING PARALLEL OPTIMIZERS 376 3 leaving the global thread limit at 1 to inhibit processing the branching and solution of the nodes in parallel On models where strong branching is already a beneficial technique this approach to parallelism can be especially attractive Root Relaxation Parallel Processing In some models the LP or QP root relaxation takes significant solution time before parallel branching begins These models have potential for additional speed increases by running the root relaxation step in parallel If the root problem is an LP and the Threads parameter is set to a value greater than 1 the concurrent optimizer is invoked by default This provides a form of parallelism that applies the available threads to multiple LP optimizers If the root problem is a QP the dual simplex optimizer alone is used You can try a different for
497. t getSize loInt m nutrMin getSize loRangeArray range env nutrMin mod add range loObjective cost IloAdd mod nutrMin nutrMax nutrPer type nutrMax IloMinimize env for j 0 j lt n j IloNumColumn col cost foodCost j for i 0 i lt m i col range i nutrPer i j l Buy add IloNumVar col foodMin j foodMax j type col end range end int main int argc char argv IloEnv env try const char filename examples data diet dat IloBool byColumn IloFalse IloNumVar Type varType ILOFLOAT IloInt i for i 1 i lt argc i if argv i 0 switch argv i 1 case c byColumn IloTrue break case i varType ILOINT break default usage argv 0 throw 1 else ILOG CPLEX 8 1 56 USER S MANUAL EXAMPLE DIETARY OPTIMIZATION filename argv il break ifstream file filename if file cerr ERROR could not open file filename for reading endl usage argv 0 throw 1 Q e O D lt E 7 zz i ES Q lt model data IloNumArray foodCost env foodMin env foodMax env IloNumArray nutrMin env nutrMax env IloNumArray2 nutrPer env file foodCost foodMin foodMax file nutrMin nutrMax file nutrPer IloInt nFoods foodCost getSize IloI
498. t levels for Probe try the aggressive setting of 3 first and then reduce it if the probing step itself takes excessive time for your purposes and MIPEmphasis Set to a value of 3 Time Wasted on Overly Tight Optimality Criteria Sometimes ILOG CPLEX finds a good integer solution early but must examine many additional nodes to prove the solution is optimal You can speed up the process in such a case if you are willing to change the optimality tolerance ILOG CPLEX supports two kinds of tolerance Relative optimality tolerance guarantees that a solution lies within a certain percentage of the optimal solution Absolute optimality tolerance guarantees that a solution lies within a certain absolute range of the optimal solution The default relative optimality tolerance is 0 0001 At this tolerance the final integer solution is guaranteed to be within 0 01 of the optimal value Of course many formulations of integer or mixed integer programs do not require such tight tolerance so requiring ILOG CPLEX to seek integer solutions that meet this tolerance in those cases is wasted computation If you can accept greater optimality tolerance in your model then you should change the parameter EpGap If however you know that the objective values of your problem are near zero then you should change the absolute gap because percentages of very small numbers are less useful as optimality tolerance Change the parameter EpAGap in this ca
499. t which point the optimization is complete and feasible solutions may be discovered along the way anyway due to branches that happen to locate feasible solutions that do not match the Best Bound A great deal of analysis may be performed on the model beyond what is done under the default emphasis Therefore it is recommended to use this setting only on models that are difficult for the default emphasis and for which you do not care about interim feasible solutions that may or may not be optimal To make clear a point that has been alluded to in the above every choice of MIPEmphasis results in the branch amp cut algorithm proceeding in a manner that eventually will find and prove an optimal solution or will prove that no integer feasible solution exists The choice of emphasis only guides ILOG CPLEX to produce feasible solutions in a way that is in keeping with the user s particular purposes but the accuracy and completeness of the algorithm is not sacrificed in the process ILOG CPLEX 8 1 USER S MANUAL USING THE MIXED INTEGER OPTIMIZER The MIPEmphasis parameter may be set in conjunction with any other ILOG CPLEX parameters discussed at length in the next section For example if you wish to set an upward branching strategy via the BrDir parameter this will be honored under any setting of MIPEmphasis Of course certain combinations of MIPEmphasis with other parameters may be counter productive such as turning off a
500. tart set threads set timelimit page 242 set workdir prompt for new directory set workmem prompt for new value page 242 of working memory available tranopt write filename type page 127 page 138 page 145 page 257 page 198 xecute command page 145 Managing Parameters in the Interactive Optimizer To see the current value of a parameter that interests you in the Interactive Optimizer use the command display settings The command display settings changed lists only those parameters whose values are not the default value The command display settings all lists all parameters and their values To change the value of a parameter in the Interactive Optimizer use the command set followed by options to indicate the parameter and the value you want it to assume The ILOG CPLEX Reference Manual documents the name of each parameter and its options in the Interactive Optimizer Saving a Parameter Specification File You can tell the ILOG CPLEX Interactive Optimizer to read customized parameter settings from a parameter specification file By default ILOG CPLEX expects a parameter specification file to be named cplex par and it looks for that file in the directory where it 400 ILOG CPLEX 8 1 USER S MANUAL Interactive Optimizer Commands is executing However you can rename the file or tell ILOG CPLEX to look for it in another directory by setting the system environment variable CPLEXPARFILE to the full path name to
501. ted a problem object you solve it by calling one of the optimizers available in the ILOG CPLEX Component Libraries Your choice of optimizer depends on the type of problem The primal simplex dual simplex and primal dual barrier methods can be used to solve linear and quadratic programs The network optimizer is appropriate for solving linear and quadratic programs with large embedded networks The branch amp cut algorithm should be used if the problem contains discrete components binary integer or semi continuous variables piecewise linear objective or SOS sets e fe 5 e Q 2 9 t o BuruiuejDoJg 1ou1inJ In ILOG CPLEX there are many possible parameter settings for each optimizer Generally the default parameter settings are best for linear programming and quadratic programming problems but Chapter 5 Solving Linear Programming Problems and Chapter 7 Solving Quadratic Programming Problems offer more detail about improving performance with respect to these problems Integer programming problems are more sensitive to specific parameter settings so you may need to experiment with them as suggested in Chapter 8 Solving Mixed Integer Programming Problems ILOG CPLEX 8 1 USER S MANUAL 115 TIPS FOR SUCCESSFUL APPLICATION DEVELOPMENT 116 In either case the Interactive Optimizer in ILOG CPLEX lets you try different parameter settings and different optimizers to determine the best optimizati
502. tells you how to use ILOG CPLEX parallel optimizers It includes sections on Threads Nondeterminism Clock Settings and Time Measurement Using Parallel Optimizers in the Interactive Optimizer Using Parallel Optimizers in the ILOG CPLEX Component Libraries Parallel MIP Optimizer Parallel Barrier Optimizer 9 9 9 9 9 9 Parallel Simplex Optimizer There are three specialized ILOG CPLEX optimizers Parallel Simplex Parallel MIP and Parallel Barrier implemented to run on hardware platforms with parallel processors These parallel optimizers like other ILOG CPLEX optimizers are available in the Interactive Optimizer and in the Component Libraries if you hold a ILOG CPLEX Parallel license Parallel barrier and MIP optimizers are included with all ILOG CPLEX libraries The parallel dual simplex optimizer is only available in OpenMP versions of the libraries which will have omp in the platform name Additional compiler linker flags may be needed when using the OpenMP versions of the libraries Consult the makefile that is provided in the ILOG CPLEX distribution for your computer platform Threads The ILOG CPLEX parallel optimizers are licensed for a specific maximum number of threads that is the number processors applied to a given problem The number of threads that ILOG CPLEX actually uses during a parallel optimization is the smaller of the number of threads made available by the operating system 4 2 o
503. teprob env net netexl net NULL if status fprintf stderr Failed to write network to disk n goto TERMINATE TERMINATE Free memory for solution data free_and_null char amp x free and null char amp dj free and null char amp pi free and null char amp slack Free up the problem as allocated by CPXNETcreateprob if necessary if net NULL CPXNETfreeprob env amp net if status fprintf stderr CPXNETfreeprob failed error code d n status Free up the CPLEX environment if necessary if env NULL ILOG CPLEX 8 1 USER S MANUAL 185 EXAMPLE USING THE NETWORK OPTIMIZER WITH THE CALLABLE LIBRARY status CPXcloseCPLEX amp env Note that CPXcloseCPLEX produces no output so the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines the errors will be seen if the CPX_PARAM_SCRIND indicator is set to CPX_ON if status char errmsg 1024 fprintf stderr Could not close CPLEX environment n CPXgeterrorstring env status errmsg fprintf stderr s errmsg return status END main static int buildNetwork CPXENVptr env CPXNETptr net int status 0 definitions to improve readability define NNODES 8 define NARCS 14 define inf CPX_INFBOUND E Define list of supply values for the nodes double supply NNODES 20 0
504. ter almost reducing the sum of infeasibilities to 0 zero then you may be able to find a feasible solution if you increase the optimality tolerance parameter EpOpt Maximum Absolute Values Detecting Ill Conditioned Problems When you are trying to determine whether your problem is ill conditioned you need to consider the following maximum absolute values all available in the infeasibility analysis that ILOG CPLEX provides you variables slack variables dual variables reduced costs that is dual slack variables ILOG CPLEX 8 1 USER S MANUAL DIAGNOSING LP INFEASIBILITY When using the Component Libraries use the method cplex getQuality or the routine CPXgetdblquality to access the information provided by the command display solution quality in the Interactive Optimizer If you determine from this analysis that your model is indeed ill conditioned then you need to reformulate it Coping with an Ill Conditioned Problem or Handling Unscaled Infeasibilities on page 140 outlines steps to follow in this situation Finding a Set of Irreducibly Inconsistent Constraints If ILOG CPLEX reports that your problem is infeasible then you should invoke the ILOG CPLEX infeasibility finder to save time and effort in the development process This diagnostic tool computes a set of infeasible constraints and column bounds that would be feasible if one of them a constraint or variable were removed Such a set is known a
505. th a 0 objective and the LP IIS finder can be applied To get the original model back simply add the objective back to the model You can then solve the relaxed linear version by means of the ILOG CPLEX primal simplex optimizer Then you can apply the ILOG CPLEX infeasibility finder to that relaxed solution with its associated original QP information to help you diagnose the source of the infeasibility Diagnosing LP Infeasibility on page 139 explains how to use the ILOG CPLEX infeasibility finder following a simplex optimizer Note that it is possible for the outcome of the above analysis to be a confirmation that your model viewed as an LP is feasible after all This is typically a symptom that your QP model is numerically unstable or ill conditioned Unlike the simplex optimizers for LP the QP optimizers are primal dual in nature and one result of that is the scaling of the objective function interacts directly with the scaling of the constraints Just as our recommendation regarding numerical difficulties on LP models see Numerical Difficulties on page 135 is for coefficients in the constraint matrix not to vary by more than about six orders of magnitude for QP this recommendation expands to include the quadratic elements of the objective function coefficients as well Fortunately in most instances it is straightforward to scale your objective function by multiplying or dividing all the coefficients linear and quadratic by a const
506. that ILOG CPLEX will branch only on variables that take a fractional solution value at a given node Thus a variable with a high priority number might still not be branched upon until late in the tree if at all and indeed if the presolve or the aggregator feature of the ILOG CPLEX Preprocessor removes a given variable then branching on that variable would never occur regardless of a high priority order assigned to it by the user You can specify priority for any variable though the priority is used only if the variable is a general integer variable a binary integer variable or a member of a special ordered set ILOG CPLEX provides the ability to generate a priority order automatically based on problem data characteristics This facility can be activated by setting the MIPOrdType parameter to one of the following Table 8 9 Parameters for Branching Priority Order Parameter Branching Priority Order 0 no automatic priority order will be generated default 1 decreasing cost coefficients among the variables 2 increasing bound range among the variables 3 increasing cost per matrix coefficient count among the variables If you explicitly read a file of priority orders its settings will override any generic priority order you may have set by interactive commands The parameter MIPOrdInd when set to 0 allows you to direct ILOG CPLEX to ignore a priority order that was previously read from a file The default setting
507. that a time limit was hit Error has not been able to be processed or an error occurred during the optimization As can be seen these statuses indicate information about the model that the ILOG CPLEX optimizer was able to prove during the last call to method solve In addition the 42 ILOG CPLEX 8 1 UsER s MANUAL ACCESSING SOLUTION INFORMATION ILOG CPLEX optimizer provides information about how it terminated For example it may have terminated with only a feasible but not optimal solution because it hit a limit or because a user callback terminated the optimization Further information is accessible by calling solution query routines such as method cplex getCplexStatus which returns a member of the nested enumeration type IloCplex CplexStatus or methods cplex isPrimalFeasible Orcplex isDualFeasible For more information about those statuses see the ILOG CPLEX Reference Manual Querying Solution Data Q e O D e m ES 7 zz i e Q lt If cplex solve returns IloTrue a feasible solution has been found and solution values for model variables are available to be queried For example the solution value for the numeric variable var1 can be accessed as follows IloNum x1 cplex getValue varl However querying solution values variable by variable may result in ugly code Here the use of Concert Technology arrays provides a much more compact way of accessing the solution v
508. that not enough memory was available or there was some other problem In the case of failure an error message will have been written to the error channel from inside CPLEX In this example the setting of the parameter CPX PARAM SCRIND causes the error message to appear on stdout lp NULL fprintf stderr Failed to create LP n goto TERMINATE Now populate the problem with the data For building large problems consider setting the row column and nonzero growth parameters before performing this task switch argv 1 1 if case r Status populatebyrow env lp nfoods cost lb ub nnutr nutrmin nutrmax nutrper break case tgr status populatebycolumn env lp nfoods cost lb ub nnutr nutrmin nutrmax nutrper break status fprintf stderr Failed to populate problem n ILOG CPLEX 8 1 USER S MANUAL EXAMPLE DIETARY OPTIMIZATION goto TERMINATE Optimize the problem and obtain solution status CPXlpopt env lp if status fprintf stderr Failed to optimize LP n goto TERMINATE x double malloc nfoods sizeof double if x NULL status CPXERR_NO_MEMORY fprintf stderr Could not allocate memory for solution n goto TERMINATE status CPXsolution env lp amp solstat amp objval x NULL NULL NULL if status fprintf stderr Failed to obtain solution Wn goto TERMINATE Write the o
509. the entire problem Nodes are called active if they have not yet been processed The tree is first initialized to contain the root node as the only active node IloCplex processes active nodes from the tree until either no more active nodes are available or some limit has been reached Once a node has been processed it is no longer active When processing a node 11oCplex starts by solving the continuous relaxation of its subproblem that is the subproblem without integrality constraints If the solution violates any cuts IloCplex adds them to the node problem and re solves This is iterated until no more violated cuts are found by 11oCplex If at any point the relaxation becomes infeasible the node is pruned that is it is removed from the tree To solve the node problem 11oCplex checks whether the solution satisfies the integrality constraints If so and if its objective value is better than that of the current incumbent the solution of the node problem is used as the new incumbent Otherwise 11oCplex splits the node problem into one or two smaller subproblems typically by branching on a variable that violates its integrality condition These subproblems are added to the tree as active nodes and the current node is deactivated The primary use of goals is to take control of these last steps namely the feasibility test and the creation of subproblems However as we will discuss later goals also allow you to add local and global cuts
510. the default In the Interactive Optimizer use the command set barrier startalg i substituting a value for i ILOG CPLEX 8 1 USER S MANUAL SOLVING LP PROBLEMS WITH THE BARRIER OPTIMIZER When using the Component Libraries set the parameter IloCplex BarStartAlg or CPX_PARAM_BARSTARTALG Overcoming Numerical Difficulties As we noted in Differences between Barrier and Simplex Optimizers on page 159 the algorithms in the barrier optimizer have very different numerical properties from those in the simplex optimizer While the barrier optimizer is often extremely fast particularly on very large problems numerical difficulties occasionally arise with it in certain classes of problems For that reason we recommend that you run simplex optimizers in conjunction with the barrier optimizer to verify solutions At its default settings the ILOG CPLEX Barrier Optimizer always crosses over after a barrier solution to a simplex optimizer so this verification occurs automatically Difficulties in the Quality of Solution Understanding Solution Quality from the Barrier LP Optimizer on page 163 lists the items that ILOG CPLEX displays about the quality of a barrier solution If the ILOG CPLEX Barrier Optimizer terminates its work with a solution that does not meet your quality requirements you can adjust parameters that influence the quality of a solution Those adjustments affect the choice of ordering algorithm the choice of barrier
511. the goal returned by method 11oCplex Goall BranchAsCplexGoal o E IloCplex branchAsCplex A goal that follows the branching performed by 2 IloCplex built in strategy can be easily implemented as Lr O ILOCPLEXGOALO DefaultSearchGoal 2 5 if isIntegerFeasible Ke return AndGoal BranchAsCplexGoal getEnv this return 0 Notice the test for integer feasibility Without that test we would create an endless loop because when an integer feasible solution has been found BranchAsCplex goal does not change the node at all and this would continue to be executed indefinitely ILOG CPLEX 8 1 USER S MANUAL 339 GOALS IN ILOCPLEX Search Limits As with node evaluators it is possible to apply search limits to the branch amp cut search controlled by goals Search limits allow you to limit the search in certain subtrees that is they allow you to discontinue processing nodes when some condition applies Search limits are implemented in subclasses of class IloCplex SearchLimitI IloCplex SearchLimit and the procedure for implementing and using them is very similar to that for node evaluators See the reference manual for more details on implementing and using search limits 340 ILOG CPLEX 8 1 USER S MANUAL Using Callbacks USING CALLBACKS This section introduces the topic of callback routines which allow you to closely monitor and guide the behavior of ILOG CPLEX optimizers It includes informa
512. the industry conventions ILOG CPLEX also supports extensions to this format for ILOG CPLEX specific cases such as names of more than eight characters blank space as delimiters between columns etc Working with MPS Files on page 293 in this manual explains more fully how to use MPS files with ILOG CPLEX MST is used to enter and save a starting solution for a MIP NET is an ILOG CPLEX specific ASCII format for network flow problems It is flexible and supports named nodes and arcs ORD is a format used to enter and to save priority orders for branching It may contain branching instructions for individual variables PPE is the format ILOG CPLEX uses to write a problem in a binary SAV file after the bounds of a problem have been perturbed for use with the primal simplex optimizer PRE is the format ILOG CPLEX uses to write a presolved reduced problem formulation to a binary SAV file Since a presolved problem has been reduced it will not correspond to the original problem QP is a format containing the values of nonzero coefficients in the Q matrix of a quadratic programming problem You must enter the linear part of that quadratic programming problem first by whichever means you choose REW is used to write a problem in MPS format with disguised row and column names This format may be useful for example for problems that you consider to be highly proprietary SAV is an ILOG CPLEX specific binary format for reading and wri
513. then ILOG CPLEX branches on a fractional variable to generate two new subproblems each with more restrictive bounds on the branching variable For example with binary variables one node will fix the variable at 0 zero the other at 1 one The subproblems may result in an all integer solution in an infeasible solution or another fractional solution If the solution is fractional ILOG CPLEX repeats the process ILOG CPLEX cuts off nodes when the value of the objective function associated with the subproblem at that node is worse than the cutoff value You set the cutoff value by means of the CutUp parameter for a minimization problem or the Cut Lo parameter for a maximization problem to indicate to ILOG CPLEX that integer feasible solutions worse than this cutoff value should be discarded The default value of the lower cutoff is 1e 7 the default value of the upper cutoff is 1e The defaults in effect mean that no cutoff is to be supplied You can supply any number that you find appropriate ILOG CPLEX 8 1 USER S MANUAL 231 v A fej ES D 7 di Bulnjos USING THE MIXED INTEGER OPTIMIZER for your problem It is never required that you supply a cutoff and in fact for most applications is it not done ILOG CPLEX will use the value of the best integer solution found so far as modified by the tolerance parameters Ob jDif or RelObjDif absolute and relative objective function difference respectively
514. ther structures distinctly from their corresponding headers and closing brackets Use uniform indentation for example three to five spaces Put at least one space before and after each relational operator as well as before and after each binary plus and minus Use space as you do in normal English Avoid Side Effects We recommend that you minimize side effects by avoiding expressions that produce internal effects In C for example try to avoid expressions of this form a c d e f A BAD IDEA where the expression assigns the values of d and a Don t Change Argument Values A user defined function should not change the values of its arguments Do not use an argument to a function on the left hand side of an assignment statement in that function Since C and C pass arguments by value treat the arguments strictly as values do not change them inside a function ILOG CPLEX 8 1 USER S MANUAL TIPS FOR SUCCESSFUL APPLICATION DEVELOPMENT Declare the Type of Return Values Always declare the return type of functions explicitly Though C has a historical tradition of making the default return type of all functions int we recommend that you explicitly declare the return type of functions that return a value and use void for procedures that do not return a value Manage the Flow of Your Code Use only one return statement in any function Limit your use of break statements to the inside of switch statemen
515. ting problems and their associated basis information ILOG CPLEX includes the basis in a SAV file only if the problem currently in memory has been optimized and a basis exists This format offers the advantage of being numerically accurate to the same degree as your platform in contrast to text file formats that may lose numerical accuracy It also has the additional benefit of being efficient with respect to read and write time However since a SAV file is binary you cannot read nor edit it with a text editor SOS is a format that declares special ordered sets the set branching order and weights for each set member ILOG CPLEX 8 1 USER S MANUAL 291 z a D3 qe oS Us a UE Q MANAGING 292 INPUT amp OUTPUT TREis a format that saves information about progress through the branch amp cut tree It is a binary format TXT files are ASCII text files ILOG CPLEX uses this format when it writes solution files in text VEC is a format that saves the solution to a pure barrier optimization prior to crossover that 1s a nonbasis solution that can later be read back in and used to initiate crossover Using VEC File Format on page 160 explains how to use this file format Working with LP Files LP files are row oriented so you can look at a problem as you enter it in a naturally and intuitively algebraic way However ILOG CPLEX represents a problem internally in a column ordered format This difference be
516. tion 9 9 9 9 9 Solving Problems with the Network Optimizer Choosing an Optimizer Network Considerations As we explain in Using the Callable Library in an Application on page 85 to exploit ILOG CPLEX in your own application you must first create a ILOG CPLEX environment instantiate a problem object and populate the problem object with data As your next step you call a ILOG CPLEX optimizer ILOG CPLEX 8 1 USER S MANUAL 175 FORMULATING A NETWORK PROBLEM If part of your problem is structured as a network then you may want to consider calling the ILOG CPLEX Network Optimizer This optimizer may have a positive impact on performance There are two alternative ways of calling the network optimizer If your problem is an LP where a large part is a network structure you may call the network optimizer for the populated LP object If your entire problem consists of a network flow you should consider creating a network object instead of an LP object Then populate it and solve it with the network optimizer This alternative generally yields the best performance because it does not incur the overhead of LP data structures This option is only available for the C library How much performance improvement you observe between using only a simplex optimizer versus using the network optimizer followed by either of the simplex optimizers depends on the number and nature of the other constraints in your problem On a pure networ
517. tion IloCplex class 40 getMessage member function IloException class 120 getMin 72 getMin member function IloCplex class 40 getObjsA 73 getObjSA member function IloCplex class 44 getOb jValue member function IloCplex class 43 getParam 71 getParam member function IloCplex class 40 getQuality member function IloCplex class 45 137 164 getRangeSA 73 getReducedCost 72 getReducedCost member function IloCplex class 43 getReducedCosts 72 getReducedCosts member function IloCplex class 43 UsER S MANUAL getRHSSA member function TloCplex class 44 getSlack member function TloCplex class 43 getSlacks member function TloCplex class 43 getStatus member function TloCplex class 42 TloCplex Exception class 120 getStatuses member function TloCplex class 148 getting see accessing getValue member function TloCplex class 43 getValues member function TloCplex class 43 global thread limit 376 global thread parameter 375 global variables 87 goal empty 321 executing 319 goal stack 325 goals as parameters 320 Gomory fractional cuts defined 236 gradient parameter primal simplex optimizer 379 graphic user interface GUI 352 GUB constraint 236 cover cuts 236 H head 176 header file 120 heap debugging 120 heuristic solutions 332 heuristics starting point 168 ILOG CPLEX 8 1 INDEX IIS 73 IIS file format 290 ill conditioned basis 142 factors in 142 problem 140 ILM Hi Hi H
518. tion is dual if it does not depend on the right hand side By default presolve performs both kinds of reductions Under the default if the presolved model is infeasible we know only that the original model is either infeasible or unbounded But if presolve has performed only primal reductions and the presolved model is infeasible then we have full assurance that the original model is also infeasible Similarly if presolve has performed only dual reductions and the presolved model is unbounded then the original model is verified as unbounded To control the types of reductions performed by the presolver set the Reduce parameter to one of the following values 0 no primal and dual reductions 1 only primal reductions 2 only dual reductions 3 both primal and dual reductions default A useful preprocessing feature for performance tuning one that is not always activated by default can be to convert the problem to its dual formulation The nature of the dual formulation is rooted in linear programming theory beyond the scope of this manual but for the purposes of this preprocessing feature it is sufficient to think of the roles of the rows and columns of the model s constraint matrix as being switched Thus the feature is especially applicable to models that have many more rows than columns When you solve with the barrier optimizer the default preprocessor settings may result in the dual formulation automatically being formed if it
519. tion on Diagnostic Callbacks Control Callbacks for 11oCplex ILOG CPLEX callbacks allow user code to be executed regularly during an optimization There are two types of callbacks diagnostic callbacks and control callbacks which are discussed separately in the following sections To use callbacks with ILOG CPLEX you must first write the callback function and then pass it to ILOG CPLEX Diagnostic Callbacks Diagnostic callbacks allow you to monitor an ongoing optimization and optionally abort it These callbacks are distinguished by the place where they are called during an optimization There are 9 such places where diagnostic callbacks are called The presolve callback is called regularly during presolve The crossover callback is called regularly during crossover from a barrier solution to a simplex basis The network callback is called regularly during the network simplex The barrier callback is called at each iteration during the barrier algorithm The simplex callback is called at each iteration during the simplex algorithm The MIP callback is called at each node during the branch amp cut search The probing callback is called regularly during probing 9 9 9 9 The fractional cut callback is called regularly during the generation of fractional cuts The disjunctive cut callback is called regularly during the generation of disjunctive cuts z EN 563 O 2 oS Us a UE Q Implementing Cal
520. tion subproblem 319 conventions character strings 93 in parameter specification file 401 naming 293 notation 26 numbering 121 292 numbering rows columns 120 convert CPLEX utility 294 converting error code to string 181 file formats 294 network flow model to LP 188 network flow problem to LP 189 convex quadratic programming see quadratic programming copying variable types in MIP 90 variable types in QP 90 cover cuts 235 defined 235 CPLEX Component Libraries 22 core 84 licensing 32 parameters 40 cplex object creating 38 USER S MANUAL 405 INDEX notifying changes to 45 cplex h header file 95 97 98 120 cplex log file changing name 160 clone logs 379 default name 131 295 cplex par parameter specification file 400 CPLEXPARFILE environment variable 401 CPX_ALG_AUTO symbolic constant 258 CPX_ALG_DUAL symbolic constant 258 CPX_ALG_HYBNETOPT symbolic constant 258 CPX_ALG_PRIMAL symbolic constant 258 CPX_PARAM_ADVIND parameter 130 CPX_PARAM_AGGIND parameter 239 CPX_PARAM_BARSTARTALG parameter 169 CPX PARAM BARTHREADS parameter 371 CPX PA BBINTERVAL parameter 232 CPX PA BNDSTRENIND parameter 239 CPX PA BRDIR parameter 232 CPX PA BTTOL parameter 232 CPX PARAM CLIQUES parameter 237 CPX PA CLOCKTYPE parameter 98 374 CPX PARAM COEREDIND parameter 239 CPX PARAM COLGROWTH parameter 90 182 CPX PARAM COVERS parameter 237 CPX PARAM DISJCUTS parameter 237 CPX PA CPX PA M FLOWCOVERS parameter 23
521. tion through the CPXcopyct ype routine In the Interactive Optimizer to indicate binary integers in the context of the enter command type binaries on a separate line followed by the designated binary variables To indicate general integers type generals on a separate line followed by the designated general variables To indicate semi continuous variables type semi continuous ona separate line followed by the designated variables Semi integer variables are indicated by being specified as both general integer and semi continuous The order of these three sections does not matter To enter the general integer variable of the Sample Stating a MIP Problem on page 224 you type this Uv zal e ES D diN Buinjos generals x4 You may also read MIP data in from a formatted file just as you do for linear programming problems Chapter 9 More About Using ILOG CPLEX in this manual describes file formats briefly and the ILOG CPLEX Reference Manual documents file formats such as MPS LP and others To read MIP problem data into the Interactive Optimizer use the read command with an option to indicate the file type ILOG CPLEX 8 1 USER S MANUAL 225 CHANGING PROBLEM TYPE IN MIPS To read MIP problem data into your application use the importModel method in the Concert Technology Library or use CPXreadcopyprob in the Callable Library from the Callable Library Displaying MIP Problems Table 8 1 su
522. tional requirements for the proposed diet and array nut rper containing the nutritional value of the foods Preparations to build and solve the model with ILOG CPLEX begin with the call to CPXopenCPLEX This establishes an ILOG CPLEX environment to contain the LP problem and succeeds only if a valid ILOG CPLEX license is found 2 D ie D D D ey A 5 lt After calls to set parameters one to control the output that comes to the user s terminal and another to turn on data checking for debugging purposes a problem object is initialized through the call to CPXcreateprob This call returns a pointer to an empty problem object which now can be populated with data Two alternative approaches to filling this problem object are implemented in this program populatebyrow and populatebycolumn and which one is executed is determined at run time by a calling parameter on the command line The routine populatebyrow operates by first defining all the columns through a call to CPXnewcols and then repeatedly calls CPXaddrows to enter the data of the constraints The routine populatebycolumn takes the complementary approach of establishing all the rows first with a call to CPXnewrows and then sequentially adds the column data by calls to CPXaddcols Solving the Model with CPX1popt The model is at this point ready to be solved and this is accomplished through the call to CPXlpopt which by def
523. tions If this parameter is increased beyond its default value the ILOG CPLEX Barrier Optimizer will be less likely to determine that the problem has an unbounded optimal face and more likely to encounter numerical difficulties Consequently you should change the barrier growth parameter only if you find that the ILOG CPLEX Barrier Optimizer is terminating its work before it finds the true optimum because it has falsely detected an unbounded face The parameter BarVarUp determines an upper bound for all variables in the model the default value of 1e is effectively treated as infinity ILOG CPLEX 8 1 USER S MANUAL 171 o gt Q T ge Uv al D 3 7 SOLVING LP PROBLEMS WITH THE BARRIER OPTIMIZER 172 Difficulties with Unbounded Problems ILOG CPLEX detects unbounded problems in either of two ways either it finds a solution with small complementarity that is not feasible for either the primal or the dual formulation of the problem or the iterations tend toward infinity with the objective value becoming very large in absolute value The ILOG CPLEX Barrier Optimizer stops when the absolute value of either the primal or dual objective exceeds the objective range parameter BarObjRng If you increase the value of BarObjRng then the ILOG CPLEX Barrier Optimizer will iterate more times before it decides that the current problem suffers from an unbounded objective value If you know that your proble
524. tmipobjval env lp amp objval if status fprintf stderr No MIP objective value available Exiting n goto TERMINATE printf Solution value f n n objval The size of the problem should be obtained by asking CPLEX what the actual size is rather than using what was passed to CPXcopylp cur_numrows and cur_numcols store the current number of rows and columns respectively cur numrows CPXgetnumrows env 1p cur numcols CPXgetnumcols env 1p status CPXgetmipx env lp x 0 cur numcols 1 if status 1 fprintf stderr Failed to get optimal integer x n goto TERMINATE ILOG CPLEX 8 1 USER S MANUAL 281 i AS fe ES D di Buinjos EXAMPLE 282 USING SOS AND PRIORITY status CPXgetmipslack env lp slack 0 cur numrows 1 if status fprintf stderr Failed to get optimal slack values n goto TERMINATE for i 0 i lt cur numrows i printf Row d Slack 10f n i slack i for j 0 j lt cur numcols j printf Column d Value 10f n j x j 1 TERMINATE Free up the problem as allocated by CPXcreateprob if necessary if lp NULL status CPXfreeprob env amp lp if status fprintf stderr CPXfreeprob failed error code d n status Free up the CPLEX environment if necessary if env NULL status CPXcloseCPLEX amp env Note that CPXcloseCPLEX produc
525. to install a new variable in all modeling objects in which it is to appear For example IloColumn col cplex column obj 1 0 and cplex column rng 2 0 can be used to create a new variable and install it in the objective function represented by obj with a linear coefficient of 1 0 and in the ranged constraint rng with a linear coefficient of 2 0 Once the proper column object has been constructed it can be used to create a new variable by passing it as the first parameter to the variable constructor The newly created variable will be immediately installed in existing modeling objects as described by the IloColumn object that has been used So the line ILOG CPLEX 8 1 USER S MANUAL 75 SOLVING THE DIET MODEL WITH THE JAVA API IloNumVar var cplex numVar col 0 0 1 0 creates a new variable with bounds 0 0 and 1 0 and immediately installs it in the objective obj with linear coefficient 1 0 and in the ranged constraint rng with linear coefficient 2 0 All constructor methods for variables come in pairs one with and one without a first IloColumn parameter Methods for constructing arrays of variables are also provided for modeling by column These methods take an IloColumnArray object as parameter that describes how each individual new variable is to be installed in existing modeling objects Solving the Diet Model with the Java API 76 The problem solved in this example is to minimize the cost of a diet that satisfies c
526. ts In C do not use continue statements and limit your use of goto statements to exit conditions that branch to the end of a function Handle error conditions in C with a try catch block and in C with a goto statement that transfers control to the end of the function so that your functions have only one exit point In other words control the flow of your functions so that each block has one entry point and one exit point This one way in one way out rule makes code easier to read and debug Localize Variables Avoid global variables at all costs Code that exploits global variables invariably produces side effects which in turn make the code harder to debug Global variables also set up peculiar reactions that make it difficult to include your code successfully within other applications Also global variables preclude multithreading unless you invoke locking techniques As an alternative to global variables pass arguments down from one function to another Name Your Constants Scalars both numbers and characters that remain constant throughout your application should be named For example if your application includes a value such as 1000 create a constant with the define statement to name it If the value ever changes in the future its occurrences will be easy to find and modify as a named constant Choose Clarity First Efficiency Later Code first for clarity Get your code working accurately first so that you maintain a g
527. ts cuts in such a way that they are valid for all subproblems even when they are discovered during analysis of a particular subproblem If the solution to a subproblem violates one of the subsequent cuts ILOG CPLEX may add a constraint to reflect this condition Clique Cuts A clique is a relationship among a group of binary variables such that at most one variable in the group can be positive in any integer feasible solution Before optimization starts ILOG CPLEX constructs a graph representing these relationships and finds maximal cliques in the graph Cover Cuts If a constraint takes the form of a knapsack constraint that is a sum of binary variables with nonnegative coefficients less than or equal to a nonnegative right hand side then there is a minimal cover associated with the constraint A minimal cover is a subset of the variables of the inequality such that if all the subset variables were set to one the knapsack constraint would be violated but if any one subset variable were excluded the constraint would be satisfied ILOG CPLEX can generate a constraint corresponding to this condition and this cut is called a cover cut i cal e ES D di Buinjos Disjunctive Cuts A MIP problem can be divided into two subproblems with disjunctive feasible regions of their LP relaxations by branching on an integer variable Disjunctive cuts are inequalities valid for the feasible regions of LP relaxations of the subpr
528. ts in the solution process Even if the coefficients are of more modest size a wide variation say six or more orders of magnitude in coefficients found in the objective function or right hand side or in any given row or column of the matrix can cause difficulty either in Presolve when it makes substitutions or in the optimizer routines particularly the barrier optimizer as convergence is approached A related source of difficulty is the form of rounding when fractions are represented as decimals expressing as 33333333 on a computer that in principle computes values to about 16 digits can introduce an apparent exact value that will be treated as given but may not represent what you intend This difficulty is compounded if similar or related values are represented a little differently elsewhere in the model For example consider the constraint x1 x2 1 Under perfect arithmetic it is equivalent to x1 2 x2 3 However if you express the fractional version with decimal data values some truncation is unavoidable If you happen to include the truncated decimal version of the constraint in the same model with some differently truncated version or even the exact integer data version an unexpected result could easily occur Consider the following problem formulation Maximize obj xl x2 Subject To cl 0 333333 x1 0 666667 x2 1 c2 xl 2 x2 23 End Under default numerical tolerances this will deliver an optimal s
529. ts strongthreads set mip limits treememory page 254 set mip ordtype set mip strategy backtrack page 232 set mip strategy bbinterval page 232 set mip strategy branch page 232 set mip strategy dive set mip strategy file set mip strategy heuristicfreq page 238 set mip strategy mipstart page 240 set mip strategy nodeselect page 232 set mip strategy order set mip strategy presolvenode set mip strategy probe page 238 set mip strategy startalgorithm set mip strategy subalgorithm page 258 set mip strategy variableselect page 232 set mip tolerances absmipgap set mip tolerances integrality set mip tolerances lowercutoff set mip tolerances mipgap set mip tolerances objdifference page 252 set mip tolerances relobjdifference set mip tolerances uppercutoff set network display page 179 set network iterations page 179 ILOG CPLEX 8 1 USER S MANUAL 397 Interactive Optimizer Commands Command Options Example set network netfind set network pricing page 179 set network tolerances feasibility page 179 set network tolerances optimality set output channel set output logonly page 141 page 143 set preprocessing aggregator page 127 page 135 page 239 set preprocessing boundstrength page 239 set preprocessing coeffreduce page 239 page 258 set preprocessing compress set preprocessing dependency page 127 page 167 set prepro
530. tween the way ILOG CPLEX accepts a problem in LP format and the way it stores the problem internally may have an impact on memory use and on the order in which variables are displayed on screen or in files Variable Order and LP Files As ILOG CPLEX reads an LP format file by rows it adds columns as it encounters them in a row This convention will have an impact on the order in which variables are named and displayed For example consider this problem Maximize 2X9 3 subject to X4 X X lt 20 Xt 3X0 X lt 30 with these bounds 0 lt x lt 40 0 lt X2 lt Too 0 lt Xa lt 00 Since ILOG CPLEX reads the objective function as the first row the two columns appearing there will become the first two variables When the problem is displayed or rewritten into another LP file the variables there will appear in a different order within each row In this example if you execute the command display problem a11 you will see this Maximize obj 2 x2 3 x3 Subject To cl x2 x3 xl lt 20 C2 3 x2 x3 x1 lt 30 Bounds 0 lt x1 lt 40 All other variables are gt 0 ILOG CPLEX 8 1 USER S MANUAL MANAGING INPUT amp OUTPUT That is x1 appears at the end of each constraint in which it has a nonzero coefficient Also while re ordering like this does not affect the optimal objective function value of the problem if there exist alternate optimal solutions at this value then the different o
531. ty with respect to the entire model including any part of the model specified through goals To test if an injected solution is feasible with all goals the execute method of a solution goal 11oCplex first creates a subnode of the current node This subnode will of course inherit the goal stack from its parent In addition the solution goal will push local cuts onto the stack of the subnode such that all variables are fixed to the values of the injected solution By processing this subnode as the next node IloCp1ex ensures that the solution is feasible with respect to all goals or is otherwise discarded Goals that have been executed so far are either reflected as global cuts or by the local cuts that are active at the current node Thus if the relaxation remains feasible after the variable fixings have been added the feasibility of these goals is assured If at that point the goal stack is not empty the goals on the goal stack need to be checked for feasibility as well Thus by continuing to execute the goals from the goal stack IloCplex will either prove feasibility of the solution with respect to the remaining goals or in case the relaxation becomes infeasible determine it to be really infeasible and discard the solution The rest of the branch amp cut search remain unaffected by all of this The benefit of this approach is that your heuristic need not be aware of the entire model including all its parts that might be implemented via
532. ual formulation of an LP automatically You no longer have to tell ILOG CPLEX to write the dual formulation to a DUA file and then tell ILOG CPLEX to read the file back in and solve it EMB is the format ILOG CPLEX uses to save an embedded network it extracts from a problem EMB files are written in MPS format IIS is the format ILOG CPLEX uses to represent irreducible inconsistent sets of constraints Finding a Set of Irreducibly Inconsistent Constraints on page 143 and Example Writing an IIS Type File on page 145 explain more about these kinds of files LP Linear Programming is an ILOG CPLEX specific file formatted for entering problems in an algebraic row oriented form In other words LP format allows you to enter problems in terms of their constraints When you enter problems interactively in ILOG CPLEX 8 1 USER S MANUAL MANAGING INPUT amp OUTPUT the Interactive Optimizer you are implicitly using LP format ILOG CPLEX will also read in files in LP format Working with LP Files on page 292 explains more fully how to use LP files with ILOG CPLEX MIN format for representing minimum cost network flow problems was introduced by DIMACS in 1991 More information about DIMACS network file formats is available via anonymous ftp from ftp dimacs rutgers edu pub net flow general info specs tex MPS Mathematical Programming System is an industry standard ASCII text file format for mathematical programming problems Besides
533. uild network problem n goto TERMINATE Optimize the problem and obtain solution status CPXNETprimopt env net if status fprintf stderr Failed to optimize network Nn goto TERMINATE get network dimensions narcs CPXNETgetnumarcs env net nnodes CPXNETgetnumnodes env net allocate memory for solution data x double malloc narcs sizeof double dj double malloc narcs sizeof double pi double malloc nnodes sizeof double slack double malloc nnodes sizeof double 184 ILOG CPLEX 8 1 USER S MANUAL EXAMPLE USING THE NETWORK OPTIMIZER WITH THE CALLABLE LIBRARY if x NULL dj NULL pi NULL slack NULL t fprintf stderr Failed to allocate arrays n goto TERMINATE status CPXNETsolution env net amp solstat amp objval x pi slack dj if status fprintf stderr Failed to obtain solution n goto TERMINATE i e ES D 3 2 Woy Bley NET UIAJOS Write the output to the screen printf nSolution status d n solstat printf Solution value f n n objval for i 0 i lt nnodes i printf Node 2d Slack 10f Pi 10f n i slack i pilil for j 0 j lt nares j printf Arc 2d Value 10f Reduced cost 10f n j x3 833l31 Finally write a copy of the problem to a file status CPXNETwri
534. ull Thus the suggested method for setting steepest edge pricing for use with the primal simplex algorithm is Cplex setParam IloCplex IntParam PPriInd IloCplex PrimalPricing Steep Table 2 5 gives an overview of the classes defining constants for parameters Table 2 5 Classes with Parameters Defined by Integers class for use with parameters IloCplex Algorithm IloCplex IntParam RootAlg IloCplex IntParam NodeAlg IloCplex MIPEmphasis IloCplex IntParam MIPEmphasis IloCplex VariableSelect IloCplex IntParam VarSel IloCplex NodeSelect IloCplex IntParam NodeSel IloCplex DualPricing IloCplex IntParam DPrilnd IloCplex PrimalPricing IloCplex IntParam PPrilInd Parameters can be queried with method IloCplex getParam and reset to their default settings with method IloCplex setDefaults The minimum and maximum value to ILOG CPLEX 8 1 USER S MANUAL 71 MORE SOLUTION INFORMATION which an integer or double parameter can be set is queried with methods IloCplex getMin and ITloCplex getMax respectively The default value of a parameter is obtained with IloCplex getDefault When solving MIPs another important way to control the solution process is by providing priority orders and branching directions for variables The methods for doing so are e IloCplex setDirection e IloCplex setDirections e IloCplex setPriority and e IloCplex setPrio
535. ult problems that are numerically difficult for one method may be easier to solve by the other Simplex and barrier optimizers have different memory requirements Depending on the size of the Cholesky factor the barrier optimizer can require significantly more memory than the simplex optimizers Simplex and barrier optimizers work well on different types of problems The barrier optimizer works well on problems where the AA remains sparse Also highly degenerate problems that pose difficulties for the primal or dual simplex optimizers may be solved quickly by the barrier optimizer In contrast the simplex optimizers will probably perform better on problems where the AAT and the resulting Cholesky factor are relatively dense though it is sometimes difficult to predict from the dimensions of the model when this will be the case Using the Barrier Optimizer We have described how the ILOG CPLEX Barrier Optimizer finds primal and dual solutions from the primal and dual formulations of a model see the section Identifying LPs for Barrier Optimization on page 157 but you do not have to reformulate the problem yourself The ILOG CPLEX Barrier Optimizer automatically creates the primal and dual formulations of the problem for you after you enter or read in the problem Specify that you want to use the barrier optimizer by setting the parameter LPMethod to the following value IloCplex Barrier Concert for C users IloCplex Alg
536. unctions in the Interactive Optimizer and by Concert Technology Again a quadratic objective function must be convex in the case of a minimization problem or concave in the case of a maximization problem When entering a quadratic objective with the algebraic view neither symmetry considerations nor any implicit factors need to be considered and indeed attempting to specify both of the off diagonal elements for one of the quadratic terms may result in double the intended value of the coefficient o gt Q 2 U Uv a e 3 Examples ILOG CPLEX LP format requires the factor of 1 2 to be explicitly specified in the file Minimize obj 100 x1 2 200 xl x2 100x2 2 2 MPS format for this same objective function would contain the following OMATRIX x1 x1 100 x1 x2 100 x2 x1 100 x2 x2 100 A C Concert program having such an objective function might include the following model add IloMinimize env 0 5 100 x 0 x 0 100 x 1 x 1 200 x 0 x 1 Or since the algebraic view is supported the factor of 1 2 could be simplified as in the following equivalent expression model add IloMinimize env 50 x 0 x 0 50 x 1 x 1 100 x 0 x 1 ILOG CPLEX 8 1 USER S MANUAL 197 SAVING QP PROBLEMS A similar Java program using Concert might express it this way IloNumExpr x00 model prod 100 model square x 0 IloNumExpr x11 model prod 100 model square x 1
537. ur processors that one concurrent execution of ILOG CPLEX can employ any number of parallel threads to increase performance up to that limit of 4 A license with the parallel option that additionally has a limit larger than one on the number of licensed uses can support that many simultaneous executions of ILOG CPLEX each with the licensed maximum number of parallel threads In such a case the operating system will manage any contention for processors The number of parallel threads used by an ILOG CPLEX optimizer is usually controlled by ILOG CPLEX parameter settings For the OpenMP version the number can also be controlled by environment variable OMP NUM THREADS Set this variable to establish an upper limit on the number of threads used by ILOG CPLEX This is discussed in more detail in the sections that follow Example Threads and Licensing For example let s assume you use ILOG CPLEX to optimize MIP models on an eight processor machine and you have purchased an ILOG CPLEX license for four parallel threads Then you can use the Interactive Optimizer command set threads i substituting values 1 through 4 for i You will not be able to set the thread count higher than 4 because you are licensed for a maximum of four threads If you set environment variable OMP NUM THREADS to 2 in the OpenMP version then you can set the thread count to no more than 2 Any MIP optimization you carry out will be limited to two processors Threads an
538. ures that the variable will be extracted This may also be important if you query solution information for the variable since solution information is available only for modeling objects that are known to ILOG CPLEX because they have been extracted from a model If you feel uncertain about whether or not an object will be extracted you can add it to the model to be sure Even if an object is added multiple times it will only be extracted once and thus will not slow the solution process down Since the sequence of creating the cplex object and extracting the model to it is such a common one IloCplex provides the shortcut IloCplex cplex model This is completely equivalent to separate calls and ensures that the environment used for the cplex object will be the same as that used for the model when it is extracted as required by Concert Technology The shortcut uses the environment from the model to construct the cplex object before extraction ILOG CPLEX 8 1 USER S MANUAL SOLVING CONCERT TECHNOLOGY MODELS WITH ILOCPLEX Solving a Model Once the model is extracted to the cplex object you are ready to solve it This is done by calling cplex solve For most problems this is all that is needed for solving the model Nonetheless ILOG CPLEX offers a variety of controls that allow you to tailor the solution process for your specific needs Q e O D m ES 7 zz i ES Q lt Choosing an Optim
539. urns a Boolean indicating whether or not a feasible solution but not necessarily the optimal one has been found To obtain more of the information about the model that ILOG CPLEX found during the call to the solve method cplex getStatus can be called It returns a member of the nested enumeration type enum IloAlgorithm Status Unknown Feasible Optimal Infeasible Unbounded InfeasibleOrUnbounded Error Notice that the fully qualified names have the IloAlgorithm prefix Table 1 3 shows what the possible return statuses mean for the extracted model Table 1 3 Algorithm Status and Information About the Model Return Status Extracted Model Feasible has been proven to be feasible A feasible solution can be queried Optimal has been solved to optimality The optimal solution can be queried Infeasible has been proven to be infeasible Unbounded has been proven to be unbounded The notion of unboundedness adopted by 11oCplex does not include that the model has been proven to be feasible Instead what has been proven is that if there is a feasible solution with objective value x there exists a feasible solution with objective value x 1 for a minimization problem or x 1 for a maximization problem InfeasibleOrUnbounded has been proven to be infeasible or unbounded Unknown has not been able to be processed far enough to prove anything about the model A common reason may be
540. us break printf s basismsg print in Display the maximum bound violation status CPXgetdblquality env lp amp maxviol CPX_MAX_PRIMAL_INFEAS if status fprintf stderr Failed to obtain bound violation n goto TERMINATE printf Maximum bound violation 17 10g n maxviol TERMINATE Free up the basis and solution 316 ILOG CPLEX 8 1 USER S MANUAL USING QUERY ROUTINES IN THE CALLABLE LIBRARY free and null char amp cstat free and null char amp rstat free and null char amp x free and null char amp cur colname free and null char amp cur colnamestore Free up the problem if necessary if lp NULL status CPXfreeprob env amp lp if status fprintf stderr CPXfreeprob failed error code d n status Free up the CPLEX environment if necessary if env NULL status CPXcloseCPLEX amp env Note that CPXcloseCPLEX produces no output so the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines the errors will be seen if the CPX_PARAM_SCRIND indicator is set to CPX_ON if status char errmsg 1024 fprintf stderr Could not close CPLEX environment Nn CPXgeterrorstring env status errmsg fprintf stderr s errmsg return status END main This simple routine frees up the pointer ptr
541. us CPXaddfuncdest env cpxresults reslabel ourmsgfunc if status CPXmsg cpxerror Failed to set up handler for cpxresults Nin goto TERMINATE Now turn on the iteration display status CPXsetintparam env CPX PARAM SIMDISPLAY 2 if status CPXmsg cpxerror Failed to turn on simplex display level n goto TERMINATE Create the problem strcpy probname example lp CPXcreateprob env amp status probname A returned pointer of NULL may mean that not enough memory was available or there was some other problem In the case of failure an error message will have been written to the error channel from inside CPLEX In this example the setting of the parameter CPX PARAM SCRIND causes the error message to appear on stdout if lp NULL CPXmsg cpxerror Failed to create LP n goto TERMINATE Now populate the problem with the data status populatebycolumn env 1p if status CPXmsg cpxerror Failed to populate problem data n goto TERMINATE Optimize the problem and obtain solution status CPXlpopt env lp if status CPXmsg cpxerror Failed to optimize LP n goto TERMINATE status CPXsolution env lp amp solstat amp objval x pi slack dj if status i1 CPXmsg cpxerror Failed to obtain solution n goto TERMINATE 302 ILOG CPLEX 8 1 USER S MANUAL MANAGING INPUT amp OU
542. utput to Screen or toa File 0 200 eee eee 297 Table 9 4 Callback Macros 0 0 cece tte tenet eee 344 Table 9 5 Status of Nonzero Callbacks for MIPS 00 0 cece eee eee ee 351 Table 9 7 Thread Limit Parameters 00 cece 371 Table 9 8 Parallel Optimizer Methods and Routines 0 0c cee eee eee eee 375 Table A 1 Parameter Name Equivalents 0 0 c eee tte eee 386 ILOG CPLEX 8 1 USER S MANUAL List of Examples Tlel Ee e o E 54 Diet javanino EUER 78 uq E 102 Example of an infeasible iis file ssessessseenenennnenn enne emen 145 Example of infeasible iis with many rows and columns ssee 146 Time limited search for an IIS esssssssssseeeeeeeeeennenneen nennen nnne nnne nennen 147 NOIPEXG COP HERO 149 IDex6 C 2t tete dee eie I dee nnde eA i ieee 151 MOLEX m H 182 gc 190 lloqpexl COP dieit eec iE bec Eh E rc Recte vei oe elie 203 ela 206 Dg 207 gDOX2 6 siding iie Ee t eet Pee 215 euler aBeoo e M 259 uiuos
543. utput to the screen printf nSolution status d n solstat printf Solution value f n n objval for j 0 j lt nfoods j printf Food d Buy 10f n j x j1 Finally write a copy of the problem to a file 2 D ie D D D o A E lt status CPXwriteprob env lp diet lp NULL if status i fprintf stderr Failed to write LP to disk in goto TERMINATE TERMINATE Free up the problem as allocated by CPXcreateprob if necessary if lp NULL status CPXfreeprob env amp lp if status fprintf stderr CPXfreeprob failed error code d n status Free up the CPLEX environment if necessary if env NULL status CPXcloseCPLEX amp env ILOG CPLEX 8 1 USER S MANUAL 105 EXAMPLE 106 DIETARY OPTIMIZATION Note that CPXcloseCPLEX produces no output so the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines if status gt 0 char errmsg 1024 fprintf stderr Could not close CPLEX environment n CPXgeterrorstring env status errmsg fprintf stderr s errmsg if nutrper NULL for i 0 i lt nnutr i free and null char amp nutrper il free_and_null char amp nutrper free_and_null char amp cost free_and_null char amp cost free and null char amp lb free and null
544. ve procedure to simplify the model If for example the model is proven to be infeasible during the presolve no current solution is generated by the optimizer If in contrast infeasibility is only proven by the optimizer current solution information is available to be queried The status returned by calling cplex getCplexStatus may help to determine which case you are facing but it is probably safer and easier to include the methods for querying the solution within try catch statements Method r1oCplex isPrimalFeasible can be called to find out if a primal feasible solution has been found and can be queried Similarly method IloCplex isDualFeasible can be called to find out if a dual feasible solution has been found and can be queried When an LP has been proven to be infeasible ILOG CPLEX provides assistance for determining the cause of the infeasibility This is done by computing what is known as an irreducibly inconsistent set IIS which is a description of the minimal subproblem that is still infeasible An infeasible subproblem is minimal if when you remove any of the constraints including finite bounds the infeasibility vanishes An IIS is computed for an infeasible model by calling method cplex get IIS Currently this method requires that the infeasibility was proven by the primal simplex method It returns an object of type 11oCplex IIS which can then be queried to find out what variables and constraints of the infe
545. ve to the total solution time and a better order can lead to a smaller total solution time In other words a change in this parameter is unlikely to improve performance very much The AMD algorithm provides good quality order within moderate ordering time AMF usually provides better order than AMD usually 5 10 smaller factors but it requires somewhat more time 10 20 more ND often produces significantly better order than AMD or AMF Ten fold reductions in runtimes of the ILOG CPLEX Barrier Optimizer have been observed with it on some problems However ND sometimes produces worse order and it requires much more time To select an ordering algorithm set the parameter BarOrder to a value 0 1 2 or 3 Using a Starting Point Heuristic ILOG CPLEX supports several different heuristics to compute the starting point for the ILOG CPLEX Barrier Optimizer The starting point heuristic is determined by the BarStartAlg parameter and Table 5 12 summarizes the possible values and their meanings Table 5 12 BarStartAlg Parameter Values for Starting Point Heuristics Value Heuristic 1 dual is 0 default 2 estimate dual 3 average primal estimate dual 0 4 average primal estimate estimate dual For most problems the default works well However if you are using the dual preprocessing option setting the parameter PreDual to 1 then one of the other heuristics for computing a starting point may perform better than
546. ved class such as IloObjective Similarly an array of range constraints with 0 expressions is created added to the model and stored in array range In the following loop the variables of the model are created one by one in columns thus the new variables are immediately installed in the model An 11o0NumColumn object col is created and initialized to describe how each new variable will be appended to the existing objective and constraints The 11oNumColumn object col is initialized to contain the objective coefficient for the new variable This is created with cost foodCost 31 that is using the overloaded operator for I1o0bjective Next an 11oNumColumn object is created for every constraint representing the coefficient the new variable has in that constraint Again these IloNumColumn objects are created with the overloaded operator this time of IloRange The IloNumColumn objects are merged together to an aggregate IloNumColumn object using operator The coefficient for row i is created with range i nutrPer i j1 which calls the overloaded operator for IloRange objects ILOG CPLEX 8 1 USER S MANUAL EXAMPLE DIETARY OPTIMIZATION When a column is completely constructed a new variable is created for it and added to the array of modeling variables Buy The construction of the variable is performed by the constructor TloNumVar col foodMin j foodMax jl type which creates the new variable with lower bound
547. veral routines in the ILOG CPLEX Callable Library make it easier to work with strings These functions are helpful when you are writing applications in a language such as Visual Basic that does not allow you to dereference a pointer The string routines in the ILOG CPLEX Callable Library are CPXmemcpy CPXstrlen CPXstrcpy and CPXmsgstr FORTRAN Interface The Callable Library can be interfaced with FORTRAN applications You can download examples of a FORTRAN application from the ILOG web site at http www ilog com products cplex Choose Tech Support then choose Callable Library Examples The examples were compiled on a particular platform Since C to FORTRAN interfaces vary across platforms operating system hardware compilers etc you may need to modify the examples for your particular system Whether you need intermediate glue routines for the interface depends on your operating system As a first step in building such an interface we advise you to study your system documentation about C to FORTRAN interfaces In that context this section lists a few considerations particular to ILOG CPLEX in building a FORTRAN interface Case Sensitivity As you know FORTRAN is a case insensitive language whereas routines in the ILOG CPLEX Callable Library have names with mixed case Most FORTRAN compilers have an option such as the option U on UNIX systems that treats symbols in a case sensitive way We recommend that you u
548. vironment you created if they need to access these objects outside the scope of the callback function Example Using Callbacks This example shows you how to use callbacks effectively with routines from the ILOG CPLEX Callable Library It is based on 1pex1 c a program described in the ILOG CPLEX Getting Started manual This example about callbacks differs from that simpler one in several ways To make the output more interesting this example optimizes a slightly different linear program z EN D3 Qe oS Us a UE Q The ILOG CPLEX screen indicator that is the parameter CPX_PARAM_SCRIND is not turned on Only the callback function produces output Consequently this program calls CPXgeterrorstring to determine any error messages and then prints them After the TERMINATE label the program uses separate status variables so that if an error ILOG CPLEX 8 1 USER S MANUAL 351 USING CALLBACKS 352 occurred earlier its error status will not be lost or destroyed by freeing the problem object and closing the ILOG CPLEX environment Table 9 6 summarizes those status variables Table 9 6 Status Variables in lpex4 c Variable Represents status returned by this routine frstatus CPXfreeprob clstatus CPXcloseCPLEX The function mycallback at the end of the program is called by the optimizer This function tests whether the primal simplex optimizer has been called If
549. x IloNumVarType Int ILOG CPLEX will only generate solutions where variable x is an integer within tolerances yet the type returned by x get Type will remain I1oNumVarType Float A variable can only be used in at most one conversion object or the model will no longer be unambiguously defined This does not imply that the type of a variable can only be changed once and never again after that Instead you can remove the conversion object and add a new one to implement consecutive variable type changes ILOG CPLEX 8 1 USER S MANUAL The ILOG CPLEX Callable Library This chapter describes how to write C programs using the ILOG CPLEX Callable Library It includes sections on Architecture of the ILOG CPLEX Callable Library including information on licensing and on compiling and linking your programs 2 D ie D D D o A 5 lt Using the Callable Library in an Application ILOG CPLEX Programming Practices Managing Parameters from the Callable Library 9 9 9 Example Dietary Optimization Architecture of the ILOG CPLEX Callable Library ILOG CPLEX includes a callable C library that makes it easier to develop applications to optimize to modify and to interpret the results of mathematical programming problems whether linear mixed integer or convex quadratic ones You can use the Callable Library to write applications that conform to many modern computer programming paradigms such as cl
550. x 2 lt 30 model add c END populatebyrow Example QPex1 java This example is almost identical to LPex1 java using only the function populatebyrow to create the model Also this function differs only in the creation of the objective from its LPex1 java counterpart Here the objective function is created and added to the model like this IloNumExpr x00 model prod 33 model square x 0 IloNumExpr x11 model prod 22 model square x 1 IloNumExpr x22 model prod 11 model square x 2 1 2 IloNumExpr x01 model prod 12 model prod x 0 x 11 IloNumExpr x12 model prod 23 model prod x 1 x 21 IloNumExpr Q model prod 0 5 model sum x00 x11 x22 x01 x12 double objvals 1 0 2 0 3 0 model add model maximize model diff model scalProd x objvals Q A quadratic objective may be built with square prod or sum methods Note that inclusion of IloPiecewiseLinear will change the model from a QP to a MIQP ILOG CPLEX 8 1 USER S MANUAL 205 EXAMPLE CREATING A QP OPTIMIZING FINDING A SOLUTION Complete Program QPex1 java a File examples src QPexl java Version 8 1 Sf eine a aa ani ie ee aie a ee Copyright C 2001 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products ar a a ES QPexl java Entering and optimizing a QP problem import
551. xample SOS Type 1 for Sizing a Warehouse To give you a feel for how SOSs can be useful here s an example of an SOS Type 1 used to choose the size of a warehouse Let s assume for this example that we can build a warehouse of 10000 20000 40000 or 50000 square feet We define binary variables for the four sizes Say Xj X2 X4 and x5 We connect these variables by a constraint defining another variable to denote available square feet like this z 70000x 20000x 40000x4 50000x5 0 Those four variables are members of a special ordered set Only one size can be chosen for the warehouse that is at most one of the x variables can be nonzero in the solution And there is an order relationship among the x variables namely the sizes that can be used as weights We say that the weights of the set members are 70000 20000 40000 and 50000 Let s say furthermore that we have a fractional that is noninteger solution of x 0 1 X5 0 9 These values indicate that other parts of the model have imposed the requirement of 46000 square feet since 0 1 10000 0 9 50000 46000 In SOS parlance we say that the weighted average of the set is 0 1 10000 0 9 50000 0 1 0 9 46000 We split the set before the variable with weight exceeding the weighted average In this case we split the set like this x x2 and x4 will be in one subset x in the other ILOG CPLEX 8 1 USER S MANUAL USING SPECIAL ORDERED SETS Now we
552. xample shows how to transform a network flow problem into its corresponding LP formulation That example also indicates why you might want to make such a change The example reads a network flow problem from a file rather than populating the problem object by adding rows and columns as we did in netex1 c It then attempts to solve the ILOG CPLEX 8 1 USER S MANUAL 189 v fa 7 MO 4 X10M N UIAJOS EXAMPLE 190 NETWORK TO LP TRANSFORMATION problem by calling the Callable Library routine CPXNETprimopt If it determines that the problem is infeasible it then transforms the problem into its LP formulation so that the infeasibility finder can analyze the problem and possibly indicate the cause of the infeasibility in an irreducibly inconsistent set IIS To perform this analysis the application calls the Callable Library routine CPXiiswrite to write the IIS to the file netex2 iis Complete Program netex2 c The complete program netex2 c appears here and online in the standard distribution VE P RP File examples src netex2 c Version 8 1 p Copyright C 1997 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products ey p o
553. xamples that we explain in the manual we ll also show you the complete code for the solution so that you can see exactly how ILOG CPLEX fits into your own applications In case you prefer to study code online you ll also find the complete code for these examples in a subdirectory of the standard distribution of ILOG CPLEX The following table describes all the examples in this manual and indicates where to find them both online and in the manual Example Source File In This Manual dietary optimization building a model by rows constraints or by columns vari ables solving with IloCplex dietary optimization building a model by rows constraints or by columns vari ables solving with IloCplex ilodiet cpp Diet java Example Dietary Optimization on page 49 Example Diet java Source Code on page 78 dietary optimization building a model by rows constraints or by columns vari ables solving with the Callable Library diet c Example Dietary Optimization on page 99 linear programming starting from an advanced basis ilolpex6 cpp lpex6 c Example ilolpex6 cpp on page 148 Example Ipex6 c on page 150 network optimization using the Callable Library netexl c Complete Program netex1 c on page 182 ILOG CPLEX 8 1 USER S MANUAL 25 NOTATION IN THIS MANUAL Example Source File In This Manual network optimization relaxing a network flow to an
554. xpression not local to the callback function itself that is constructed and end ed in it The only exception is the modification of array elements For example x i 0 would be permissible whereas x add 0 would not unless x is a local array of the callback The Continuous Callback The second special callback class is IloCplex Cont inuousCallbackI TloCplex Cont inuousCallback If you create a Continuous callback and use it with an IloCplex object it will be used for both the barrier and the simplex callback In other words implementing and using one Continuous callback is equivalent to writing and using these two callbacks independently ILOG CPLEX 8 1 USER S MANUAL 345 z a 563 O 2 oS Us a UE o USING CALLBACKS Example Deriving the Simplex Callback Example ilolpex4 cpp demonstrates the use of the simplex callback to print logging information at each iteration It is a modification of example ilolpex1 cpp so we will restrict our discussion to the differences The following code ILOSIMPLEXCALLBACKO MyCallback cout lt lt Iteration lt lt getNiterations lt lt if isFeasible cout lt lt Objective lt lt getObjValue lt lt endl else cout lt lt Infeasibility measure lt lt getInfeasibility lt lt endl defines the callback MyCallback without parameters with the code enclosed in the outer In Java the same callback is de
555. y CPXcreateprob if necessary if lp NULL status CPXfreeprob env amp lp if status fprintf stderr CPXfreeprob failed error code d n status Free up the CPLEX environment if necessary if env NULL status CPXcloseCPLEX amp env Note that CPXcloseCPLEX produces no output so the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines the errors will be seen if the CPX_PARAM_SCRIND indicator is set to CPX_ON if status char errmsg 1024 fprintf stderr Could not close CPLEX environment Nn CPXgeterrorstring env status errmsg fprintf stderr s errmsg Free up the problem data arrays if necessary free and null char amp probname free and null char amp obj free and null char free and null char amp rhs free and null char amp sense amp matbeg ILOG CPLEX 8 1 USER S MANUAL 265 i AS fe ES D di Buinjos EXAMPLE 266 OPTIMIZING A BASIC MIP PROBLEM free_and_null free_and_null free_and_null free_and_null free_and_null free_and_null return status END main char char char char char char This function fills in Maximize obj Subject To Gl c2 eis Bounds 0 lt x1 2 lt x4 Integers x4 End xy static int setproblemdata char sense p int matind p doub
556. y a node LP solution in about the same way this example handles them Whether this or adding the cuts directly to the model gives better performance when solving the model depends on the individual problem ILOG CPLEX 8 1 USER S MANUAL USING CALLBACKS Complete Program iloadmipex5 cpp The complete program iloadmipex5 cpp appears here and online in the standard distribution The Java version is found in file AGMIPex5 java at the same location ffo MM M M M M M M M e MM QR File examples src iloadmipex5 cpp Version 8 1 x BSR a a Sa Se SS SS Copyright C 1999 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products a a a aaa aa a iloadmipex5 cpp Solving noswot by adding cuts in a cut callback finclude lt ilcplex ilocplex h gt ILOSTLBEGIN ILOCUTCALLBACK3 CtCallback IloExprArray lhs IloNumArray rhs IloNum eps IloInt n lhs getSize for IloInt i 0 i lt n i IloNum xrhs rhs i if xrhs lt IloInfinity amp amp getValue lhs i gt xrhs eps loRange cut try cut lhs i lt xrhs add cut end rhs i IloInfinity catch cut end throw void makeCuts const IloNumVarArray vars IloExprArray lhs IloNumArray rhs loNumVar x11 x12 x13 x14 x15 loNumVar x21 x22 x23 x2
557. y for C Users shows a program using the ILOG CPLEX Concert Technology Library to solve optimization problems The optimization part of the user s application program is captured in a set of interacting C or ILOG CPLEX 8 1 USER S MANUAL 31 THE DESIGN OF THE ILOG CPLEX CONCERT TECHNOLOGY LIBRARY 32 objects that the application creates and controls These objects can be divided into two categories 1 Modeling objects are used to define the optimization problem Generally an application creates several modeling objects to specify the optimization problems Those objects are grouped into an IloMode1 object representing the complete optimization problem 2 IloCplex objects are used to solve models created with the modeling objects An IloCplex object reads a model and extracts its data to the appropriate representation for the ILOG CPLEX optimizer Then the 11oCp1ex object is ready to solve the model it extracted and be queried for solution information User Written Application lloCplex objects Concert Technology modeling objects Y ILOG CPLEX database Figure 1 1 A View of Concert Technology for C Users Licenses ILOG CPLEX runs under the control of the ILOG License Manager ILM Before you can run any application program that calls ILOG CPLEX you must have established a valid license that it can read Licensing instructions are provided to you separately when you buy
558. y hard to solve without adding special cuts Although it is now solvable directly the computation time is in the order of several hours on state of the art computers However cuts can be derived and the addition of these cuts makes the problem solvable in a matter of minutes or seconds These cuts are x21 x22 lt 0 x22 x23 lt 0 x23 x24 lt 0 2 08 x1ll 2 98 x21 3 47 x31 2 24 x41 2 08 x51 0 25 w11 0 25 w21 0 25 w31 0 25 w41 0 25 w51 lt 20 25 2 08 x12 2 98 x22 3 47 x32 2 24 x42 2 08 x52 0 25 w12 0 25 w22 0 25 w32 0 25 w42 0 25 w52 lt 20 25 2 08 x13 2 98 x23 3 47 x33 2 24 x43 2 08 x53 0 25 w13 0 25 w23 0 25 w33 0 25 w43 0 25 w53 lt 20 25 2 08 x14 2 98 x24 3 47 x34 2 24 x44 2 08 x54 0 25 w14 0 25 w24 0 25 w34 0 25 w44 0 25 w54 lt 20 25 2 08 x15 2 98 x25 3 47 x35 2 24 x45 2 08 x55 0 25 w15 0 25 w25 0 25 w35 0 25 w45 0 25 w55 lt 16 25 These cuts have been derived after interpreting the model as a resource allocation model on five machines with scheduling horizon constraints and transaction times The first three cuts break symmetries among the machines while the others capture minimum bounds on transaction costs Of course the best way to solve the noswot model with these cuts is to simply add them to the model before calling the optimizer However for demonstration purposes we will add the cuts using a goal The
559. y well be possible to improve performance by changing the parameter that determines the pricing algorithm DPriiInd for the dual simplex optimizer or PPriInd for the primal simplex optimizer The symbolic names for the acceptable values for these parameters are given in Table 5 3 and Table 5 4 below The default value in both cases is 0 Table 5 3 DPrilnd Parameter Values for Dual Simplex Pricing Algorithm Description Concert Callable Library 0 determined automatically DPriIndAuto CPX DPRIIND AUTO 1 standard dual pricing DPriIndFull CPX DPRIIND FULL 2 steepest edge pricing DPriIndSteep CPX DPRIIND STEEP 3 steepest edge in slack space DPriIndFullSteep CPX DPRIIND FULLSTEEP 4 steepest edge unit initial norms DPriIndSteepQStart CPX DPRIIND STEEPOSTART Table 5 4 PPrilnd Parameter Values for Primal Simplex Pricing Algorithm Description Concert Callable Library 1 reduced cost pricing PPriIndPartial CPX PPRIIND PARTIAL 0 hybrid reduced cost and devex PPriIndAuto CPX PPRIIND AUTO 1 devex pricing PPrilndDevex CPX PPRIIND DEVEX 2 steepest edge pricing PPriIndSteep CPX PPRIIND STEEP 3 steepest edge slack initial PPriIndSteepQStart CPX PPRIIND STEEPOSTART norms 4 full pricing PrilndFull CPX PPRIIND FULL For the dual simplex pricing parameter the default value selects steepest edge pricing
560. your parameter specification file You set that environment variable in the customary way for your platform For example on a Unix platform you might use a shell command to set the environment variable or on a personal computer running NT you might click on the System icon in the control panel then select the environment tab from the available system properties tabs During initialization in the Interactive Optimizer ILOG CPLEX locates any available parameter specification file by checking the current execution directory for cplex par and by checking the environment variable CPLEXPARFILE and reads that file As it opens the file ILOG CPLEX displays the message Initial parameter values are being read from cplex par or from the parameter specification file you specified As ILOG CPLEX displays that message on the screen it also writes the message to the log file If ILOG CPLEX cannot open the file it displays no message records no note in the log file and uses default parameter settings You can use a parameter specification file to change any parameter or parameters accessible by the set command in the Interactive Optimizer The parameter types names and options are those used by the set command in the Interactive Optimizer To create a parameter specification file you can use either of these alternatives Use an ordinary text editor to create a file where each line observes the following syntax parameter
561. your software for additional information on activating and maintaining ILM license keys 384 ILOG CPLEX 8 1 USER S MANUAL ILOG CPLEX Parameter Names In the parts of this manual where the algorithmic discussion is independent of the compiler or language CPLEX parameter names are generally given in terms of their Concert naming convention For convenience Table A 1 Parameter Name Equivalents in this appendix lists the correspondence of these names to those used by the Callable Library and the Interactive Optimizer For details of each of these parameters consult Appendix A of the ILOG CPLEX Reference Manual In most cases parameter names follow these conventions Concert Technology in C Programs In C programs using Concert the parameter name is preceded by IloCplex It is not generally necessary to distinguish among integer Boolean numeric and string parameters Example usage cplex setParam IloCplex AdvInd 0 Concert Technology in Java Programs In Java programs using Concert the parameter name is preceded by 11oCplex then either IntParam or NumParam BooleanParam Or StringParam depending on the entry shown in the Type column of the table Example usage cplex setParam IloCplex BooleanParam Advind false Callable Library The Callable Library puts the parameter name in all capital letters preceded by CPX PARAM Parameters are accessed by functions such as CPXsetintpa

ILOG CPLEX 8.1 User's Manual

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