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ILOG CPLEX 9.0 Getting Started

1. Changing the Problem Object A major consideration in the design of ILOG CPLEX is the need to efficiently re optimize modified linear programs In order to accomplish that ILOG CPLEX must be aware of ILOG CPLEX 9 0 GETTING STARTED 123 a r O 2 Keq 91qel1eo CREATING A SUCCESSFUL CALLABLE LIBRARY APPLICATION changes that have been made to a linear program since it was last optimized Problem modification routines are available in the Callable Library Do not change the problem by changing the original problem data arrays and then making a call to CPXcopylp Instead change the problem using the problem modification routines allowing ILOG CPLEX to make use of as much solution information as possible from the solution of the problem before the modifications took place For example suppose that a problem has been solved and that the user has changed the upper bound on a variable through an appropriate call to the ILOG CPLEX Callable Library A re optimization would then begin from the previous optimal basis and if that old basis were still optimal then that information would be returned without even the need to refactor the old basis Creating a Successful Callable Library Application 124 Callable Library applications are created to solve a wide variety of problems Each application shares certain common characteristics regardless of its apparent uniqueness The following steps can help you minimize development
2. GETTING STARTED 163 INDEX name 38 representing in model 70 sensitivity analysis 49 154 operator 75 operator 75 optimal solution 97 optimization model creating 69 defining extractable objects 70 extracting 69 optimization problem interrupting 48 reading from file 82 representing 74 solving with IloCplex 71 optimize Interactive Optimizer command 45 re solving 47 syntax 47 optimizer choosing by problem type 126 choosing by switch in application 82 choosing in Interactive Optimizer 47 options 12 parallel 122 syntax for choosing in C 81 ordering variables 43 out Concert method 98 Output Stream 98 P parallel choosing optimizers for 12 linking for optimizers 122 parameter Boolean 88 changing 56 88 displaying settings 57 integer 88 list of settable 56 numeric 88 resetting to defaults 57 string 88 parameter specification file 57 path names 52 164 ILOG CPLEX 9 0 populateByColumn 98 populateByNonzero 98 100 populateByRow 98 primal simplex optimizer availability 47 selecting 81 primopt Interactive Optimizer command 47 problem change options 59 changing 58 creating binary representation 127 data entry options 13 display options 40 displaying 40 displaying a part 42 displaying statistics 41 entering from the keyboard 36 entering in LP format 37 naming 36 reading files 138 solving 45 128 verifying entry 40 59 problem file reading 53 writing 50 problem formulation ilolpexl cpp 74 Inte
3. 3x x3 lt 30 with these bounds 0 x 40 0 lt x lt 20 OS x38 20 General Structure of an ILOG CPLEX Concert Technology Application The first operation is to create the environment object env and the last operation is to destroy it by calling env end The rest of the code is enclosed in a try catch clause to gracefully handle any errors that may occur First the example creates the model object and after checking the correctness of command line parameters it creates empty arrays for storing the variables and range constraints of the optimization model Then depending on the command line parameter the example calls one of the functions populatebyrow populatebycolumn or populatebynonzero to fill the model object with a representation of the optimization problem These functions return the variable and range objects in the arrays var and con which are passed to them as parameters After the model has been populated the 11oCplex algorithm object cplex is created and the model is extracted to it The following call of the method so1ve invokes the optimizer If it fails to generate a solution an error message is issued to the error stream of the environment cplex error and the integer 1 is thrown as an exception IloCplex provides the output streams out for general logging warning for warning messages and error for error messages They are preconfigured to cout cerr and cerr respectively Thus by default you will s
4. ILOG CPLEX 9 0 GETTING STARTED 103 e O E 9 O r E O O zz S o Ko lt COMPLETE CODE OF LPEX1 JAVA X 1 model prod 3 r 1 0 x 21 0 model prod 0 104 ILOG CPLEX 9 0 GETTING STARTED Concert Technology Tutorial for NET Users This chapter introduces ILOG CPLEX through ILOG Concert Technology in the NET framework It gives you an overview of a typical application and highlights procedures for Creating a model Populating the model with data either by rows by columns or by nonzeros Solving that model Displaying results after solving This chapter concentrates on an example using C NET There are also examples of VB NET Visual Basic in the NET framework delivered with ILOG CPLEX in yourCPLEXhome examples i86_2000_7 1 vb Because of their NET framework those VB NET examples differ from the traditional Visual Basic examples that may already be familiar to some ILOG CPLEX users The traditional Visual Basic examples are available in yourCPLEXhome examples msvc6 vb 3 9 95 o e 3 Z ma E gt c5 0 o 25 n Q lt ILOG CPLEX 9 0 GETTING STARTED 105 WHAT You NEED TO KNOW PREREQUISITES Note This chapter consists of a tutorial based on a procedure based learning strategy The tutorial is built around a sample problem available in a file that can be opened in an integrated development environment such as Microsoft Visual Studio As you follow th
5. goto TERMINATE status CPXsetintparam env CPX_PARAM_LPMETHOD CPX_ALG_NET if status fprintf stderr Failed to set the optimization method error d n status goto TERMINATE status CPXlpopt env 1p if status fprintf stderr Failed to optimize LP n goto TERMINATE status CPXgetobjval env lp amp objval if status fprintf stderr CPXgetobjval failed n ILOG CPLEX 9 0 GETTING STARTED 151 g r O 2 Aseaqiy aqe ADDING ROWS TO A PROBLEM EXAMPLE LPEX3 C 152 goto TERMINATE printf After network optimization objective is 10g1n objval Now add the extra rows to the problem status CPXaddrows env lp 0 ROWSCOMP Armatbeg ROWSCOMP Arhs Asense Armatbeg Armatind Armatval NULL NULL if status 4 fprintf stderr CPXaddrows failed n goto TERMINATE Because the problem is dual feasible with the rows added using the dual simplex method is indicated status CPXsetintparam env CPX PARAM LPMETHOD CPX ALG DUAL if status 1 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 status CPXsolution env lp amp lpstat amp objval x NULL NULL NULL if status fprintf stderr CPXsolution failed n goto TERMINATE printf
6. 20 Again many methods are provided for adding other constraint types including equality constraints greater than or equal to constraints and ranged constraints Internally they are all represented as IloRange objects with appropriate choices of bounds which is why all these methods return 11oRange objects Also note that the expressions above could have been created in many different ways including the use of IloLinearNumExpr Solve the Model So far you have seen some methods of 11oCplex for creating models All such methods are defined in the interfaces I1loModeler and its extension 110MPModeler However IloCplex not only implements these interfaces but also provides additional methods for solving a model and querying its results After you have created a model as explained in the previous section the IloCplex object cplex is ready to solve the the problem which consists of the model and all the modeling objects that have been added to it Invoking the optimizer then is as simple as calling the method solve The method solve returns a Boolean value indicating whether the optimization succeeded in finding a solution If no solution was found false is returned If t rue is returned then ILOG CPLEX found a feasible solution though it is not necessarily an optimal solution More precise information about the outcome of the last call to the method solve can be obtained by calling IloCplex getStatus ILOG CPLEX 9 0 GETTI
7. Changing the rules of business ILOG CPLEX 9 0 Getting Started October 2003 Copyright O 1987 2003 ILOG S A All rights reserved Preface Chapter 1 Table of Contents Introducing ILOG CPLEX o coooocococcco nnn 9 What IS ILOG CPLEX i i Rx mx x emm eae ee els Sete 10 ILOG CPLEX Components 0 0 hrs 11 Optimizer Options pri mE HT iar Oe ee a eae ae 12 Data Entry ODtOns ccena sre ot a Braye del e ose er ood eae ete eee 13 Solving an LP with LOG CPLEX eseseeeeees eee nnn 13 Using the Interactive Optimizer 1 0 0 tte eee 14 Concert Technology for C Users 0 0 cect ete nee 14 Concert Technology for NET Users oocccccccco e n 15 Concert Technology for Java US8rS oooooooooooor eee eens 16 Using the Callable Library o ooococoocccccco RII Ir 16 What You Need to KNOW zeci ee sist erama iaae nia n n n nnn 18 What s in This Manual oo ooococccnc RR III 3 hn 19 Notation in this Manual lesser Rh n hh hn 19 Related Documentation 0 0 0 0 cece eR n n nh nnn 20 Setting Up ILOG CPLEX o oococoococ n nnn nnn 25 Installing LOG CPLEX sseeeeeeee RI RII hn 26 Setting Up Licensing siss 202iee oe lad Ir ra A eee NES EG 28 Using the Component Libraries celles IIR 28 ILOG CPLEX 9 0 GETTING STARTED 3 CONTENTS Chapter 2 Interactive Optimizer Tutorial ooooococcoooncrr ao 33 Starting ILOG CP
8. ILOG CPLEX 9 0 GETTING STARTED READING A PROBLEM FROM A FILE EXAMPLE LPEX2 C int rstat NULL CPXENVptr env NULL CPXLPptr lp NULL int status 0 int ub int cur numrows cur numcols int method char basismsg Check the command line arguments if argo 3 strchr podhbnsc argv 2 0 NULL 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 Nn 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 y 1 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 CPXcreateprob env amp status argv 1 A returned pointer of NULL may mean that not enough memory ILOG CPLEX 9 0 GETTING STARTED 141 g r O
9. X x 3 2 x 6 3 x 7 4 2 x 2 3 x 3 1 x 6 1 x 7 2 IloCplex Dual GETTING STARTED and solve with dual ILOLPEX3 CPP 89 g r le E O ie o o N bo ouy2a WI 070 MODIFYING AN OPTIMIZATION PROBLEM EXAMPLE ILOLPEX3 CPP IloNumArray vals env cplex getValues vals x cplex out lt lt Solution status lt lt cplex getStatus lt lt endl cplex out lt lt Objective value lt lt cplex getObjValue lt lt endl cplex out lt lt Solution is lt lt vals lt lt endl cplex exportModel lpex3 sav 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 90 ILOG CPLEX 9 0 GETTING STARTED Concert Technology Tutorial for Java Users This chapter is an introduction to using ILOG CPLEX through ILOG Concert Technology in the Java programming language It gives you an overview of a typical application program and highlights procedures for Creating a model Solving that model Querying results after solving Handling error conditions ILOG Concert Technology allows your application to call ILOG CPLEX directly through the Java Native Interface JNI This Java interface supplies a rich means for you to use Java objects to build your optimizat
10. 1 0 2 0 3 0 model AddMaximize model ScalProd x objvals rng 0 new IRange 2 rng 0 0 model AddLe model Sum model Prod 1 0 x 0 model Prod 1 0 x 1 model Prod 1 0 x 2 20 0 rng 0 1 model AddLe model Sum model Prod 1 0 x 0 model Prod 3 0 x 1 model Prod 1 0 x 2 30 0 internal static void PopulateByColumn IMPModeler model INumVar var IRange rng IObjective obj model AddMaximize rng 0 new IRange 2 rng 0 0 model AddRange System Double MaxValue 20 0 rng 0 1 model AddRange System Double MaxValue 30 0 IRange r0 rng 0 0 IRange rl rng 0 1 var 0 new INumVar 3 var 0 0 model NumVar model Column obj 1 0 And model Column r0 1 0 And model Column r1 LOYA Fy 0 0 40 0 var 0 1 model NumVar model Column obj 2 0 And model Column r0 1 0 And model Column r1 3 0 0 0 System Double MaxValue ILOG CPLEX 9 0 GETTING STARTED 117 EXAMPLE 118 LIPExXI 68 var 0 2 model NumVar model Column obj 3 0 And model Column r0 1 0 And model Column r1 1 0 0 0 System Double MaxValue internal static void PopulateByNonzero IMPModeler model double lb double ub INumVar x var 0 double Xx INumVar var IRange rng 19 0 0 0 0 0 4 40 0 System Double MaxValue System Double MaxValue model NumVarArray 3 lb
11. 2 Aseaqiy aqe READING A PROBLEM FROM A FILE EXAMPLE LPEX2 C 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 1n 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 switch argv 2 0 case o method CPX ALG AUTOMATIC break case p method CPX ALG PRIMAL break case d method CPX ALG DUAL break case n method CPX ALG NET break case h method CPX ALG BARRIER break case b method CPX ALG BARRIER Status CPXsetintparam env CPX PARAM BARCROSSALG CPX ALG NONE Xf status fprintf stderr Failed to set the crossover method error d Wn status goto TERMINATE break case s method CPX ALG SIFTING break Nar case c method CPX ALG CONCURRENT 142 ILOG CPLEX 9 0 GETTING STARTED READING A PROBLEM FROM A FILE EXAMPLE LPEX2 C break de
12. Am2Xo2 T AmnXn bg with these bounds lE x lt Uy where can be S gt or and the upper bounds u and lower bounds may be positive infinity negative infinity or any real number The elements of data you provide as input for this LP are Objective function coefficients Cy Co C Constraint coefficients 11 amp 21 Any Amt Am2 say Amn Right hand sides b Do Dm Upper and lower bounds Us Uo Uy and Ij Io In The optimal solution that ILOG CPLEX computes and returns is Variables X1 Xo Xn ILOG CPLEX also can solve several extensions to LP Network Flow problems a special case of LP that CPLEX can solve much faster by exploiting the problem structure Quadratic Programming QP problems where the LP objective function is expanded to include quadratic terms Quadratically Constrained Programming QCP problems that include quadratic terms among the constraints 10 ILOG CPLEX 9 0 GETTING STARTED WHAT Is ILOG CPLEX Mixed Integer Programming MIP problems where any or all of the LP or QP variables are further restricted to take integer values in the optimal solution and where MIP itself is extended to include constructs like Special Ordered Sets SOS and semi continuous variables ILOG CPLEX Components CPLEX comes in three forms to meet a wide range of users needs The CPLEX Interactive Optimizer is an executable program that can read a problem
13. O static int Aseaqiy 91qel1eo ILOG CPLEX 9 0 GETTING STARTED 135 BUILDING AND SOLVING A SMALL LP MODEL IN C 136 populatebycolumn CPXENVptr env 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 CPXLPptr 1p CPXchgobjsen env lp CPX MAX Problem is maximization Now create the new rows rowname 0 c1 sense 0 cCL rhs 0 20 0 rowname 1 c2 sense 1 cCL rhs 1 30 0 status CPXnewrows env lp if status Now add the new columns First populate the arrays NUMROWS rhs sense NULL rowname goto TERMINATE 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 return status ILOG
14. Though the Describe step of the process may seem trivial in a simple problem like this one you will find that taking the time to fully describe a more complex problem is vital for creating a successful application You will be able to code your application more quickly and effectively if you take the time to describe the model isolating the decision variables constraints and objective Model The second stage is for you to use the classes of ILOG Concert Technology for NET users to build a model of the problem The model is composed of decision variables and constraints on those variables The model of this problem also contains an objective Solve The third stage is for you to use an instance of the class Cplex to search for a solution and to solve the problem Solving the problem consists of finding a value for each variable while simultaneously satisfying the constraints and minimizing the objective The aim in this tutorial is to to see three different ways to build a model by rows by columns or by nonzeros After building the model of the problem in one of those ways the application optimizes the problem and displays the solution Describe the Problem Write a natural language description of the problem and answer these questions What is known about the problem What are the unknown pieces of information the decision variables in this problem What are the limitations the constraints on the decision variables
15. What is the purpose the objective of solving this problem ILOG CPLEX 9 0 GETTING STARTED MODEL Building a Small LP Problem in Cf Here is a conventional formulation of the problem that the example optimizes Maximize Xj 2X 3X4 subject to X Xx X 20 Xj 3 X4 lt 30 with these bounds 0 lt x lt 40 0 X 00 0 x4 00 What are the decision variables in this problem X X5 X3 What are the constraints X Xx X 20 X 3 9 X 0 x 40 0 X S 00 0 X4 S 00 What is the objective Maximize X 2X 3X3 Model After you have written a description of the problem you can use classes of ILOG Concert Technology for NET users with ILOG CPLEX to build a model Open the file Open the file yourCPLEXhome examples src tutorials LPexllesson cs in your integrated development environment such as Microsoft Visual Studio ILOG CPLEX 9 0 GETTING STARTED 109 3 8 95 o o oO 3 Z ma E gt c5 0 o Ro 0 Q lt MODEL 110 Create the model object Go to the comment Step 3 in that file and add this statement to create the Cp1ex model for your application Cplex cplex new Cplex That statement creates an empty instance of the class Cplex In the next steps you will add methods that make it possible for your application populate the model with data either by rows by columns or by nonzeros Populate the model by ro
16. following prompt about file formats on the screen File Type Options bas INSERT format basis file lp LP format problem file min DIMACS min cost network flow format file mps MPS format problem file mst MIP start file net CPLEX Network flow format file ord Integer priority order file qp Quadratic coefficient matrix file sav Binary matrix and basis file sos Special ordered sets file tre Branch and bound treesave file vec Vector solution format file File Type Options ILOG CPLEX 9 0 GETTING STARTED 53 READING PROBLEM FILES 54 Reminder All these file formats are documented in more detail in the reference manual ILOG CPLEX File Formats Reading LP Files At the CPLEX gt prompt type read The following message appears requesting a file name Name of file to read Four files have been saved at this point in our tutorial example example2 example lp example bas Specify the file named example that you saved while practicing the write command You recall that the example problem was saved in LP format so in response to the file type prompt enter lp ILOG CPLEX displays a confirmation message like this Problem example read Read Time 0 03 sec The example problem is now in memory and you can manipulate it with ILOG CPLEX commands Tip The intermediate prompts for the read command can be avoided by entering the entire command on one line like this read example lp Using Fil
17. include L ilcplex lib NNNM platform L lt lib format gt L lt cpLex LIBRARY gt Figure 1 1 Installation Directory Structures ILOG CPLEX 9 0 GETTING STARTED 27 SETTING UP LICENSING Setting Up Licensing ILOG CPLEX 9 0 runs under the control of the ILOG License Manager ILM Before you can run ILOG CPLEX or any application that calls it you must have established a valid license that ILM can read Licensing instructions are provided in the ILOG License Manager User s Guide amp Reference which is included with the standard ILOG CPLEX product distribution The basic steps are 1 Install ILM Normally you obtain ILM distribution media from the same place that you obtain ILOG CPLEX 2 Run the ihostid program which is found in the directory where you install ILM 3 Communicate the output of step 2 to your local ILOG sales administration department They will send you a license key in return 4 Create a file on your system to hold this license key and set the environment variable ILOG LICENSE FILE so that ILOG CPLEX will know where to find the license key The environment variable need not be used if you install the license key in a platform dependent default file location Using the Component Libraries 28 After you have completed the installation and licensing steps you can verify that everything is working by running one or more of the examples that are provided with the standard dist
18. interactively 57 objective shortcut 96 objective function to model 71 rows to a problem 147 addLe Concert method 99 addMinimize Concert method 96 99 advanced basis advanced start indicator 47 using 52 algorithm ILOG CPLEX 9 0 Index automatic Aut oA1g 81 creating object 71 74 and Concert method 100 application and Callable Library 11 and Concert Technology 11 compiling and linking Callable Library 120 compiling and linking Component Libraries 29 compiling and linking Concert Technology 67 development steps 124 error handling 72 126 B baropt Interactive Optimizer command 47 barrier optimizer availability 47 selecting 81 BAS file format 52 55 basis accessing information 82 basis information 97 periodically written 52 starting from previous 88 see also advanced basis basis file reading 55 writing 52 Boolean parameter 88 Boolean variable GETTING STARTED 157 INDEX representing in model 70 bound adding 57 changing 60 default values 38 displaying 44 entering in LP format 38 removing 60 sensitivity analysis 50 154 box variable 41 branch amp bound 81 branch amp cut 81 C Callable Library 119 to 154 application development steps 124 compiling and linking applications 120 conceptual design 119 CPLEX operation 122 description 11 distribution file 120 error handling 126 example model 16 opening CPLEX 122 see also individual CPXxxx routines change Interactive Optimizer command 58
19. lowerr upperr if status 4 fprintf stderr Failed to obtain RHS sensitivity Nin goto TERMINATE printf nRight hand side coefficient sensitivity n for i 0 i lt cur numrows 1 printf Row d Lower 10g Upper 10g n i lowerr i upperr i This sample is familiarly known as throw away code For production purposes you probably want to observe good programming practices such as freeing these allocated arrays at the TERMINATE label in the application A bound value of 1e 20 cpx_INFBOUND is treated as infinity within ILOG CPLEX so this is the value printed by our sample code in cases where the upper or lower sensitivity range on a row or column is infinite a more sophisticated program might print a string such as inf or inf when negative or positive CPX_INFBOUND is encountered as a value Similar code could be added to perform sensitivity analysis with respect to bounds via CPXboundsa 154 ILOG CPLEX 9 0 GETTING STARTED Part Ill Index A accessing basic rows and columns of solution 48 basis information 82 dual values 49 dual values Interactive Optimizer 48 objective function value 48 reduced cost in Java 97 reduced costs in Interactive Optimizer 48 slack values 48 solution values 48 72 add Interactive Optimizer command 57 syntax 58 add obj Concert method 96 adding bounds 57 constraint to model 87 constraints 57 from a file 58
20. model prod 1 0 x 2 30 0 static void populateByColumn IloMPModeler model IloNumVar var IloRange l rng throws IloException IloObjective obj model addMaximize rng 0 new IloRange 2 rng 0 0 model addRange Double MAX VALUE 20 0 rng 0 1 model addRange Double MAX VALUE 30 0 IloRange r0 rng 0 0 IloRange rl rng 0 1 var 0 new IloNumVar 3 var 0 0 model numVar model column obj 1 0 and model column r0 1 0 and model column r1 LEONI 0 0 40 0 var 0 1 model numVar model column obj 2 0 and model column r0 1 0 vand model column r1 E y 0 0 Double MAX ERE var 0 2 model numVar model column obj 3 0 and model column r0 0 and model column r1 M MG 0 0 Double MAX VALUE static void populateByNonzero IloMPModeler model IloNumVar var IloRange rng throws IloException double lb 0 0 0 0 0 0 double ub 40 0 Double MAX VALUE Double MAX VALUE D IloNumVar x model numVarArray 3 lb ub E var 0 x en 7 O double objvals 1 0 2 0 3 0 mi model add model maximize model scalProd x objvals rng 0 new IloRange 2 rng 0 0 model addRange Double MAX VALUE 20 0 rng 0 1 model addRange Double MAX VALUE 30 0 rng 0 0 setExpr model sum model prod 1 0 x 0 model prod 1 0 x 1 model prod 1 0 x 2 rng 0 1 setExpr model sum model prod 1 0 x 0
21. 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 filename algorithm n progname fprintf stderr where filename is a file with extension Wn fprintf stderr MPS SAV or LP lower case is allowed Wn fprintf stderr and algorithm is one of the letters Wn fprintf stderr o default n fprintf stderr p primal simplexin fprintf stderr d dual simplex Nn fprintf stderr n network simplex n fprintf stderr b barrier n fprintf stderr h barrier with crossoverWn fprintf stderr S siftingin fprintf stderr c concurrent Nn fprintf stderr Exiting Wn END usage 146 ILOG CPLEX 9 0 GETTING STARTED ADDING ROWS TO A PROBLEM EXAMPLE LPEX3 C Adding Rows to a Problem Example Ipex3 c This example illustrates how to develop your own solution algorithms with routines from the Callable Library It also shows you how to add rows to a problem object Here is the problem example 1pex3 solves Minimize c x subject to Hx d Ax b 1 x amp u where Hz 310101000 d 3 1 1010000 1 01 1001 10 4 000 10 101 3 0000 101 1 5 A 2 1 2 1 2 1 2 3 b 4 1323 1211 2 C 9 142 8 2 812 l 00000000 u 50 50 50 50 50 50 50 50 The constraints Ax d represent a pure netwo
22. unless another method has been specified by setting the LPMETHOD parameter Entering the Optimize Command At the CPLEX gt prompt type the command ILOG CPLEX 9 0 GETTING STARTED 45 SOLVING A PROBLEM 46 optimize Preprocessing First ILOG CPLEX tries to simplify or reduce the problem using its presolver and aggregator If any reductions are made a message will appear However in our small example no reductions are possible Monitoring the Iteration Log Next an iteration log appears on the screen ILOG CPLEX reports its progress as it solves the problem The solution process involves two stages during Phase I ILOG CPLEX searches for a feasible solution in Phase II ILOG CPLEX searches for the optimal feasible solution The iteration log periodically displays the current iteration number and either the current scaled infeasibility during Phase I or the objective function value during Phase II Once the optimal solution has been found the objective function value solution time and iteration count total with Phase I in parentheses are displayed This information can be useful for monitoring the rate of progress The iteration log display can be modified by the set simplex display command to display differing amounts of data while the problem is being solved Reporting the Solution After it finds the optimal solution ILOG CPLEX reports the objective function value the problem solution time in
23. 1 30 0 ILOG CPLEX 9 0 GETTING STARTED 17 WHAT YOU NEED TO KNOW status CPXaddrows env lp rmatind if t status 4 fprintf stderr Failed to goto TERMINATE status CPXlpopt env lp if status 1 fprintf stderr Failed to goto TERMINATE status CPXsolution env lp if status fprintf stderr Failed to goto TERMINATE printf nSolution status printf Solution value S printf Solution f TERMINATE if lp NULL status CPXfreeprob env 1 status pot fprintf stderr CPXfre if env NULL status CPXcloseCPLEX amp en if status char errmsg 1024 fprintf stderr Could CPXgeterrorstring env fprintf stderr s e return status END main What You Need to Know 0 NUMROWS NUMNZ rhs rmatval NULL NULL sense rmatbeg populate problem in optimize LP n amp solstat amp objval x NULL NULL NULL obtain solution Nn solstat objval sf n n x 0 x 1 x 2 amp 1p eprob failed error code d n status v not close CPLEX environment n status errmsg rrmsg In order to use ILOG CPLEX effectively you need to be familiar with your operating system whether UNIX or Windows This manual 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 yo
24. 119 COMPILING AND LINKING CALLABLE LIBRARY APPLICATIONS ILOG CPLEX environment and all problem defining data are established inside the ILOG CPLEX core User Written Application ILOG CPLEX Callable Library ILOG CPLEX database Figure 6 1 A View of the ILOG CPLEX Callable Library The ILOG CPLEX Callable Library includes several categories of routines optimization and result routines for defining a problem optimizing it and getting the results utility routines for addressing application programming matters problem modification routines to change a problem once it has been created within the ILOG CPLEX database problem query routines to access information about a problem once it has been created file reading and writing routines to move information from the file system into your application or out of your application to the file system parameter setting and query routines to access and modify the values of control parameters maintained by ILOG CPLEX Compiling and Linking Callable Library Applications 120 Each Callable Library is distributed as a single library file 1ibcplex a or cplex90 1lib Use of the library file is similar to that with o or obj files Simply substitute the library file in the link procedure This procedure simplifies linking and ensures that the smallest possible executable is generated ILOG CPLEX 9 0 GETTING STARTED COMPILING AND LINKING CAL
25. 52 lpexl c sensitivity and 153 lpexl c example 127 LPex1 java example 97 PMETHOD parameter 45 makefile 92 maximization in LP problem 37 memory management by environment object 69 minimization in LP problem 37 MIP description 11 optimizer 48 solving 81 mipopt Interactive Optimizer command 48 Mixed Integer Programming MIP problem see MIP model adding constraints 87 creating 69 creating IloModel 69 creating objects in 74 extracting 74 modifying 86 reading from file 80 82 solving 82 writing to file 80 see also optimization model modeling by columns in C 75 by columns in Java 99 by nonzeros in C 76 objects 66 modeling by nonzeros 100 modeling by rows 75 99 ILOG CPLEX 9 0 INDEX modeling variables 95 modifying problem object 123 monitoring iteration log 46 MPS file format 55 multiple algorithms 81 N netopt Interactive Optimizer command 47 network description 10 flow 87 Network Flow problem see network network optimizer availability 47 selecting 81 solving with 87 Nmake 92 no license found 93 NoClassDefFoundError 93 node LP solving 81 nonzereos modeling in Java 100 nonzeros modeling in C 76 notation in this manual 19 notification 86 numeric parameter 88 numVarArray Concert method 99 O objective function accessing value 48 adding to model 71 changing coefficient 61 changing sense 60 creating 75 80 default name 38 displaying 44 entering 38 entering in LP format 37
26. Concert Technology to solve the example An expanded version of this example is discussed in detail in Chapter 4 Concert Technology Tutorial for Java Users import ilog concert import ilog cplex public class Example public static void main String args try IloCplex cplex new IloCplex double lb double ub IloNumVar x 0 0 0 0 0 0 cplex numVarArray 3 double objvals 1 0 2 0 3 0 40 0 Double MAX VALUE Double MAX VALUE lb ub cplex addMaximize cplex scalProd x objvals cplex addLe cplex sum cplex prod cplex prod cplex prod cplex addLe cplex sum cplex prod cplex prod cplex prod da 3 if cplex solve cplex out println Solution status cplex out println Solution value double val cplex getValues x int ncols cplex getNcols for int j 0 j lt ncols j cplex out println Column cplex end catch IloException e System err println Concert exception x 0 x 1 x 21 20 0 x 0 x 1 1 x 2 5 3050 cplex getStatus cplex getObjValue j Value val 3 Me 4 6 caught Using the Callable Library Here is a C program using the CPLEX Callable Library to solve the example An expanded version of this example is discussed in detail in Chapter 6 Callable Library Tutorial include lt ilcplex cplex h gt include lt stdlib
27. IloCplex RootAlg IloCplex Concurrent IloObjective obj IloNumVarArray var env IloRangeArray rng env cplex importModel model argv 1 obj var rng cplex extract model if cplex solve env error Failed to optimize LP endl throw 1 84 ILOG CPLEX 9 0 GETTING STARTED READING A PROBLEM FROM A FILE EXAMPLE ILOLPEX2 CPP IloNumArray vals env cplex getValues vals var 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 env out lt lt Solution vector lt lt vals lt lt endl try basis may not exist IloCplex BasisStatusArray cstat env cplex getBasisStatuses cstat var env out lt lt Basis statuses lt lt cstat lt lt endl p catch Qo d env out lt lt Maximum bound violation lt lt cplex getQuality IloCplex MaxPrimalInfeas lt lt endl catch IloException amp e cerr Concert exception caught e endl catch e A 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 algorithm lt lt endl cerr lt lt where filename is a file with extension lt lt endl cerr MPS SAV or LP low
28. License Manager User s Guide and Reference to see whether you can correct the problem If not call the technical support hotline and repeat the error message there If you successfully compile link and execute one of the examples in the standard distribution then you can be sure that your installation is correct and you can begin to use ILOG CPLEX in ILOG Concert Technology seriously The Anatomy of an ILOG Concert Technology Application 68 ILOG Concert Technology is a C class library and therefore ILOG Concert Technology applications consist of interacting C objects This section gives a short introduction to the most important classes that are usually found in a complete ILOG Concert Technology CPLEX application Constructing the Environment lloEnv An environment that is an instance of IloEnv is typically the first object created in any Concert Technology application You construct an IloEnv object by declaring a variable of type IloEnv For example to create an environment named env you do this IloEnv env Note The environment object created in an ILOG Concert Technology application is different from the environment created in the ILOG CPLEX C library by calling the routine CPXopenCPLEX ILOG CPLEX 9 0 GETTING STARTED THE ANATOMY OF AN ILOG CONCERT TECHNOLOGY APPLICATION The environment object is of central importance and needs to be available to the constructor of all other ILOG Concert
29. Use the ca command to move to the top level directory into which you want to install the cplex subdirectory Then type this command gzip dc lt path cplex tgz tar xf where path is the full path name pointing to the location of the ILOG CPLEX distribution file either on the CD ROM or on a disk where you performed the FTP download On UNIX systems both ILOG CPLEX and ILOG Concert Technology are installed when you execute the above command Installation on Windows Before you install ILOG CPLEX you need to identify the correct distribution file for your platform There are instructions on how to identify your distribution in the booklet that comes with the CD ROM or with the FTP instructions for download This booklet also tells how to start the ILOG CPLEX installation on your platform Directory Structure After completing the installation you will have a directory structure like the one in Figure 1 1 Be sure to read the readme html carefully for the most recent information about the version of ILOG CPLEX you have installed 26 ILOG CPLEX 9 0 GETTING STARTED INSTALLING ILOG CPLEX concert I include iL ilconcert L lib I oen ks lt lib format gt o 1 Ss e O U E m x L lt CONCERT LIBRARY gt cplex bin O l lt EXECUTABLE FILES Interactive Optimizer dll and so files examples data src platform L lt lib format gt Lo Makefile or MSVC project files
30. appears on the screen Welcome to CPLEX Interactive Optimizer 9 0 0 with Simplex Mixed Integer amp Barrier Optimizers Copyright c ILOG 1997 2003 CPLEX is a registered trademark of ILOG Type help for a list of available commands Type help followed by a command name for more information on commands CPLEX gt The last line CPLEX gt is the prompt indicating that the product is running and is ready to accept one of the available ILOG CPLEX commands Use the help command to see a list of these commands ILOG CPLEX accepts commands in several different formats You can type either the full command name or any shortened version that uniquely identifies that name For example enter help after the CPLEX gt prompt as shown CPLEX gt help You will see a list of the ILOG CPLEX commands on the screen Since all commands start with a unique letter you could also enter just the single letter h CPLEX gt h ILOG CPLEX does not distinguish between upper and lower case letters so you could enter h H help or HELP All of these variations invoke the help command The same rules apply to all ILOG CPLEX commands You need only type enough letters of the command to distinguish it from all other commands and it does not matter whether you type upper or lower case letters This manual uses lower case letters ILOG CPLEX 9 0 GETTING STARTED USING HELP After you type the help command a list of available comma
31. bounds 60 change options 59 coefficient 61 delete 61 delete options 62 objective 61 rhs 61 sense 59 syntax 62 changing bounds 60 coefficients 61 constraint names 59 objective in Interactive Optimizer 61 parameters 56 88 problem 58 righthand side rhs in Interactive Optimizer 61 sense 59 158 ILOG CPLEX 9 0 variable names 59 choosing optimizer 47 81 126 class library 92 classpath 93 command line option 92 coefficient changing 61 column expressions 75 command executing from operating system 63 input formats 34 Interactive Optimizer list 35 compiler DNDEBUG option 73 error messages 67 Microsoft Visual C Command Line 122 using with CPLEX 67 compiling applications 29 Callable Library applications 120 Concert Technology applications 67 Component Libraries defined 11 running examples 28 verifying installation 28 Concert Technology Library 65 to 90 C classes 68 C objects 66 compiling and linking applications 67 CPLEX design in 66 description 11 error handling 72 example model 14 running examples 67 see also individual Iloxxx routines constraint adding 57 87 changing names 59 changing sense 59 creating 75 default names 38 deleting 61 displaying 44 GETTING STARTED displaying names 42 displaying nonzero coefficients 41 displaying number of 41 displaying type 41 entering in LP format 38 name limitations 38 naming 38 range 75 representing in model 70 constraints adding
32. called The importance of the class IloExpr becomes clear when expressions can no longer be fully spelled out in the source code but need instead to be built up in a loop Operators like provide an efficient way to do this g r le E O Oo c o D L2 bo ouy2a 1199u09 Solving the Model lloCplex Once the optimization problem has been created in an I1oMode1 object it is time to create the IloCplex object for solving the problem This is done by creating a variable of type IloCplex For example to create an object named cplex do the following IloCplex cplex env again using the environment env as parameter The ILOG CPLEX object can then be used to extract the model to be solved This can be done by calling cplex extract model ILOG CPLEX 9 0 GETTING STARTED 71 THE ANATOMY OF AN ILOG CoNcERT TECHNOLOGY APPLICATION 72 However experienced Concert users recommend a shortcut that performs the construction of the cplex object and the extraction of the model in one line IloCplex cplex model This works because the modeling object model contains within it the reference to the environment named env After this line object cp1ex is ready to solve the optimization problem defined by model Solving the model is done by calling cplex solve This method returns an 110Boo1 value where IloTrue indicates that cplex successfully found a feasible yet not necessarily optim
33. entered Changing Coefficients Up to this point all of the changes that have been made could be referenced by specifying a single constraint or variable In changing a coefficient however a constraint and a variable must be specified in order to identify the correct coefficient As an example change the coefficient of x3 in the new3 constraint from 3 to 30 As usual you must first specify which change command option to use change coefficient You must now specify both the constraint row and the variable column identifying the coefficient you wish to change Enter both the constraint name or number and variable name or number on the same line separated by at least one space The constraint name is new3 and the variable is number 3 so in response to the following prompt type new3 and 3 like this to identify the one to change e r O D Change which coefficient constraint variable new3 3 Present coefficient of constraint new3 variable 3 is 3 000000 JOZIWNdO 8A1 9e19 U The final step is to enter the new value for the coefficient of x3 Change coefficient of constraint new3 variable 3 to what 30 Coefficient of constraint new3 variable 3 changed to 30 000000 Objective amp RHS Coefficients To change a coefficient in the objective function or in the right hand side use the corresponding change command option objective or rhs For example to specify the righ
34. functions for modeling objects of the following types which can be used with I11oCplex IloNumVar modeling variables IloRange ranged constraints of the type lb lt expr lt ub IloObjective optimization objective IloNumExpr expression using variables Modeling variables are represented by objects implementing the 11oNumvVar interface defined by ILOG Concert Technology Here is how to create three continuous variables all with bounds 0 and 100 IloNumVar x cplex numVarArray 3 0 0 100 0 There is a wealth of other functions for creating arrays or individual modeling variables The documentation for IloModeler and 11oMPModeler will give you the complete list Modeling variables are typically used to build expressions of type IloNumExpr for use in constraints or the objective function of an optimization model For example the expression SEO 4 Z xILp Se 25 can be created like this IloNumExpr expr cplex sum x 0 cplex prod 2 0 x 1 cplex prod 3 0 x 2 Another way of creating an object representing the same expression is to use an IloLinearNumExpr expression Here is how IloLinearNumExpr expr cplex linearNumExpr expr addTerm 1 0 x 0 expr addTerm 2 0 x 1 2 a 33 lt x Go sd lt 5 p ES 5 go 9 Oo ro lt expr addTerm 3 0 x 2 The advantage of using IloLinearNumExpr over the first way is that you can more easily build up your linear expre
35. h gt include lt string h gt ILOG CPLEX 9 0 GETTING STARTED SOLVING AN LP WITH ILOG CPLEX define NUMROWS 2 define NUMCOLS 3 define NUMNZ 6 int main int argc char argv int status 0 CPXENVptr env NULL CPXLPptr lp NULL double obj NUMCOLS double lb NUMCOLS double ub NUMCOLS double x NUMCOLS int rmatbeg NUMROWS int rmatind NUMNZ double rmatval NUMNZ double rhs NUMROWS char sense NUMROWS int solstat double objval 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 lp CPXcreateprob env amp status lpex1 if lp NULL fprintf stderr goto TERMINATE Failed to create LP n CPXchgobjsen env lp CPX_MAX ob3 0 1505 obj 1 2 0 obj 2 3 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 status CPXnewcols env lp NUMCOLS obj 1b ub NULL NULL if status 1 fprintf stderr Failed to populate problem n goto TERMINATE rmatbeg 0 0 rmatind 0 0 rmatind 1 1 rmatind 2 2 sense 0 L rmatval 0 1 0 rmatval 1 1 0 rmatval 2 1 0 rhs 0 20 0 rmatbeg 1 3 rmatind 3 0 rmatind 4 1 rmatind 5 2 sense 1 L rmatval 3 1 0 rmatval 4 3 0 rmatval 5 1 0 rhs
36. in contrast the objective function is needed later for example to change it and reoptimize the model when doing scenario analysis the variable ob j must be created in order to refer to the objective function From the standpoint of algorithmic efficiency the two approaches are comparable Creating constraints and adding them to the model can be done just as easily with the following statement model add x1 x2 x3 lt 20 The part x1 x2 x3 lt 20 creates an object of class 11oRange that is immediately added to the model by passing it to the method I1oMode1 add Again if a reference to the IloRange object is needed later an IloRange handle object must be stored for it Concert Technology provides flexible array classes for storing data such as these IloRange objects As with variables Concert Technology provides a variety of constructors that help create range constraints While those examples use expressions with modeling variables directly for modeling it should be pointed out that such expressions are themselves represented by yet another Concert Technology class 11oExpr Like most Concert Technology objects IloExpr objects are handles Consequently the method ena must be called when the object is no longer needed The only exceptions are implicit expressions where the user does not create an IloExpr object such as when writing for example x1 2 x2 For such implicit expressions the method end should not be
37. of coefficients T 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 include lt stdlib h gt Bring in the declarations for the string functions include lt string h gt Include declaration for functions at end of program static int populatebyrow CPXENVptr env CPXLPptr lp ILOG CPLEX 9 0 GETTING STARTED 129 g r O Aseaqiy 91qel1eo BUILDING AND SoLviNG A SMALL LP MODEL IN C populatebycolumn CPXENVptr env CPXLPptr lp populatebynonzero CPXENVptr env CPXLPptr lp 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 objective value variable values dual values row slacks and variable reduced costs int solstat double objval double x NULL double pi NULL double slack NULL double dj NULL CPXENVptr env NULL CPXLPptr lp NULL int status 0 int du jg int cur numrows cur numcols Check the command line arguments if argo 2 BI argv 1 0 11 strchr rcn argv 1 1 NULL yc usage argv 0 goto TERMINATE Initialize the CPLEX environment env CPXopenCPLEX amp status If an error occurs the status value indicates
38. or Enter Related Documentation 20 In addition to this introductory manual the standard distribution of ILOG CPLEX comes with the ILOG CPLEX User s Manual and the ILOG CPLEX Reference Manuals All ILOG documentation is available in an online version in hypertext mark up language HTML It is delivered with the standard distribution of the product and accessible through conventional HTML browsers The ILOG CPLEX User s Manual explains the relationship between the Interactive Optimizer and the Component Libraries It enlarges on aspects of linear programming with ILOG CPLEX and shows you how to handle quadratic programming QP problems quadratically constrained programming QCP problems and mixed integer programming MIP problems It tells you how to control ILOG CPLEX parameters debug your applications and efficiently manage input and output It also explains how to use parallel CPLEX optimizers The ILOG CPLEX Callable Library and C API Reference Manual documents the Callable Library routines and their arguments as well as the C API of the Concert Technology classes methods and functions This manual also includes additional documentation about error codes solution quality and solution status The ILOG CPLEX Java API Reference Manual supplies detailed definitions of the Concert Technology interfaces and CPLEX Java classes It is available online as HTML and Microsoft compiled HTML help CHM The ILOG CPLEX C NE
39. programming problem the opt imize command is equivalent to the mipopt command Interrupting the Optimization Process Our short example was solved very quickly However larger problems particularly mixed integer problems can take much longer Occasionally it may be useful to interrupt the optimization process ILOG CPLEX allows such interruptions if you use cont rol c The control and c keys must be pressed simultaneously Optimization is interrupted and ILOG CPLEX issues a message indicating that the process was stopped and displays progress information If you issue another optimization command in the same session ILOG CPLEX will resume optimization from where it was interrupted Displaying Post Solution Information Once an optimal solution is found ILOG CPLEX can provide many different kinds of information for viewing and analyzing the results This information is accessed via the display command and via some write commands Information about the following is available with the display solution command objective function value solution values slack values reduced costs dual values shadow prices basic rows and columns For information on the write commands see Writing Problem and Solution Files on page 50 Sensitivity analysis can also be performed in analyzing results as explained in Performing Sensitivity Analysis on page 49 For example to view the optimal value of each variable enter the comma
40. respectively cl lpexl c cplex90 1ib This command will create the executable file 1pex1 exe Using Dynamic Loading Some projects require more precise control over the loading and unloading of DLLs For information on loading and unloading DLLs without using static linking please refer to the compiler documentation or to a book such as Advanced Windows by Jeffrey Richter from Microsoft Press If this is not a requirement the static link implementations mentioned above are easier to use Building Applications that Use the ILOG CPLEX Parallel Optimizers When you are compiling and linking programs that use the ILOG CPLEX Parallel Optimizers it is especially important to review the relevant flags for the compiler and linker These are found in the makefile provided with UNIX distributions or in the sample project files provided with Windows distributions It is also a good idea to review the section on Using Parallel Optimizers in the ILOG CPLEX User s Manual for important details pertaining to each specific parallel optimizer How ILOG CPLEX Works 122 When your application uses routines of the ILOG CPLEX Callable Library it must first open the ILOG CPLEX environment then create and populate a problem object before it solves a problem Before it exits the application must also free the problem object and release the ILOG CPLEX environment The following sections explain those steps Opening the ILOG CPLEX Environment IL
41. seconds the total iteration count the Phase I iteration count in parentheses Optimizing our example problem produces a report like the following one although the solution times vary with each computer Tried aggregator 1 time No presolve or aggregator reductions Presolve Time 0 00 sec Iteration Log Iteration 1 Dual infeasibility 0 000000 Iteration 2 Dual objective 202 500000 Dual simplex Optimal Objective 2 0250000000e 02 Solution Time 0 00 sec Iterations 2 1 CPLEX gt ILOG CPLEX 9 0 GETTING STARTED SOLVING A PROBLEM In our example ILOG CPLEX finds an optimal solution with an objective value of 202 5 in two iterations For this simple problem 1 Phase I iteration was required Summary To solve an LP problem use the command optimize Solution Options Here are some of the basic options in solving linear programming problems Although the tutorial example does not make use of these options you will find them useful when handling larger more realistic problems Filing Iteration Logs on page 47 Re Solving on page 47 Using Alternative Optimizers on page 47 Interrupting the Optimization Process on page 48 For detailed information about performance options refer to the ILOG CPLEX User s Manual Filing Iteration Logs Every time ILOG CPLEX solves a problem much of the information appearing on the screen is also directed into a log file This file is automati
42. straightforward and natural there are some models where population by columns is a more natural or more efficient approach to implement For example problems with network structure typically lend themselves well to modeling by column Readers familiar with matrix algebra may view the method populateByColumn as the transpose of populateByRow Range objects are created for modeling by column with only their lower and upper bound No expressions are given building them at this point would be impossible since the variables have not been created yet Similarly the objective function is created only with its intended optimization sense and without any expression Next the variables are created and installed in the existing ranges and objective These newly created variables are introduced into the ranges and the objective by means of column objects which are implemented in the class IloColumn Objects of this class are created with the methods 11oCplex column and can be linked together with the method IloColumn and to form aggregate 11oColumn objects An IloColumn object created with the method IloCplex column contains information about how to use this column to introduce a new variable into an existing modeling object For example if obj is an 1100bjective object cplex column obj 2 0 creates an IloColumn object containing the information to install a new variable in the expression of the 1100bjective object obj with a linear coefficient of 2 0
43. the aggregate column object Once installed the new variable is returned and stored in var 0 0 Modeling by Nonzeros The last of the three functions for building the model is populateByNonzero This function creates the variables with only their bounds and the empty constraints that is ranged constraints only with lower and upper bound but with no expression Only after that are the expressions constructed in a manner similar to the ones already described using these existing variables they are installed in the existing constraints with the method IloRange setExpr Complete Code of LPex1 java 100 File examples src LPex1 java Version 9 0 Wu APR ES AS A O UEM RATA Copyright C 2001 2003 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products YI AS SS SS AS SA eMe O lUo E eser SS pS use e eie LPexl java Entering and optimizing an LP problem Demonstrates different methods for creating a problem The user has to choose the method on the command line java LPexl r generates the problem by adding constraints java LPexl c generates the problem by adding variables java LPexl n generates the problem by adding expressions ILOG CPLEX 9 0 GETTING STARTED COMPLETE CODE OF LPEX1 JAVA import ilog concert import ilog cplex public class LPexl static void
44. 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 130 ILOG CPLEX 9 0 GETTING STARTED BUILDING AND SOLVING A SMALL LP MODEL IN C fprintf stderr Could not open CPLEX environment Nn 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 Turn on data checking Status CPXsetintparam env CPX PARAM DATACHECK CPX ON if status fprintf stderr Failure to turn on data checking error d n status goto TERMINATE Create the problem lp CPXcreateprob env amp status lpex1 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 c
45. to see if it has been changed back to its original form display problem all Maximize obj xL 2 x2 3 x3 Subject To cl xl x2 x3 lt 20 c2 gt CIRO LAS x3 lt 30 Bounds 0 lt x1 lt 40 All other variables are gt O0 When you remove a constraint with the delete option that constraint no longer exists in memory however variables that appear in the deleted constraint are not removed from memory If a variable from the deleted constraint appears in the objective function it may still influence the solution process If that is not what you want these variables can be explicitly removed using the delete option Summary The general syntax for the change command is change option identifier identifier2 new value 62 ILOG CPLEX 9 0 GETTING STARTED EXECUTING OPERATING SYSTEM COMMANDS Executing Operating System Commands The execute command xecut e is simple but useful It executes operating system commands outside of the ILOG CPLEX environment By using xecute you avoid having to save a problem and quit ILOG CPLEX in order to carry out a system function such as viewing a directory for example As an example if you wanted to check whether all of the files saved in the last session are really in the current working directory the following ILOG CPLEX command shows the contents of the current directory in a UNIX operating system using the UNIX command 1s xecute Ls 1 3 total 7448 2 Sinni e 1
46. usage System out println usage LPexl option System out println options Y build model row by row System out println options 6 build model column by column System out println options n build model nonzero by nonzero public static void main String args if args length 1 args 0 charAt 0 usage return try 1 Create the modeler solver object IloCplex cplex new IloCplex IloNumVar var new IloNumVar 1 IloRange rng new IloRange 1 l Evaluate command line option and call appropriate populate method The created ranges and variables are returned as element 0 of arrays var and rng switch args 0 charAt 1 write model to file cplex exportModel lpexl 1p case r populateByRow cplex var rng break case c populateByColumn cplex var rng 9 break ah S case n populateByNonzero cplex var rng o 9 break S A default usage PEE vo return 2 cz a 5 2 o o o Q lt solve the model and display the solution if one was found if cplex solve double x cplex getValues var 0 double dj cplex getReducedCosts var 0 double pi cplex getDuals rng 0 double slack cplex getSlacks rng 0 cplex output println Solution status cplex getStatus ILOG CPLEX 9 0 GETTING STARTED 101 COMPLETE CODE OF LPEX1 JAVA cplex output println Solution valu
47. values of the input data in your problem if you set the datacheck parameter before you type the display command Parameters are explained Setting ILOG CPLEX Parameters on page 56 later in this tutorial To set the datacheck parameter type the following for now Set read datacheck yes ILOG CPLEX 9 0 GETTING STARTED 41 e r O E gt JOZIWNdO 8A1 9e19 U DISPLAYING A PROBLEM 42 With this setting the command display problem stats shows this additional information Variables Min LB 0 000000 ax UB 40 00000 Objective nonzeros Min 1 000000 ax 3 000000 Linear constraints Nonzeros Min 1 000000 ax 3 000000 RHS nonzeros Min 20 00000 ax 30 00000 Another way to avoid displaying an entire problem is to display a specific part of it by using one of the following three options of the display problem command names documented in Displaying Variable or Constraint Names on page 42 can be used to display a specified set of variable or constraint names constraints documented in Displaying Constraints on page 44 can be used to display a specified set of constraints bounds documented in Displaying Bounds on page 44 can be used to display a specified set of bounds Specifying Item Ranges For some options of the display command you must specify the item or range of items you want to see Whenever input defining a range of items is required ILOG CPLEX expects two indices separated by a
48. your problem data When using the Interactive Optimizer most users will enter problem data from formatted files CPLEX supports the industry standard MPS Mathematical Programming System file format as well as CPLEX LP format a row oriented format many users may find more natural Interactive entry using CPLEX LP format is also a possibility for small problems Data entry options are described briefly in this manual File formats are documented in the reference manual ILOG CPLEX File Formats Concert Technology and Callable Library users may read problem data from the same kinds of files as in the Interactive Optimizer or they may want to pass data directly into CPLEX to gain efficiency These options are discussed in a series of examples that begin with Building and Solving a Small LP Model in C Building and Solving a Small LP Model in Java and Building and Solving a Small LP Model in C for the CPLEX Callable Library users Solving an LP with ILOG CPLEX To help you learn which CPLEX component best meets your needs this section briefly demonstrates how to create and solve an LP model using four different interfaces to CPLEX Full details of writing a practical program are in the chapters containing the tutorials The problem to be solved is Maximize X 2x 3x3 subject to X X X3 amp 20 X 3x x3 lt 30 with these bounds 0 x 40 OSx8 Too 0 lt x3 lt Too ILOG CPLEX 9 0 GETTING STARTED 13 SOL
49. 3258 Jul 14 10 34 afiro mps 2 rwWXr Xr x 1 3783416 Apr 22 10 32 cplex e Le zrw r r 1 3225 Jul 14 14 21 cplex log 3 CEWSGE C E 1 145 Jul 14 11 32 example Mo rw r r 1 112 Jul 14 11 32 example bas 5o rw r r 1 148 Jul 14 11 32 example lp rw r r pi 146 Jul 14 11 32 example2 j After the command is executed the CPLEX gt prompt returns indicating that you are still in E ILOG CPLEX Most commands that can normally be entered from the prompt for your operating system can also be entered with the xecute command The command may be as simple as listing the contents of a directory or printing the contents of a file or as complex as starting a text editor to modify a file Anything that can be entered on one line after the operating system prompt can also be executed from within ILOG CPLEX However this command differs from other ILOG CPLEX commands in that it must be entered on a single line No prompt will be issued In addition the operating system may fail to carry out the command if insufficient memory is available In that case no message is issued by the operating system and the result is a return to the CPLEX gt prompt Summary The general syntax for the xecute command is xecute command line Quitting ILOG CPLEX When you are finished using ILOG CPLEX and want to leave it type quit If a problem has been modified be sure to save the file before issuing a quit command ILOG CPLEX will not promp
50. 9u09 Modeling objects like IloEnv objects are handles to implementation objects Though you will be dealing only with the handle objects it is the implementation objects that contain the data that specifies the optimization model If you need to remove an implementation object from memory you need to call the end method for one of its handle objects Modeling objects are also known as extractables because it is the individual modeling objects that are extracted one by one when you extract an optimization model to IloCplex So extractables are characterized by the possibility of being extracted to algorithms such as IloCplex In fact they all are inherited from the class IloExtractable In other words IloExtractable is the base class of all classes of extractables or modeling objects The most fundamental extractable class is 110Mode1 Objects of this class are used to define a complete optimization model that can later be extracted to an 110Cp1ex object You create a model by constructing a variable of type IloMode1 For example to construct a modeling object named mode1 within an existing environment named env you would do the following ILOG CPLEX 9 0 GETTING STARTED 69 THE ANATOMY OF AN ILOG CoNcERT TECHNOLOGY APPLICATION 70 IloModel model env At this point it is important to note that the environment is passed as a parameter to the constructor There is also a constructor that does not use the environment p
51. ADDING CONSTRAINTS AND BOUNDS Resetting Defaults After making parameter changes it is possible to reset all parameters to default values by issuing one command set defaults This resets all parameters to their default values except for the name of the log file Summary The general syntax for the set command is set parameter option new value Displaying Parameter Settings The current values of the parameters can be displayed with the command display settings all e r O E gt A list of parameters with settings that differ from the default values can be displayed with the command display settings changed JOZIWNdO 8A1 9e19 U For a description of all parameters and their default values see the reference manual ILOG CPLEX Parameters ILOG CPLEX also accepts customized system parameter settings via a parameter specification file See the reference manual ILOG CPLEX File Formats for a description of the parameter specification file and its use Adding Constraints and Bounds If you wish to add either new constraints or bounds to your problem use the add command This command is similar to the enter command in the way it is used but it has one important difference the enter command is used to start a brand new problem whereas the add command only adds new information to the current problem Suppose that in the example you need to add a third constraint Xj 2x5 3x3 250 You may do either interactively or fr
52. BLEM FROM A FILE EXAMPLE LPEX2 C 140 Permission is expressly granted to use this example in the course of developing applications that use ILOG products po M M P e lpex2 c Reading in and optimizing a problem To run this example command line arguments are required i e lpex2 filename method where filename is the name of the file with mps lp or sav extension method is the optimization method o default primal simplex dual simplex network with dual simplex cleanup barrier with crossover barrier without crossover sifting Quo ad concurrent Example lpex2 example mps o 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 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 objective value maximum bound violation variable values and basis int solnstat solnmethod solntype double objval maxviol double x NULL int cstat NULL
53. CPLEX 9 0 GETTING STARTED BUILDING AND SOLVING A SMALL LP MODEL END populatebycolumn To populate by nonzero we first create the rows then create the columns and then change the nonzeros of the matrix 1 at a time static int populatebynonzero CPXENVptr env CPXLPptr lp int status 0 double obj NUMCOLS double lb NUMCOLS double ub NUMCOLS char colname NUMCOLS double rhs NUMROWS char sense NUMROWS char rowname NUMROWS int rowlist NUMNZ int collist NUMNZ double vallist NUMNZ 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 1b 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 CPXnewcols env lp NUMCOLS obj lb ub NULL colname if status goto TERMINATE Now create the list of coefficients rowlist 0 0 collist 0 0 vallist 0 1 0 ILOG CPLEX 9 0 GETTING STARTED IN C 137 g r O E Aseaqiy aqe READING A P
54. EX 9 0 GETTING STARTED 29 USING THE COMPONENT LIBRARIES 30 ILOG CPLEX 9 0 GETTING STARTED Part ll Tutorials This part provides tutorials to introduce you to each of the components of ILOG CPLEX Interactive Optimizer Tutorial on page 33 Concert Technology Tutorial for C Users on page 65 Concert Technology Tutorial for Java Users on page 91 Concert Technology Tutorial for NET Users on page 105 9 9 Callable Library Tutorial on page 119 Interactive Optimizer Tutorial e r O E D J9ziundo 3A1 9819 U This step by step tutorial introduces the major features of the ILOG CPLEX Interactive Optimizer In this chapter you will learn about Starting ILOG CPLEX on page 34 Using Help on page 34 Entering a Problem on page 36 Displaying a Problem on page 40 Solving a Problem on page 45 Performing Sensitivity Analysis on page 49 Writing Problem and Solution Files on page 50 Reading Problem Files on page 53 Setting ILOG CPLEX Parameters on page 56 Adding Constraints and Bounds on page 57 Changing a Problem on page 58 Executing Operating System Commands on page 63 9 9 99 9 9 FH FH 9 9 o Quitting ILOG CPLEX on page 63 ILOG CPLEX 9 0 GETTING STARTED 33 STARTING ILOG CPLEX Starting ILOG CPLEX Using Help 34 To start the ILOG CPLEX Interactive Optimizer at your operating system prompt type the command cplex A message similar to the following one
55. EX displays these three names xl x2 x3 If you want to see only the second and third names you could either enter the range as 2 3 or specify everything following the second variable with 2 Try this technique display problem names variables Display which variable name s 2 x2 x3 g If you enter a number without a hyphen you will see a single variable name e r 4 display problem names variables S e Display which variable name s 2 2 3 x2 El Summary n o You can display variable names by entering the command display problem names variables You can display constraint names by entering the command display problem names constraints Ordering Variables In the example problem there is a direct correlation between the variable names and their numbers x1 is variable 1 x2 is variable 2 etc that is not always the case The internal ordering of the variables is based on their order of occurrence when the problem is entered For example if x2 had not appeared in the objective function then the order of the variables would be x1 x3 x2 You can see the internal ordering by using the hyphen when you specify the range for the variables option The variables are displayed in the order corresponding to their internal ordering All of the options of the display command can be entered directly after the word display to eliminate intermediate steps The following command is correct for example di
56. LABLE LIBRARY APPLICATIONS The following compilation and linking instructions assume that the example source programs and ILOG CPLEX Callable Library files are in the directories associated with a default installation of the software If this is not true additional compile and link flags would be required to point to the locations of the include file cplex h and Callable Library files respectively Note The instructions below were current at the time of publication As compilers linkers and operating systems are released different instructions may apply Be sure to check the Release Notes that come with your ILOG CPLEX distribution for any changes Also check the ILOG CPLEX web page http www ilog com products cplex Building Callable Library Applications on UNIX Platforms To compile and execute an example 1pex1 do the following cd examples machine libformat make lpexl to compile and execute the first CPLEX example In that command macnine indicates the name of the subdirectory corresponding to your type of machine and 1ibformat indicates your particular platform A list of all the examples that can be built this way is to be found in the makefile by looking for C_EX C examples or you can view the files listed in examples src The makefile contains recommended compiler flags and other settings for your particular computer which you can find by searching in it for Compiler options and use in your applications tha
57. LEX eee Illu eee ar Re eee ee eee ee Tam E 34 Using Help iis s p A CR nea Gor os RU aa E 34 Entering a Problem oo coococcccccn ee e hm nm hm nnn nn 36 Entering the Example Problem o ooccoccccco I Ih 36 Using the EP Format zio Lo ht bd geen e eee Ree ve e ees 37 Entering Data 22 cox rece ex ARE A LEE Ed Ere Pe e ERA EE E 39 Displaying a ProbleM oocoocccccn n Rh hh m nn 40 Displaying Problem Statistics liiis 41 Specifying Item Ranges oooococococnc e mmn 42 Displaying Variable or Constraint Names ocococcccccoc ee 42 Ordering Variables ss saie d e e e e a e mm hn 43 Displaying Constraints s sitan r a a a a I m 44 Displaying the Objective Function lisse RII 44 Displaying Bo tidS ore REED a INIM Ir ESAME 44 Displaying a Histogram of NonZero Counts eee 44 Solving a Problem 2 xri petat eet bot iene dioecesi n eiit es 45 Solving the Example Problem 00 cece e n 45 Solution Options eI eb DE RI RP ET RE Rec RU ARA e 47 Displaying Post Solution Information llle 48 Performing Sensitivity Analysis esee RII 49 Writing Problem and Solution Files 0c cece eee eee eee BI 50 Selecting a Write File Format 0 0 00 51 Writing EP Files cette n dst wd D ep a ERI RI gy eee 51 Writing Basis Files x eR SOLAR ERR DEDE whatever Be iia 52 Using Path Namies uem Dit a ERURE TU EE UO 52 Reading Problem Files 0 ce
58. LL LP MODEL objective using column expressions 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 add IloNumVar tob 2 0 c 0 1 0 c 1 3 0 x add IloNumVar ob3 3 0 c 0 1 0 c 1 1 0 x model add obj model add c END populatebycolumn To populate by nonzero we first create the rows then create the columns and then change the nonzeros of the matrix 1 at a time static void populatebynonzero 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 env 0 0 40 0 add IloNumVar env add IloNumVar env x x obj setCoef x 0 1 0 obj setCoef x 1 2 0 obj setCoef x 2 3 0 c 0 setCoef x 0 1 0 c 0 setCoef x 1 0 c 0 setCoef x 2 1 0 c 1 setCoef x 0 1 0 c 1 setCoef x 1 3 0 c 1 setCoef x 2 1 0 model add obj model add c END populatebynonzero ILOG CPLEX 9 0 GETTING STARTED IN C 79 z le E O ie c 4 D o PXeTe Co VITE YR W e 70 WRITING AND
59. NG STARTED BUILDING AND SOLVING A SMALL LP MODEL IN JAVA The returned value tells you what ILOG CPLEX found out about the model whether it found the optimal solution or only a feasible solution whether it proved the model to be unbounded or infeasible or whether nothing at all has been determined at this point Even more detailed information about the termination of the solver call is available through the method IloCplex getCplexStatus Query the Results If the solve method succeeded in finding a solution you will then want to access that solution The objective value of that solution can be queried using a statement like this double objval cplex getObjValue Similarly solution values for all the variables in the array x can be queried by calling double xval cplex getValues x More solution information can be queried from IloCplex including slacks and depending on the algorithm that was applied for solving the model duals reduced cost information and basis information Building and Solving a Small LP Model in Java The example LPex1 java part of the standard distribution of ILOG CPLEX is a program that builds a specific small LP model and then solves it This example follows the general structure found in many ILOG CPLEX Concert Technology applications and demonstrates three main ways to construct a model e Modeling by Rows on page 99 e Modeling by Columns on page 99 9 al e Modeling by Nonze
60. OG CPLEX requires a number of internal data structures in order to execute properly These data structures must be initialized before any call to the ILOG CPLEX Callable Library The first call to the ILOG CPLEX Callable Library is always to the function CPXopenCPLEX This routine checks for a valid ILOG CPLEX license and returns a pointer to the ILOG CPLEX environment This pointer is then passed to every ILOG CPLEX Callable Library routine except CPXmsg ILOG CPLEX 9 0 GETTING STARTED How ILOG CPLEX WORKS The application developer must make an independent decision as to whether the variable containing the environment pointer is a global or local variable Multiple environments are allowed but extensive opening and closing of environments may create significant overhead on the licensor and degrade performance typical applications make use of only one environment for the entire execution since a single environment may hold as many problem objects as the user wishes After all calls to the Callable Library are complete the environment is released by the routine CPXcloseCPLEX This routine indicates to ILOG CPLEX that all calls to the Callable Library are complete any memory allocated by ILOG CPLEX is returned to the operating system and the use of the ILOG CPLEX license is ended for this run Instantiating the Problem Object A problem object is instantiated created and initialized by ILOG CPLEX when you call the routine CPXc
61. Optimization ProbleM ooococccccccccoco II en 88 Starting from a Previous Basis oooocococcococ rn 88 Complete Programi s socia arar bn 88 Concert Technology Tutorial for Java USerS o oooomomommo mo 91 Compiling ILOG CPLEX Applications in ILOG Concert Technology 91 In Case Problems Arise oooooococccc Rhe 92 The Design of ILOG CPLEX in ILOG Concert Technology o oooooocoocmommoo 93 The Anatomy of an ILOG Concert Technology Applicati0N o o ooooo 94 Create the Model esl ole vlr ek RE RR ERR EE RARE ER 95 Solve the Model 12 wt iat ona a he decer WEISS 96 Query the ResullS o wae cle din lis ey eae ER eere 97 Building and Solving a Small LP Model in Java 0 0 cee eee eee eee eee 97 Modeling by ROWS e en bec a duque p EPUM i EIER 99 Modeling by Columrs uc eres RR YR eR eri ee iU E ee n 99 Modeling by Nonzeros 0 0 cece RR I I 3 hh 100 Complete Code of LPex7 jaVa oooooooccoccrnrane n nn nn 100 Concert Technology Tutorial for NET UsSerS 0o0ooooooomomooo 105 What You Need to Know PrerequisiteS 00 00 cece eee eee eee eee 106 What You Will Be Doing 0 cc cece eee eee eee 107 Describe cis s eens RAD RV E A A NT RE PA ANE DE PES 107 ILOG CPLEX 9 0 GETTING STARTED Chapter 6 CONTENTS Model iens ra a Side A RU Ren RE ER EDU 108 SII rt A A a o aia 108 Describe ri A aa a aire dd a 108 Building a Small L
62. P Problem in C 0 0 0 cece e 109 Model ic ic ee ce cies wee nau a ra Era a Rad exime aa Ed eet a 109 S0lVe eus ellipsis E oic EE eise nce Mond dd pei LAE 113 Example LP X1 CS Ancre nei a t a a a 115 Callable Library Tutorial oooooooncrrorancrrr 119 The Design of the ILOG CPLEX Callable Library eee eee eee eee eee 119 Compiling and Linking Callable Library Applications o oooooommmmo 120 Building Callable Library Applications on UNIX Platforms lessen 121 Building Callable Library Applications on Win32 Platforms llle cee eee 121 Building Applications that Use the ILOG CPLEX Parallel Optimizers 122 How ILOG CPLEX Works i i cece ects alsin a uem el Rr nee hb RE mn Ripa n 122 Opening the ILOG CPLEX Environment o coccccccccoc tee 122 Instantiating the Problem Object oococcoccoccccc III 123 Populating the Problem Object lssssseseeeee e n 123 Changing the Problem Object o oococcccocccoc ee mn 123 Creating a Successful Callable Library Application 0c eee ee eens 124 Prototype the Model 02 00 e eee ee e m rm 124 Identify the Routines to be Called 0 00 00 eee 125 Test Procedures in the Application oooooooocrorcnor IR 125 Assemble the Data ooooocrorocoor hr 125 Choose an Optimizer uris ER mu EET Uy CERCA oe hee DE Ug 126 Observe Good Programming Practices eee 126 D
63. READING MODELS AND FILES Writing and Reading Models and Files In example ilolpex1 cpp one line is still unexplained cplex exportModel lpexl 1p This statement causes cplex to write the model it has currently extracted to the file called lpex1 1p In this case the file will be written in LP format Use of that format is documented in the reference manual JLOG CPLEX File Formats Other formats supported for writing problems to a file are MPS and SAV also documented in the reference manual ILOG CPLEX File Formats 11oCplex decides which file format to write based on the extension of the file name IloCplex also supports reading of files through one of its importModel methods A call to cplex importModel model file lp causes ILOG CPLEX to read a problem from the file i1e 1p and add all the data in it to model as new objects Again MPS and SAV format files are also supported In particular ILOG CPLEX creates an instance of IloObjective for the objective function found in file 1p IloNumVar for each variable found in file 1p except IloSemiContVar for each semi continuous or semi integer variable found in file 1p IloRange for each row found in file 1lp Ilosos1 for each SOS of type 1 found in file 1p and I10S082 for each SOS of type 2 found in file lp If you also need access to the modeling objects created by importModel two additional signatures are provided void IloCplex importModel IloModel amp m const c
64. RIG define ROWSTOT ROWSSUB ROWSCOMP define NZTOT NZCOMP NZSUB int main Oo S Data for original problem Arrays have to be big enough to hold E D DN i c o problem plus additional constraints 3 o i double Hrhs ROWSTOT 3 1 4 3 5 2s double Hlb COLSORIG 0 0 0 0 O O O 0 S lt ILOG CPLEX 9 0 GETTING STARTED 149 ADDING ROWS TO A PROBLEM EXAMPLE LPEX3 C 150 double Hub COLSORIG 507 S0 505 DU S0 905 S04 SO 1H double Hcost COLSORIG SOL du ALA A ZS char Hsense ROWSTOT MEY CESA Bf EM VE jg int Hmatbeg COLSORIG 0 2 4 6 8 10 12 14 int Hmatcnt COLSORIG 25 Z2 2 An Z5 2 255 ZIG int Hmatind NZTOT Of zh U2 5 3 0 4 2 3 2 4 3 4 double Hmatval NZTOT L 0 1x07 1407 120 120 L 0y 1 0 Hi 130 el20 205 1 0 Sly 2 0 Led HL 0 ug Data for CPXaddrows call double Arhs ROWSCOMP 4 2 char Asense ROWSCOMP E W Note use a trick for rmatbeg by putting the total nonzero count in the last element This is not required by the CPXaddrows call int Armatbeg ROWSCOMP 1 0 8 16 int Armatind NZCOMP me 152 3 45 55 06 7 OF 2 3 4 95 Op d E double Armatval NZCOMP fo 204 AGr 200 10 00 Za Slay 2 205 Sa dy Wey 3 045 0 Sey DO Ey Sig UNE double x COLSORIG CPXENVptr env NULL CPXLPptr lp NULL int 3 int status lpstat double objval Initialize the CPLEX environmen
65. ROBLEM FROM A FILE rowlist 1 rowlist 2 rowlist 3 rowlist 4 rowlist 5 status CPXchgcoeflist if status TERMINATE collist 1 H collist 2 collist 3 collist 4 collist 5 PrRROoOO return status END populatebynonzero Reading a Problem from a File Example Ipex2 c 138 env EXAMPLE LPEX2 C 1 vallist 1 1 0 2 vallist 2 1 0 0 vallist 3 1 0 1 vallist 4 3 0 2 vallist 5 1 0 lp 6 rowlist collist vallist goto TERMINATE The previous example 1pex1 c shows a way to copy problem data into a problem object as part of an application that calls routines from the ILOG CPLEX Callable Library Frequently however a file already exists containing a linear programming problem in the industry standard MPS format the ILOG CPLEX LP format or the ILOG CPLEX binary SAV format In example 1pex2 c ILOG CPLEX file reading and optimization routines read such a file to solve the problem Example 1pex2 c uses command line arguments to determine the name of the input file and the optimizer to call Usage lpex2 filename optimizer Where filename is a file with extension MPS SAV or LP lower case is allowed and optimizer is one of the following letters oO 00 25 5 Q O O default primal simplex dual simplex network with dual simplex cleanup barrier with crossover barrier without crossover sifting concurrent For example this com
66. Similarly for an IloRange constraint rng the method call cplex column rng 1 0 creates an I1oColumn object containing the information to install a new variable into the expression of rng as a linear term with coefficient 1 0 2 a 33 lt x qj nr tQ lt 53 ES 5 go vo roy lt When using a modeling by column approach new columns are created and installed as variables in all existing modeling objects where they are needed To do this with ILOG Concert Technology you create an 110Co1umn object for every modeling object in which you want to install a new variable and link them together with the method ILOG CPLEX 9 0 GETTING STARTED 99 COMPLETE CODE OF LPEX1 JAVA IloColumn and For example the first variable in populateByColumn is created like this var 0 0 model numVar model column obj 1 0 and model column r0 1 0 and model column r1 1 0 0 0 40 0 The three methods model column create I1oColumn objects for installing a new variable in the objective obj and in the constraints x0 and r1 with linear coefficients 1 0 1 0 and 1 0 respectively They are all linked to an aggregate column object using the method ana This aggregate column object is passed as the first argument to the method numvar along with the bounds 0 0 and 40 0 as the other two arguments The method numvar now creates a new variable and immediately installs it in the modeling objects obj ro and r1 as defined by
67. Solution status d n lpstat printf Objective value g n objval printf Solution 1s lnM for j 0 j lt COLSORIG j printf x d 9gin 3 x 31 Put the problem and basis into a SAV file to use it in the Interactive Optimizer and see if problem is correct status CPXwriteprob env lp lpex3 sav NULL if status fprintf stderr CPXwriteprob failed n goto TERMINATE ILOG CPLEX 9 0 GETTING STARTED PERFORMING SENSITIVITY ANALYSIS 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 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 An CPXgeterrorstring env status errmsg fprintf stderr s errmsg return status END main Performing Sensitivity Analysis In Performing Sensitivity Analysis on page 49 there is a discussion of how to perform sensitivity analysis in the Interactive Optimizer As with most in
68. T Reference Manual documents the C NET API for CPLEX The reference manual ILOG CPLEX Parameters contains a table of parameters that can be modified by parameter routines The reference manual LOG CPLEX File Formats contains a list of file formats that ILOG CPLEX supports and details about using them in your applications ILOG CPLEX 9 0 GETTING STARTED RELATED DOCUMENTATION The reference manual ILOG CPLEX Interactive Optimizer contains the commands of the Interactive Optimizer along with the command options and links to examples of their use in the ZLOG CPLEX User s Manual As you work with ILOG CPLEX on a long term basis you should read the complete User s Manual to learn how to design models and implement solutions to your own problems Consult the reference manuals for authoritative documentation of the Component Libraries their application programming interfaces APIs and the Interactive Optimizer ILOG CPLEX 9 0 GETTING STARTED 21 RELATED DOCUMENTATION 22 ILOG CPLEX 9 0 GETTING STARTED Part Setting Up This part shows you how to set up ILOG CPLEX and how to check your installation It includes information for users of Microsoft and UNIX platforms Setting Up ILOG CPLEX You install ILOG CPLEX in two steps first install the files from the distribution medium a CD or an FTP site into a directory on your local file system then activate your license At that point all of the features o
69. TTING STARTED BUILDING AND SoLviNG A SMALL LP MODEL IN C Examples of this kind are trying to use empty handle objects or passing arrays of incompatible lengths to functions This kind of error is usually an oversight and should not occur in a correct program In order not to pay any runtime cost for correct programs asserting such conditions the conditions are checked using assert statements The checking is disabled for production runs if compiled with the DNDEBUG compiler option The second kind of error is more complex and cannot generally be avoided by correct programming An example is memory exhaustion The data may simply require too much memory even when the program is correct This kind of error is always checked at runtime In cases where such an error occurs Concert Technology throws a C exception In fact Concert Technology provides a hierarchy of exception classes that all derive from the common base class 110Except ion Exceptions derived from this class are the only kind of exceptions that are thrown by Concert Technology The exceptions thrown by 11oCplex objects all derive from class IloAlgorithm Exception or IloCplex Exception To gracefully handle exceptions in a Concert Technology application include all of the code ina try catch clause like this IloEnv env try catch IloException amp e cerr Concert Exception e endl oeatch t e 4 cerr Other Excepti
70. Table 2 summarizes these possible choices Table 2 Optimizers LP Network QP QCP MIP Dual Optimizer yes yes Primal Optimizer Barrier Optimizer Mixed Integer Optimizer yes Network Optimizer Note 1 yes Note 1 Note 1 The problem must contain an extractable network substructure The choice of optimizer or other parameter settings may have a very large effect on the solution speed of your particular class of problem The ILOG CPLEX User s Manual describes the optimizers provides suggestions for maximizing performance and notes the features and algorithmic parameters unique to each optimizer Using the Parallel Optimizers On a computer with multiple CPUs the Barrier Optimizer and the MIP Optimizer are each capable of running in parallel that is they can apply these additional CPUs to the task of ILOG CPLEX 9 0 GETTING STARTED SOLVING AN LP WITH ILOG CPLEX optimizing the model The number of CPUs used by an optimizer is controlled by the user under default settings these optimizers run in serial single CPU mode When solving small models such as those in this document the effect of parallelism will generally be negligible On larger models the effect is ordinarily beneficial to solution speed See the section Using Parallel Optimizers in the ILOG CPLEX User s Manual for information on using CPLEX on a parallel computer Data Entry Options CPLEX provides several options for entering
71. Technology classes because among other things it provides optimized memory management for objects of ILOG Concert Technology classes This provides a boost in performance compared to using the system memory management system As is the case for most ILOG Concert Technology classes 11oEnv is a handle class This means that the variable env is a pointer to an implementation object which is created at the same time as env in the above declaration One advantage of using handles is that if you assign handle objects all that is assigned is a pointer So the statement IloEnv env2 env creates a second handle pointing to the implementation object that env already points to Hence there may be an arbitrary number of 11oEnv handle objects all pointing to the same implementation object When terminating the ILOG Concert Technology application the implementation object must be destroyed as well This must be done explicitly by the user by calling env end for just ONE of the 11oEnv handles pointing to the implementation object to be destroyed The call to env end is generally the last ILOG Concert Technology operation in an application Creating a Model lloModel After creating the environment a Concert application is ready to create one or more optimization models Doing so consists of creating a set of modeling objects to define each optimization model a et le O ie c o O LZ bo ouy2a 119
72. VING AN LP WITH ILOG CPLEX Using the Interactive Optimizer The following sample is screen output from a CPLEX Interactive Optimizer session where the model of an example is entered and solved CPLEX gt indicates the CPLEX prompt and text following this prompt is user input Welcome to CPLEX Interactive Optimizer 9 0 0 with Simplex Mixed Integer amp Barrier Optimizers Copyright c ILOG 1997 2003 CPLEX is a registered trademark of ILOG Type help for a list of available commands Type help followed by a command name for more information on commands CPLEX enter example Enter new problem end on a separate line terminates maximize xl 2 x2 3 x3 subject to x1 x2 x3 lt 20 xl 3 x2 x3 lt 30 bounds 0 lt x1 lt 40 0 lt x2 0 lt x3 end CPLEX gt optimize Tried aggregator 1 time No LP presolve or aggregator reductions Presolve time 0 00 sec Iteration log Iteration E Dual infeasibility 0 000000 Iteration 2 Dual objective 202 500000 Dual simplex Optimal Objective 2 0250000000e 002 Solution time 0 01 sec Iterations 2 1 CPLEX gt display solution variables x1 x3 Variable Name x1 x2 x3 CPLEX quit Solution Value 40 000000 17 500000 42 500000 Concert Technology for C Users Here is a C program using CPLEX in Concert Technology to solve the example An expanded version of this example is discussed in detail in Chapter 3 Concert Te
73. ables 61 directory installation structure 26 display Interactive Optimizer command 40 59 options 40 problem 40 bounds 44 constraints 44 names 42 43 options 40 stats 41 syntax 41 sensitivity 49 syntax 50 settings 57 solution 48 syntax 49 specifying item ranges 42 syntax 44 GETTING STARTED 159 INDEX displaying basic rows and columns 48 bounds 44 constraint names 42 constraints 44 nonzero constraint coefficients 41 number of constraints 41 objective function 44 optimal solution 46 parameter settings 57 post solution information 48 problem 40 problem options 40 problem part 42 problem statistics 41 sensitivity analysis 49 153 type of constraint 41 variable names 42 variables 41 dual simplex optimizer as default 45 availability 47 finding a solution 128 selecting 81 dual values accessing 49 accessing Interactive Optimizer 48 accessing Java 97 E enter Interactive Optimizer command 36 bounds 38 maximize 37 minimize 37 subject to 38 57 syntax 37 entering bounds 38 constraint names 38 constraints 38 example problem 36 item ranges 42 keyboard data 39 objective function 37 38 160 ILOG CPLEX 9 0 objective function names 38 problem 36 37 problem name 36 variable bounds 38 variable names 37 environment object creating 68 74 destroying 69 memory management and 69 equality constraints add to a model 96 error invalid encrypted key 93 no license found 93 NoClassDefFoundError 93 Un
74. al solution and IloFalse indicates that no solution was found More precise information about the outcome of the last call to the method solve can be obtained by calling cplex getStatus The returned value tells you what ILOG CPLEX found out about the model whether it found the optimal solution or only a feasible solution whether it proved the model to be unbounded or infeasible or whether nothing at all has been determined at this point Even more detailed information about the termination of the solve call is available through method I1oCplex getCplexStatus Querying Results After successfully solving the optimization problem you probably are interested in accessing the solution The following methods can be used to query the solution value for a variable or a set of variables IloNum IloCplex getValue IloNumVar var const void IloCplex getValues IloNumArray val const IloNumVarArray var const For example IloNum vall cplex getValue x1 stores the solution value for the modeling variable x1 in variable va11 Other methods are available for querying other solution information For example the objective function value of the solution can be accessed using IloNum objval cplex getObjValue Handling Errors Concert Technology provides two lines of defense for dealing with error conditions suited for addressing two kinds of errors The first kind covers simple programming errors ILOG CPLEX 9 0 GE
75. and Note that unlike the cplex jar file the shared library is system dependent thus the exact pathname of the location for the library to be used differs depending on the platform you are using Pre configured compilation and runtime commands are provided in the standard distribution through the UNIX makefiles and Windows javamake file for Nmake However these scripts presume a certain relative location for the files mentioned above and for application development most users will have their source files in some other location Below are suggestions for establishing build procedures for your application 1 First check the readme htm1 file in the standard distribution under the Supported Platforms heading to locate the machine and 1ibformat entry for your UNIX platform or the compiler and library format combination for Windows 2 Goto the subdirectory in the examples directory where ILOG CPLEX is installed on your machine On UNIX this will be machine libformat and on Windows it will be compiler Mlibformat This subdirectory will contain a makefile or javamake appropriate for your platform 3 Then use these files to compile the examples that came in the standard distribution by calling make execute java UNIX or nmake f javamake execute Windows 4 Carefully note the locations of the needed files both during compilation and at run time and convert the relative path names to absolute path names for use in your own working
76. arameter but this constructor creates an empty handle the handle corresponding to a NULL pointer Empty handles cannot be used for anything but for assigning other handles to them Unfortunately itis a common mistake to try to use empty handles for other things Once an 11oModel object has been constructed it is populated with the extractables that define the optimization model The most important classes here are IloNumVar representing modeling variables IloRange defining constraints of the form lt expr lt u where expr is a linear expression and IloObjective representing an objective function You create objects of these classes for each variable constraint and objective function of your optimization problem Then you add the objects to the model by calling model add object for each extractable object There is no need to explicitly add the variable objects to a model as they are implicitly added when they are used in the range constraints instances of IloRange or the objective At most one objective can be used in a model with 11oCplex Modeling variables are constructed as objects of class I1oNumVar by defining variables of type IloNumvar Concert Technology provides several constructors for doing this the most flexible version for example is IloNumVar xl env 0 0 40 0 ILOFLOAT This definition creates the modeling variable x1 with lower bound 0 0 upper bound 40 0 and type ILOFLOAT which indicates the varia
77. ard distribution Notation in this Manual To make this manual easier to use we ve followed a few conventions in notation and names Important ideas are italicized the first time they appear 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 Entries that you must fill in appear in this typeface for example write filename 4 The names of C routines and parameters in the ILOG CPLEX Callable Library begin with CPX the names of C classes in the CPLEX Concert Technology Library begin with 110 and both appear in this typeface for example CPXcopyob jnames or IloCplex ILOG CPLEX 9 0 GETTING STARTED 19 RELATED DOCUMENTATION The names of Java classes begin with Ilo and appear in this typeface for example IloCplex The name of a class or method in C NET is written as concatenated words with the first letter of each word in upper case for example IntVar or IntVar VisitChildren Generally accessors begin with the key word Get Accessors for Boolean members begin with 1s Modifiers begin with Set Combinations of keys from the keyboard are hyphenated For example control c indicates that you should press the control key and the c key simultaneously The symbol return indicates end of line or end of data entry On some keyboards the key is labeled enter
78. ary like ILOG CPLEX in ILOG Concert Technology you need to tell your compiler where to find the ILOG CPLEX and Concert include files that is the header files and you also need to tell the inker where to find the ILOG CPLEX and Concert libraries The sample projects and makefiles illustrate how to carry out these crucial steps for the examples in the standard distribution They use relative path names to indicate to the compiler where the header files are and to the linker where the libraries are Testing Your Installation on UNIX To run the test follow these steps 1 First check the readme html file in the standard distribution to locate the right subdirectory containing a makefile appropriate for your platform 2 Go to that subdirectory 3 Then use the sample makefile located there to compile and link the examples that came in the standard distribution 4 Execute one of the compiled examples Testing Your Installation on Windows To run the test on a Windows platform first consult the readme html file in the standard distribution That file will tell you where to find another text file that contains information about your particular platform That second file will have an abbreviated name that corresponds to a particular combination of machine architecture and compiler For example if you are working on a personal computer with Windows NT and Microsoft Visual C compiler version 6 then the readme html file will dir
79. ate memory for solution n goto TERMINATE status CPXsolution env lp amp solstat amp objval x pi slack dj if status 1 fprintf stderr Failed to obtain solution Nn goto TERMINATE Write the output to the screen printf nSolution status dWMn solstat printf Solution value f n n objval for i 0 i lt cur numrows i printf Row d Slack 10f Pi 10f n i slack 1 pilil ILOG CPLEX 9 0 GETTING STARTED BUILDING AND SOLVING A SMALL LP MODEL IN C for 3 0 4 cur numcols j printf Column d Value 10f Reduced cost 10fWn j xIjl 43131 Finally write a copy of the problem to a file status CPXwriteprob env lp lpexl lp NULL if stat s 4 fprintf stderr Failed to write LP to disk Wn goto TERMINATE TERMINATE Free up the solution char amp x free and null char amp slack free and null char amp dj amp pi free and null free and null char Free up the problem as allocated by CPXcreateprob if necessary if lp NULL status CPXfreeprob env amp lp if status 4 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
80. ault The upper bound 40 however is not the default so you must enter it explicitly You must type bounds on a separate line before you enter the bound information bounds xl lt 40 ILOG CPLEX 9 0 GETTING STARTED ENTERING A PROBLEM Since the bounds on x2 and x3 are the same as the default bounds there is no need to enter them You have finished entering the problem so to indicate that the problem is complete type end on the last line The CPLEX gt prompt returns indicating that you can again enter a ILOG CPLEX command Summary Entering a problem in ILOG CPLEX is straightforward provided that you observe a few simple rules The terms maximize or minimize must precede the objective function the term subject to must precede the constraints section both must be separated from the beginning of each section by at least one space e r O E D The word bounds must be alone on a line preceding the bounds section On the final line of the problem end must appear JOZIWNdO sA119e 19 u Entering Data You can use the lt return gt key to split long constraints and ILOG CPLEX still interprets the multiple lines as a single constraint When you split a constraint in this way do not press return in the middle of a variable name or coefficient The following is acceptable time xl x2 return x3 lt 20 return labor xl 3x2 x3 lt 30 return The entry below how
81. ble is continuous Other possible variable types include ILOINT for integer variables and ILOBOOL for Boolean variables For each variable in the optimization model a corresponding object of class IloNumVar must be created Concert Technology provides a wealth of ways to help you construct all the IloNumVar objects Once all the modeling variables have been constructed they can be used to build expressions which in turn are used to define objects of class IloObjective and IloRange For example IloObjective obj IloMinimize env xl 2 x2 3 x3 This creates the extractable obj of type 1100bjective which represents the objective function of the example presented in Introducing ILOG CPLEX Consider in more detail what this line does The function IloMinimize takes the environment and an expression as arguments and constructs a new I1o0bjective object ILOG CPLEX 9 0 GETTING STARTED THE ANATOMY OF AN ILOG CONCERT TECHNOLOGY APPLICATION from it that defines the objective function to minimize the expression This new object is returned and assigned to the new handle ob3 After an objective extractable is created it must be added to the model As noted above this is done with the add method of 11oMode1 If this is all that the variable obj is needed for it can be written more compactly like this model add IloMinimize env xl 2 x2 3 x3 This way there is no need for the program variable obj and the program is shorter If
82. ble of the solution The file to read and the optimizer choice are passed to the program via command line parameters For example this command ilolpex2 example mps d reads the file example mps and solves the problem with the dual simplex optimizer Example ilolpex2 demonstrates Reading the Model from a File Selecting the Optimizer Accessing Basis Information Querying Quality Measures The general structure of this example is the same as for example i 101pex1 cpp It starts by creating the environment and terminates with destroying it by calling the end method The code in between is enclosed in try catch statements for error handling Reading the Model from a File The model is created by reading it from the file specified as the first command line argument argv 1 This is done using the method importModel of an 11oCplex object Here the IloCplex object is used as a model reader rather than an optimizer Calling importModel does not extract the model to the invoking cplex object This must be done later by a call to cplex extract model The objects obj var and rng are passed to importModel so that later on when results are queried the variables will be accessible Selecting the Optimizer The selection of the optimizer option is done in the switch statement controlled by the second command line parameter A call to setParam IloCplex RootAlg alg selects the desired 11o0Cplex Algorithm option Accessing Basis I
83. cally created by ILOG CPLEX with the name cplex log If there is an existing cplex 10g file in the directory where ILOG CPLEX is launched ILOG CPLEX will append the current session data to the existing file If you want to keep a unique log file of a problem session you can change the default name with the set logfile command See the ILOG CPLEX User s Manual The log file is written in standard ASCII format and can be edited with any text editor Re Solving You may re solve the problem by reissuing the optimize command ILOG CPLEX restarts the solution process from the previous optimal basis and thus requires zero iterations If you do not wish to restart the problem from an advanced basis use the set advance command to turn off the advanced start indicator Remember that a problem must be present in memory entered via the enter command or read from a file before you issue the optimize command Using Alternative Optimizers In addition to the optimize command ILOG CPLEX can use the primal simplex optimizer primopt command the dual simplex optimizer tranopt command the barrier optimizer baropt command and the network optimizer netopt command Many ILOG CPLEX 9 0 GETTING STARTED 47 e r O E D JOZIWNdO sa119e 19 u SOLVING A PROBLEM 48 problems can be solved faster using these alternative optimizers which are documented in more detail in the ILOG CPLEX User s Manual If you want to solve a mixed integer
84. ce ee eee cece eee eee eee eee e II In 53 Selecting a Read File Format 0 0 00 c eect tet n 53 Reading LP Files tr ee Re GE Gee ne SS aN ee 54 Using File Exterisloris x oss Peek Wee ee Geek ee ae We SE vu ee ees 54 Reading MPS FileS op eR deed dude Mpeg Bek tated ie e 55 ILOG CPLEX 9 0 GETTING STARTED Chapter 3 CONTENTS Reading Basis Files 1 3 Selle a a dd RUE Acum dba peser 55 Setting ILOG CPLEX Parameters 0 00 eee eee eee n nnn 56 Adding Constraints and Bounds ocoococccn ene 57 Changinga Problem 2 1 uc ler rx ee ne RAN USER PE 58 Changing Constraint or Variable Names oooococccccoc eh 59 Changing Sense it s nce vehe er coe t bee ibt er DRE EDO Mate gerit ia 59 Changing BOUNAS 32 bois taa IXGRERESR RARI AME as eas 60 Removing Bounds via a ln E A da EET 60 Changing Coefficients oooooocococccnorrar n 61 Deleting m 61 Executing Operating System Commands ooococccco eee eee eee 63 Quitting ILOG CPLEX 23 A ea 63 Concert Technology Tutorial for C Users 2 0000 cece eee eee 65 The Design of CPLEX in Concert Technology 0ceeeeeee ee eee e een nee 66 Compiling and Linking ILOG CPLEX in Concert Technology Applications 67 Testing Your Installation on UNIX 0 0 ee RR III 67 Testing Your Installation on Windows 0 0 00 tee eee 67 Ini Gase of Problems vin ete Re E d ERE A tied RACE 67 The Anatomy of an ILOG Concert Technology Applica
85. chnology Tutorial for C Users include lt ilcplex ilocplex h gt ILOSTLBEGIN int 14 ILOG CPLEX 9 0 GETTING STARTED SOLVING AN LP WITH ILOG CPLEX main int argc char argv IloEnv env try IloModel model env IloNumVarArray x env x add IloNumVar env 0 0 40 0 x add IloNumVar env x add IloNumVar env model add IloMaximize env x 0 2 x 1 3 x 2 model add x 0 x 1 x 2 lt 20 model ada x 0 3 x 1 x 2 lt 30 IloCplex cplex model 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 lt lt Values lt lt vals lt lt endl catch IloException amp e cerr lt lt Concert exception caught lt lt e lt lt endl catch cerr Unknown exception caught endl env end return 0 END main Concert Technology for NET Users There is an interactive tutorial based on that same example for NET users of ILOG CPLEX in Chapter 5 Concert Technology Tutorial for NET Users ILOG CPLEX 9 0 GETTING STARTED 15 SOLVING AN LP WITH ILOG CPLEX 16 Concert Technology for Java Users Here is a Java program using ILOG
86. cols is then called to supply the columns of the matrix and the associated column bounds names and objective coefficients The routine populatebynonzero calls both CPXnewrows and CPXnewcols to supply all the problem data except the actual constraint matrix At this point the rows and columns are well defined but the constraint matrix remains empty The routine CPXchgcoeflist is then called to fill in the nonzero entries in the matrix Once the problem has been specified the application optimizes it by calling the routine CPX1popt Its default behavior is to use the ILOG CPLEX Dual Simplex Optimizer If this routine returns a nonzero result then an error occurred If no error occurred the application allocates arrays for solution values of the primal variables dual variables slack variables and reduced costs then it obtains the solution information by calling the routine CPXsolution This routine returns the status of the problem whether optimal infeasible or unbounded and whether a time limit or iteration limit was reached the objective value and the solution vectors The application then displays this information on the screen ILOG CPLEX 9 0 GETTING STARTED BUILDING AND SOLVING A SMALL LP MODEL IN C As a debugging aid the application writes the problem to a ILOG CPLEX LP file named lpex1 1p by calling the routine CPXwriteprob This file can be examined to determine whether any errors occurred in the setproblemdata or CPXcopyl
87. cplex GetValues var 0 double dj cplex GetReducedCosts var 0 double pi cplex GetDuals rng 0 double slack cplex GetSlacks rng 0 cplex Output WriteLine Solution status cplex GetStatus cplex Output WriteLine Solution value cplex ObjValue int ncols cplex Ncols for tint J 0 j neolse 4 3 4 cplex Output WriteLine Column t j Value x j Reduced cost d3 31 a int nrows cplex Nrows for int i 0 i lt nrows i cplex Output WriteLine Row i Slack slack i Pi pi i Save the model to a file If you want to save your model to a file in LP format go to the comment Step 11 in your application file and add this line cplex ExportModel lpexl 1p If you have followed the steps in this tutorial interactively you now have a complete application that you can compile and execute 114 ILOG CPLEX 9 0 GETTING STARTED EXAMPLE LPEX1 CS Example LPex1 cs e E aa a go File examples src LPexl cs a 3 Version 9 0 Q E ES ENEE RE E EEES EEN E z Y Copyright C 2001 2003 by ILOG m 9 All Rights Reserved E 7 Permission is expressly granted to use this example in the O course of developing applications that use ILOG products 2 o p TERA ARE RS EA T D E A ie E n Q lt LPexl cs Entering and optimizing an LP problem del Demonstrates different method
88. cts that extracted the model They then track the modification in their internal representations Moreover 11oCplex tries to maintain as much information from a previous solution as is possible and reasonable when the model is modified in order to have a better start when solving the modified model In particular when solving LPs or QPs with a simplex method IloCplex attempts to maintain a basis which will be used the next time the method solve is invoked with the aim of making subsequent solves go faster Modifying an Optimization Problem Example ilolpex3 cpp This example demonstrates Setting ILOG CPLEX Parameters on page 88 Modifying an Optimization Problem on page 88 Starting from a Previous Basis on page 88 86 ILOG CPLEX 9 0 GETTING STARTED MODIFYING AN OPTIMIZATION PROBLEM EXAMPLE ILOLPEX3 CPP Here is the problem example ilolpex3 solves Minimize c x subject to Ax d Ax b 1 lt x lt u where H 10101000 d 3 1 1010000 1 01 100 1 10 4 000 10 10 1 3 0000 10 1 1 5 A 2 1 2 1 2 1 2 3 b 4 1 323 121 1 2 c 9 142 8 2 812 l 00000000 u 50 50 50 50 50 50 50 50 The constraints Ax d represent a pure network flow The example solves this problem in two steps 1 The ILOG CPLEX Network Optimizer is used to solve Minimize C x subject to Hx d I lt x lt u 2 The constraints Ax b are added to the problem and the dual simplex optimizer is used to solve the full p
89. de to obtain the objective function value for this solution and report it Next preparations are made to print the solution value and basis status of each individual variable by allocating arrays of appropriate size these sizes are determined by calls to the routines CPXgetnumcols and CPXgetnumrows Note that a basis is not guaranteed to exist depending on which optimizer was selected at run time so some of these steps including the call to CPXgetbase are dependent on the solution type returned by CPXsolninfo The primal solution values of the variables are obtained by a call to CPXget x and then these values along with the basis statuses if available are printed in a loop for each variable After that a call to CPXgetdb1quality provides a measure of the numerical roundoff error present in the solution by obtaining the maximum amount by which any variable s lower or upper bound is violated After the TERMINATE label the data for the solution x cstat and rstat are freed Then the problem object is freed by CPX reeprob After the problem is freed the ILOG CPLEX environment is freed by CPXcloseCPLEX Complete Program The complete program follows You can also view it online in the file 1pex2 c File examples src lpex2 c Version 9 0 A A A e e G e e E Copyright C 1997 2003 by ILOG All Rights Reserved ILOG CPLEX 9 0 GETTING STARTED g r O 2 Aseaqiy aqe READING A PRO
90. del AddRange System Double MaxValue 20 0 rng 0 1 model AddRange System Double MaxValue 30 0 IRange r0 rng 0 0 TRange rl rng 0 1 var 0 new INumVar 3 var 0 0 model NumVar model Column obj 1 0 And model Column r0 1 0 And model Column r1 1 50 0 0 40 0 var 0 1 model NumVar model Column obj 2 0 And model Column r0 1 0 And model Column r1 3 0 0 0 System Double MaxValue var 0 2 model NumVar model Column obj 3 0 And model Column r0 1 0 And model Column r1 1 0 0 0 System Double MaxValue Again those lines populate the model with data specific to this problem From them you can see how to use the interface IMPModeler to add columns to an empty model While for many examples population by rows may seem most straightforward and natural there are some models where population by columns is a more natural or more efficient approach to implement For example problems with network structure typically lend themselves well to modeling by column Readers familiar with matrix algebra may view the method populateByColumn as the transpose of populateByRow In this approach range objects are created for modeling by column with only their lower and upper bound No expressions over variables are given because building them at this point would be impossible since the variables have not been created yet Similarly the objective f
91. diagnostics IIS constraints problem display problem characteristics sensitivity display sensitivity analysis settings display parameter settings solution display existing solution Display what If you type problem in reply to that prompt that option will list a set of problem characteristics like this Display Problem Options all display entire problem binaries display binary variables bounds display a set of bounds constraints display a set of constraints or node supply demand values generals display general integer variables histogram display a histogram of row or column counts integers display integer variables names display names of variables or constraints qpvariables display quadratic variables semi continuous display semi continuous and semi integer variables sos display special ordered sets stats display problem statistics variable display a column of the constraint matrix Display which problem characteristic Enter the option a11 to display the entire problem Maximize cbjs xl 222 3x3 Subject To cio Tp x2 x3 lt 20 EL xl cxx x3 lt 30 Bounds 0 lt x1 lt 40 All other variables are gt O0 ILOG CPLEX 9 0 GETTING STARTED DISPLAYING A PROBLEM The default names obj c1 c2 are provided by ILOG CPLEX If that is what you want you are ready to solve the problem If there is a mistake you must use the change command to modify the problem The change command is documented
92. e int ncols for int j 0 int nrows for int i 0 cplex getObjValue cplex getNcols j lt ncols 3 cplex output println Column j Value x j Reduced cost dj j cplex getNrows i lt nrows i cplex output println Row DIE a A Slack slack i Pi pi il cplex end catch IloException e System err println Concert exception The following methods following linear program Maximize xl 2 x2 3 x3 Subject To xl x2 x3 lt xl 3 x2 x3 lt Bounds 0 lt x1 lt 40 End e 7 caught all populate the problem with data for the 20 30 using the IloMPModeler API static void populateByRow IloMPModeler model TloNumVar var IloRange rng throws IloException double lb 0 0 0 0 0 0 double ub 40 0 Double MAX VALUE Double MAX VALUE IloNumVar x var 0 x double objvals rng 0 rng 0 0 102 ILOG CPLEX 9 0 model numVarArray 3 1 0 model addMaximize model scalProd x model addLe model sum model prod 1 0 150 lb ub 2 0 3 0 objvals new IloRange 2 x 01 model prod X 11 GETTING STARTED COMPLETE CODE OF LPEX1 JAVA model prod 1 0 x 2 20 0 rng 0 1 model addLe model sum model prod 1 0 x 0 model prod 3 0 x 1
93. e like this write example2 lp Another way of avoiding the prompt for a file format is by specifying the file type explicitly in the file name extension Try the following as an example write example lp Using a file extension to indicate the file type is the recommended naming convention This makes it easier to keep track of your problem and solution files When the file type is specified by the file name extension ILOG CPLEX ignores subsequent file type information issued within the write command For example ILOG CPLEX responds to the following command by writing an LP format problem file write example lp mps Writing Basis Files Another optional file format is BAS Unlike the LP and MPS formats this format is not used to store a description of the problem statement Rather it is used to store information about the solution to a problem information known as a basis Even after changes are made to the problem using a prior basis to jump start the optimization can speed solution time considerably A basis can be written only after a problem has been solved Try this now with the following command write example bas In response ILOG CPLEX displays a confirmation message like this Basis written to file example bas When a very large problem is being solved by the primal or dual simplex optimizer a file with the format extension xxx is automatically written after every 50 000 iterations a frequency that can be adjust
94. e steps in the tutorial you can examine the code and apply concepts explained in the tutorials Then you compile and execute the code to analyze the results Ideally as you work through the tutorial you are sitting in front of your computer with ILOG Concert Technology for NET users and ILOG CPLEX already installed and available in your integrated development environment What You Need to Know Prerequisites 106 This tutorial requires a working knowledge of C NET If you are experienced in mathematical programming or operations research you are probably already familiar with many concepts used in this tutorial However little or no experience in mathematical programming or operations research is required to follow this tutorial You should have ILOG CPLEX and ILOG Concert Technology for NET users installed in your development environment before starting this tutorial In your integrated development environment you should be able to compile link and execute a sample application provided with ILOG CPLEX and ILOG Concert Technology for NET users before starting the tutorial To check your installation before starting the tutorial open yourCPLEXhomeNexamplesNi86 2000 7 1NformatNexamples net sln in your integrated development environment where yourCPLEXhome indicates the place you installed ILOG CPLEX on your platform and ormat indicates one of these possibilities stat mda stat mta or vb An integrated development environm
95. e Extensions If the file name has an extension that corresponds to one of the supported file formats ILOG CPLEX automatically reads it without your having to specify the format Thus the following command automatically reads the problem file example 1p in LP format read example lp ILOG CPLEX 9 0 GETTING STARTED READING PROBLEM FILES Reading MPS Files ILOG CPLEX can also read industry standard MPS formatted files The problem called afiro mps provided in the ILOG CPLEX distribution serves as an example If you include the mps extension in the file name ILOG CPLEX will recognize the file as being in MPS format If you omit the extension you must specify that the file is of the type MPS read afiro mps Once the file has been read the following message appears Selected objective sense MINIMIZE Selected objective name obj Selected RHS name rhs Problem afiro read Read time 0 01 sec ILOG CPLEX reports additional information when it reads MPS formatted files Since these files can contain multiple objective function right hand side bound and other information ILOG CPLEX displays which of these is being used for the current problem See the ILOG CPLEX User s Manual to learn more about special considerations for using MPS formatted files Reading Basis Files In addition to other file formats the xead command is also used to read basis files These files contain information for ILOG CPLEX that tells
96. ebug Your Program siaii paare e eee hmm rh 126 Test Your Applicatlori 22 Le a IT ep PEE oa a e rend 127 Use the Examples i cnt urort oa a he Bore Mw et ruber Pe A RARE ERR 127 Building and Solving a Small LP Model in C esee 127 Complete Program sucum e Gu X E a PI GR a 129 Reading a Problem from a File Example lpex2 C 0 0 cece eee eee eee eee 138 ILOG CPLEX 9 0 GETTING STARTED 7 CONTENTS Complete PrograM oooococcoc eee rre 139 Adding Rows to a Problem Example Ipex3 c oooooccooccoccr oo 147 Complete Program eiue doe ERE d per bee dul dede d 148 Performing Sensitivity Analysis 00 ccc eee eee eee nn 153 ag Se santas hoes A AS A Vata ie aise at a Sele Mears A A E ida 157 ILOG CPLEX 9 0 GETTING STARTED Introducing ILOG CPLEX This preface introduces ILOG CPLEX 9 0 It includes sections about What Is ILOG CPLEX on page 10 Solving an LP with ILOG CPLEX on page 13 What You Need to Know on page 18 What s in This Manual on page 19 Notation in this Manual on page 19 9 9 9 9 Related Documentation on page 20 ILOG CPLEX 9 0 GETTING STARTED 9 WHAT Is ILOG CPLEX What Is ILOG CPLEX ILOG CPLEX is a tool for solving linear optimization problems commonly referred to as Linear Programming LP problems of the form Maximize or Minimize C1X1 CoXo d CpXp subject to Q11X4 Q12X2o d AJpXp by 21X1 dppoXo A9pXn bo Qm1X1
97. ect you to the msvc html file where you will find detailed instructions about how to create a project to compile link and execute the examples in the standard distribution bo ouy2a 1199u09 g r 2 e e c o 1 N The examples have been tested repeatedly on all the platforms compatible with ILOG CPLEX so if you successfully compile link and execute them then you can be sure that your installation is correct In Case of Problems If you encounter difficulty when you try this test then there is a problem in your installation and you need to correct it before you begin real work with ILOG CPLEX For example if you get a message from the compiler such as ilolpex3 cpp 1 Can t find include file ilcplex ilocplex h ILOG CPLEX 9 0 GETTING STARTED 67 THE ANATOMY OF AN ILOG CoNcERT TECHNOLOGY APPLICATION then you need to verify that your compiler knows where you have installed ILOG CPLEX and its include files that 1s its header files If you get a message from the linker such as ld lcplex No such file or directory then you need to verify that your linker knows where the ILOG CPLEX library is located on your system If you get a message such as ilm CPLEX no license found for this product or ilm CPLEX invalid encrypted key MNJVUXTDJV82 in usr ilog ilm access ilm run ilmcheck then there is a problem with your license to use ILOG CPLEX Review the ILOG
98. ed by the set simplex basisinterval command This periodically written basis can be useful as insurance against the possibility that a long optimization may be unexpectedly interrupted due to power failure or other causes because the optimization can then be restarted using this advanced basis Using Path Names A full path name may also be included to indicate on which drive and directory any file should be saved The following might be a valid write command if the disk drive on your system contains a root directory named problems write problems example lp ILOG CPLEX 9 0 GETTING STARTED READING PROBLEM FILES Summary The general syntax for the write command is write filename file_format or write filename file extension where file extension indicates the format in which the file is to be saved Reading Problem Files When you are using ILOG CPLEX to solve linear optimization problems you may frequently enter problems by reading them from files instead of entering them from the keyboard e r O E D Continuing the tutorial from Writing Problem and Solution Files on page 50 the topics are Selecting a Read File Format on page 53 JOZIWNdO 8AI9e19 U Reading LP Files on page 54 Using File Extensions on page 54 Reading MPS Files on page 55 Reading Basis Files on page 55 Selecting a Read File Format When you type the read command in the Interactive Optimizer ILOG CPLEX displays the
99. ee logging output on the screen when invoking the method solve This can be turned off by calling cplex setOut env getNullStream thatis by redirecting the out stream of the IloCplex object cplex to the null stream of the environment ILOG CPLEX 9 0 GETTING STARTED BUILDING AND SoLviNG A SMALL LP MODEL IN C If a solution is found solution information is output through the channel env out which is initialized to cout by default The output operator is defined for type IloAlgorithm Status as returned by the call to cplex getStatus Itis also defined for 11oNumArray the ILOG Concert Technology class for an array of numerical values as returned by the calls to cplex getValues cplex getDuals cplex getSlacks and cplex getReducedCosts In general the output operator is defined for any ILOG Concert Technology array of elements if the output operator is defined for the elements The functions named populateby are purely about modeling and are completely decoupled from the algorithm IloCplex In fact they don t use the cplex object which is created only after executing one of these functions Modeling by Rows The function populatebyrow creates the variables and adds them to the array x Then the objective function and the constraints are created using expressions over the variables stored in x The range constraints are also added to the array of constraints c The objective and the constraints are added to the mode
100. ent such as Microsoft Visual Studio will then check for the DLLs of ILOG CPLEX and ILOG Concert Technology for NET users and warn you if they are not available to it Another way to check your installation is to load the project for one of the samples delivered with your product For example you might load the following project into Microsoft Visual Studio to check a C example of the diet problem yourCPLEXhomeNexamplesNi86 2000 7 1NformatNDiet csproj ILOG CPLEX 9 0 GETTING STARTED WHAT YOU WILL BE DOING What You Will Be Doing ILOG CPLEX can work together with ILOG Concert Technology for NET users a C NET library that allows you to model optimization problems independently of the algorithms used to solve the problem It provides an extensible modeling layer adapted to a variety of algorithms ready to use off the shelf This modeling layer enables you to change your model without completely rewriting your application To find a solution to a problem by means of ILOG CPLEX with ILOG Concert Technology for NET users you use a three stage method describe model and solve 38 95 o omy 3 Z ma E gt c5 0 o Ro n Q lt The first stage is to describe the problem in natural language The second stage is to use the classes and interfaces of ILOG Concert Technology for NET users to model the problem The model is composed of data decision variables and constraints Decision variables are the unknown informa
101. environment In Case Problems Arise If a problem occurs in the compilation phase make sure your java compiler is correctly set up and that your classpath includes the cplex jar file If compilation is successful and the problem occurs when executing your application there are three likely causes ILOG CPLEX 9 0 GETTING STARTED THE DESIGN OF ILOG CPLEX iN ILOG CoNcERT TECHNOLOGY 1 If you get a message like java lang NoClassDefFoundError your classpath is not correctly set up Make sure you use classpath path to cplex jar in your java command 2 If you get a message like java lang UnsatisfiedLinkError you need to set up the path correctly so that the JVM can locate the ILOG CPLEX shared library Make sure you use the following option in your java command Djava library path path to shared library 3 If you get a message like ilm CPLEX no license found for this product or ilm CPLEX invalid encrypted key MNJVUXTDJV82 in usr ilog ilm access ilm run ilmcheck then there is a problem with your license to use ILOG CPLEX Review the ILOG License Manager User s Guide and Reference to see whether you can correct the problem If you have verified your system and license setup but continue to experience problems contact ILOG Technical Support and report the error messages The Design of ILOG CPLEX in ILOG Concert Technology User Written Application e 2 Concert Technolog
102. er case is allowed endl cerr and algorithm is one of the letters endl cerr o default lt lt endl cerr lt lt p primal simplex endl cerr d dual simplex lt lt endl cerr lt lt b barrier lt lt endl cerr lt lt h barrier with crossover lt lt endl cerr lt lt n network simplex lt lt endl cerr lt lt S sifting endl Corr lt A e concurrent endl cerr lt lt Exiting lt lt endl END usage ILOG CPLEX 9 0 GETTING STARTED 85 bo ouy2a W e 70 A le E O ie c Y o MODIFYING AND REOPTIMIZING Modifying and Reoptimizing In many situations the solution to a model is only the first step One of the important features of Concert Technology is the ability to modify and then re solve the model even after it has been extracted and solved one or more times A look back to examples ilolpex1 cpp and ilolpex2 cpp reveals that models have been modified all along Each time an extractable is added to a model it changes the model However those examples made all such changes before the model was extracted to ILOG CPLEX Concert Technology maintains a link between the model and all 110Cp1ex objects that may have extracted it This link is known as notification Each time a modification of the model or one of its extractables occurs the change is notified to the 110Cp1ex obje
103. ert method 98 shadow prices see dual values sifting algorithm 81 slack accessing in Interactive Optimizer 48 accessing in Java 97 accessing values 48 solution accessing basic rows and columns 48 accessing values 48 displaying 48 displaying basic rows and columns 48 outputting 75 process 46 querying results 72 reporting optimal 46 restarting 47 sensitivity analysis 49 153 solution file writing 50 solve 96 solve Concert method 98 solve method IloCplex class 72 74 82 86 solving model 71 82 node LP 81 GETTING STARTED 165 INDEX problem 45 128 root LP 81 with network optimizer 87 SOS creating 80 sparse matrix 87 Special Ordered Set see SOS starting CPLEX 34 from previous basis 88 Interactive Optimizer 34 new problem 36 string parameter 88 structure of a CPLEX application 94 Supported Platforms 92 System out 98 T tranopt Interactive Optimizer command 47 U unbounded 97 UNIX building Callable Library applications 121 executing commands 63 installation directory 26 installing CPLEX 26 testing CPLEX in Concert Technology 67 verifying installation 28 UnsatisfiedLinkError 93 V variable Boolean 70 box 41 changing bounds 60 changing names 59 continuous 70 creating 80 deleting 61 displaying 41 166 ILOG CPLEX 9 0 displaying names 42 entering bounds 38 entering names 37 integer 70 modeling 95 name limitations 37 ordering 43 removing bounds 60 representing in model 70 W wa
104. eved by CPXgetobjval Then the extra rows are added by calling CPXaddrows For convenience the total number of nonzeros in the rows being added is stored in an extra element of the array rmatbeg and this element is passed for the parameter nzcnt The name arguments to CPXaddrows are NULL since no variable or constraint names were defined for this problem After the CPXaddrows call parameter CPX PARAM LPMETHOD is set to CPX ALG DUAL and the routine CPX1popt is called to re optimize the problem using the dual simplex optimizer After re optimization CPXsolution is called to determine the solution status the objective value and the primal solution NULL is passed for the other solution values since they are not printed by this example At the end the problem is written as a SAV file by CPXwriteprob This file can then be read into the ILOG CPLEX Interactive Optimizer to analyze whether the problem was correctly generated Using a SAV file is recommended over MPS and LP files as SAV files preserve the full numeric precision of the problem After the TERMINATE label CPX reeprob releases the problem object and CPXcloseCPLEX releases the ILOG CPLEX environment Complete Program The complete program follows You can also view it online in the file 1pex3 c o M File examples src lpex3 c Version 9 0 AAA A A E A E E ne Copyr
105. ever is incorrect since the return key splits a variable name time x1 x2 x return 3 2 20 return labor xl 3x2 x3 lt 30 return If you type a line that ILOG CPLEX cannot interpret a message indicating the problem will appear and the entire constraint or objective function will be ignored You must then re enter the constraint or objective function The final thing to remember when you are entering a problem is that once you have pressed return you can no longer directly edit the characters that precede the return As long as you have not pressed the return key you can use the backspace key to go back and change what you typed on that line Once return has been pressed the change command must be used to modify the problem The change command is documented in Changing a Problem on page 58 ILOG CPLEX 9 0 GETTING STARTED 39 DISPLAYING A PROBLEM Displaying a Problem Now that you have entered a problem using ILOG CPLEX you must verify that the problem was entered correctly To do so use the display command At the CPLEX gt prompt type display A list of the items that can be displayed then appears Some of the options display parts of the problem description while others display parts of the problem solution Options about the problem solution are not available until after the problem has been solved The list looks like this Display Options iis display infeasibility
106. ex allows you to control which option to use for solving the root and for solving the nodes respectively by the following lines euo go void IloCplex setParam IloCplex RootAlg alg S 3 void IloCplex setParam IloCplex NodeAlg alg D 2 rum where 11oCplex Algorithmis an enumeration type It defines the following symbols S a with their meaning o 9 c 2 IloCplex AutoAlg allow ILOG CPLEX to choose the algorithm S o 3 o Q IloCplex Dual use the dual simplex algorithm 6 lt IloCplex Primal use the primal simplex algorithm IloCplex Barrier use the barrier algorithm IloCplex Network use the network simplex algorithm for the embedded network IloCplex Sifting use the sifting algorithm IloCplex Concurrent allow ILOG CPLEX to use multiple algorithms on multiple computer processors For QP models only the AutoAlg Dual Primal Barrier and Network algorithms are applicable The optimizer option used for solving pure LPs and QPs is controlled by setting the root algorithm parameter This is demonstrated next in example ilolpex2 cpp ILOG CPLEX 9 0 GETTING STARTED 81 READING A PROBLEM FROM A FILE EXAMPLE ILOLPEX2 CPP Reading a Problem from a File Example ilolpex2 cpp 82 This example shows how to read an optimization problem from a file and solve it with a specified optimizer option It prints solution information including a Simplex basis if available Finally it prints the maximum infeasibility of any varia
107. example command line arguments are required Oo i e ilolpex2 filename method x 3 where Cc e I filename is the name of the file with mps lp or sav extension a e method is the optimization method m lt Vf o default p primal simplex d dual simplex LE h barrier with crossover b barrier without crossover n network with dual simplex cleanup S sifting c concurrent Example ilolpex2 example mps o include lt ilcplex ilocplex h gt ILOSTLBEGIN Static void usage const char progname int main int argc char argv ILOG CPLEX 9 0 GETTING STARTED 83 READING A PROBLEM FROM A FILE EXAMPLE ILOLPEX2 CPP IloEnv env try IloModel model env IloCplex cplex env if arge 3 strchr podhbnsc argv 2 0 NULL usage argv 0 throw 1 switch argv 2 0 case o cplex setParam IloCplex RootAlg IloCplex AutoAlg Lu break case p cplex setParam IloCplex RootAlg IloCplex Primal Lu break case d cplex setParam IloCplex RootAlg IloCplex Dual break case b cplex setParam IloCplex RootAlg IloCplex Barrier cplex setParam IloCplex BarCrossAlg IloCplex NoAlg break case h cplex setParam IloCplex RootAlg IloCplex Barrier break ies cplex setParam IloCplex RootAlg IloCplex Network cplex setParam IloCplex RootAlg IloCplex Sifting cplex setParam
108. f CPLEX become functional and are available to you The chapters that follow this one provide tutorials in the use of each of the Technologies that ILOG CPLEX provides the ILOG Concert Technology Tutorials for C Java and NET users and the Callable Library Tutorial for C and other languages This chapter provides guidelines for Installing ILOG CPLEX Setting Up Licensing Using the Component Libraries Important Please read these instructions in their entirety before beginning the installation Remember that most ILOG CPLEX distributions will operate correctly only on the specific platform and operating system version for which they are designed If you upgrade your operating system you may need to obtain a new ILOG CPLEX distribution ILOG CPLEX 9 0 GETTING STARTED 25 o 1 gt Ke O U r m x INSTALLING ILOG CPLEX Installing ILOG CPLEX The steps to install ILOG CPLEX involve identifying the correct distribution file for your particular platform and then executing a command that uses that distribution file The identification step is explained in the booklet that comes with the CD ROM or is provided with the FTP instructions for download Once the correct distribution file is at hand the installation proceeds as follows Installation on UNIX On UNIX systems ILOG CPLEX 9 0 is installed in a subdirectory named cplex90 under the current working directory where you perform the installation
109. fault method CPX ALG NONE break status CPXsetintparam env CPX PARAM LPMETHOD method if status A 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 solnstat CPXgetstat env lp 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 1574 status y 1 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 x1 fprintf stderr Failed to obtain objective value Nn goto TERMINATE g r O E 2 Aseaqiy 91qel1eo ILOG CPLEX 9 0 GETTING STARTED 143 READING A PROBLEM FROM A FILE EXAMPLE LPEX2 C 144 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 numc
110. ged The sense of the objective function may be changed by specifying the objective function name its default is obj or the number 0 when ILOG CPLEX prompts you for the constraint You are then prompted for a new sense The sense of an objective function can take the value maximum or minimum or the abbreviation max or min Changing Bounds When the example was entered bounds were set specifically only for the variable x1 The bounds can be changed on this or other variables with the bounds option Again start by selecting the command and option change bounds Select the variable by name or number and then select which bound you would like to change For the example change the upper bound of variable x2 from to 50 Change bounds on which variable x2 Present bounds on variable x2 The indicated variable is gt 0 Change lower or upper bound or both 1 u or b u Change upper bound to what inf for no upper bound 50 New bounds on variable x2 0 lt x2 lt 50 Removing Bounds To remove a bound set it to or ee Interactively use the identifiers inf and inf instead of the symbols To change the upper bound of x2 back to 2 use the one line command change bounds x2 u inf You receive the message New bounds on variable x2 The indicated variable is gt 0 ILOG CPLEX 9 0 GETTING STARTED CHANGING A PROBLEM The bound is now the same as it was when the problem was originally
111. h IloException amp e cerr lt lt Concert exception caught IN C vals lt lt endl vals lt lt endl lt lt e lt lt endl catch 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 X lt lt endl cerr lt lt where X is one of the following options lt lt endl cerr lt lt r generate problem by row endl cerr generate problem by column lt lt endl cerr lt lt n generate problem by nonzero lt lt endl cerr lt lt Exiting lt lt endl END usage To populate by row we first create the variables and then use them to create the range constraints and objective static void populatebyrow IloModel model IloEnv env model getEnv x add IloNumVar env 0 0 x add IloNumVar env x add IloNumVar env model add IloMaximize env 40 0 XO 2 c add x 0 x 1 x 2 c add x 0 3 x 1 x 2 model add c END populatebyrow To populate by column objective ILOG CPLEX 9 0 78 IloNumVarArray x IloRangeArray c XL 3 121995 lt 20 lt 30 we first create the range constraints and the and then create the variables and add them to the ranges and GETTING STARTED BUILDING AND SOLVING A SMA
112. har filename IloObjective amp obj IloNumVarArray vars IloRangeArray rngs const and void IloCplex importModel IloModel amp m const char filename IloObjective amp obj loNumVarArray vars loRangeArray rngs loSOSlArray sosl I I I I loSOS2Array sos2 const ILOG CPLEX 9 0 GETTING STARTED SELECTING AN OPTIMIZER They provide additional parameters so that the newly created modeling objects will be returned to the caller Example program ilolpex2 cpp gives an example of how to use method importModel Selecting an Optimizer IloCplex treats all problems it solves as Mixed Integer Programming MIP problems The algorithm used by 11oCplex for solving MIP is known as branch amp cut referred to in some contexts as branch amp bound and is documented in more detail in the ILOG CPLEX User s Manual For this tutorial it is sufficient to know that this algorithm consists of solving a sequence of LPs or QPs that are generated in the course of the algorithm The first LP or QP to be solved is known as the root while all the others are referred to as nodes and are derived from the root or from other nodes If the model extracted to the cp1ex object is a pure LP or QP no integer variables then it will be fully solved at the root As mentioned in Optimizer Options on page 12 various optimizer options are provided for solving LPs and QPs While the default optimizer works well for a wide variety of models IloCpl
113. hyphen the range character The indices can be names or matrix index numbers You simply enter the starting name or index number a hyphen and finally the ending name or index number ILOG CPLEX automatically sets the default upper and lower limits defining any range to be the highest and lowest possible values Therefore you have the option of leaving out either the upper or lower name or index number on either side of the hyphen To see every possible item you would simply enter Displaying Variable or Constraint Names You can display a variable name by using the display command with the options problem names variables If you do not enter the word variables ILOG CPLEX prompts you to specify whether you wish to see a constraint or variable name Type display problem names variables In response ILOG CPLEX prompts you to specify a set of variable names to be displayed like this Display which variable name s Specify these variables by entering the names of the variables or the numbers corresponding to the columns of those variables A single number can be used or a range such as 1 2 All ILOG CPLEX 9 0 GETTING STARTED DISPLAYING A PROBLEM of the names can be displayed at once if you type a hyphen the character Try this by entering a hyphen at the prompt and pressing the return key Display which variable name s In the example there are three variables with default names ILOG CPL
114. iables Nonzero Count 2 Number of Columns 3 It tells you that there are three columns each having two nonzeroes and no other columns Similarly the row histogram of the same small problem looks like this Row counts excluding fixed variables Nonzero Count 3 Number of Rows 2 5 3 It tells you that there are two rows with three nonzeroes in each of them S o Of course in a more complex model there would usually be a wider variety of nonzero e counts than those histograms show Here is an example in which there are sixteen columns ME ps where only one row is non zero 736 columns where two rows are non zero and so forth D El Column counts excluding fixed variables El Nonzero Count 1 2 3 4 5 6 15 16 5 Number of Columns 16 756 1054 547 267 113 2 1 p If there has been an error during entry of the problem perhaps a constraint coefficient having been omitted by mistake for example summaries like these of a model where the structure of the constraint matrix is known may help you find the source of the error Solving a Problem The problem is now correctly entered and ILOG CPLEX can be used to solve it This example continues with the following topics Solving the Example Problem on page 45 Solution Options on page 47 Displaying Post Solution Information on page 48 Solving the Example Problem The opt imize command tells ILOG CPLEX to solve the LP problem ILOG CPLEX uses the dual simplex optimizer
115. ight C 1997 2003 by ILOG All Rights Reserved Permission is expressly granted to use this example in the El course of developing applications that use ILOG products ARRE AR ER A O A E A a lpex3 c example of using CPXaddrows to solve a problem 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 ILOG CPLEX 9 0 GETTING STARTED ADDING ROWS TO A PROBLEM EXAMPLE LPEX3 C include lt stdio h gt include lt stdlib h gt Modified example from Chvatal Linear Programming Chapter 26 Treat the constraints with A as the complicating constraints and the constraints with H as the simple problem and then add the and solve with dual The idea is to solve the simple problem first constraints for the complicating constraints x minimize c x m subject to Hx d gi Ax b l lt x lt u where H 1 101000 d 3 1 1 0 1 0 0 0 1 0 1 1 0 0 1 10 4 0 0 0 1 0 1 0 1 3 0 0 0 0 1 0 1 1 75 A 2 1 2 1 2 1 2 3 b 4 3 2 3 12 1 1 2 x e S I 4 2 8 2 8 12 d L 0 0 8 0 O0 BD 0j 5050 50 50 50 50 50 50 define COLSORIG define ROWSSUB define NZSUB 2 COLSORIG define ROWSCOMP define NZCOMP ROWSCOMP COLSO
116. in Changing a Problem on page 58 Summary Display problem characteristics by entering the command display problem Displaying Problem Statistics When the problem is as small as our example it is easy to display it on the screen however many real problems are far too large to display For these problems the stat s option of the display problem command is helpful When you select stats information about the attributes of the problem appears but not the entire problem itself These attributes include the number and type of constraints variables nonzero constraint coefficients Try this feature by typing display problem stats For our example the following information appears Problem name example Variables 3 Nneg 2 Box 1 Objective nonzeros 3 Linear constraints 2 Less 2 Nonzeros 6 RHS nonzeros 2 This information tells us that in the example there are two constraints three variables and six nonzero constraint coefficients The two constraints are both of the type less than or equal to Two of the three variables have the default nonnegativity bounds 0 x 09 and one is restricted to a certain range a box variable In addition to a constraint matrix nonzero count there is a count of nonzero coefficients in the objective function and on the right hand side Such statistics can help to identify errors in a problem without displaying it in its entirety You can see more information about the
117. ing object in which you want to install a new variable and link them together with the method IColumn And Populate the model by nonzeros Go to the comment Step 6 in the file and add these lines to create a method to populate the empty model with data by nonzeros internal static void PopulateByNonzero IMPModeler model INumVar var IRange rng double lb 0 0 0 0 0 0 double ub 40 0 System Double MaxValue System Double MaxValue INumVar x model NumVarArray 3 lb ub var 0 x double objvals 1 0 2 0 3 0 model Add model Maximize model ScalProd x objvals rng 0 new IRange 2 rng 0 0 model AddRange System Double MaxValue 20 0 rng 0 1 model AddRange System Double MaxValue 30 0 rng 0 0 Expr model Sum model Prod 1 0 x 0 model Prod 1 0 x 1 model Prod 1 0 x 2 rng 0 1 Expr model Sum model Prod 1 0 x 0 model Prod 3 0 x 1 model Prod 1 0 x 2 In those lines you can see how to populate an empty model with data indicating the nonzeros of the constraint matrix Those lines first create objects for the objective and the ranges without expressions They also create variables without columns that is variables with only their bounds Then those lines create expressions over the objective ranges and variables and add the expressions to the model ILOG CPLEX 9 0 GETTING STARTED SOLVE Add an interface Go t
118. ing the complete optimization problem 2 IloCplex objects are used to solve the problems that have been created with the modeling objects An 11oCplex object reads a model and extracts its data to the appropriate representation for the ILOG CPLEX optimizer Then the 11oCplex object is ready to solve the model it extracted and be queried for solution information Thus the modeling and optimization parts of a user written application program are represented by a group of interacting C objects created and controlled within the application Figure 3 1 shows a picture of an application using ILOG CPLEX with ILOG Concert Technology to solve optimization problems User Written Application lloCplex object Concert Technology modeling objects Bel AA ee CPLEX database Figure 3 1 A View of ILOG CPLEX with ILOG Concert Technology The ILOG CPLEX database includes the computing environment its communication channels and your problem objects This chapter gives a brief tutorial illustrating the modeling and solution classes provided by ILOG Concert Technology and ILOG CPLEX More information about the algorithm class IloCplex and its nested classes can be found in the ILOG CPLEX User s Manual and ILOG CPLEX Reference Manual ILOG CPLEX 9 0 GETTING STARTED Cc a9 MPNSING AND LINKING ILOG CPLEX IN CONCERT TECHNOLOGY APPLI Compiling and Linking ILOG CPLEX in Concert Technology Applications To exploit a C libr
119. ing way st x1 x2 x3 lt 20 xl 3x2 x3 lt 30 Constraint Names In this simple example it is easy to keep track of the small number of constraints but for many problems it may be advantageous to name constraints so that they are easier to identify You can do so in ILOG CPLEX by typing a constraint name and a colon before the actual constraint If you do not give the constraints explicit names ILOG CPLEX will give them the default names c1 c2 cn In the example if you want to call the constraints time and labor for example enter the constraints like this st time x1 x2 x3 lt 20 labor xl 3x2 x3 lt 30 Constraint names are subject to the same guidelines as variable names They must have no more than 16 characters consist of only allowed characters and not begin with a number a period or the letter e followed by a positive or negative number or another e Objective Function Names The objective function can be named in the same manner as constraints The default name for the objective function is obj ILOG CPLEX assigns this name if no other is entered Bounds Finally you must enter the lower and upper bounds on the variables If no bounds are specified ILOG CPLEX will automatically set the lower bound to 0 and the upper bound to You must explicitly enter bounds only when the bounds differ from the default values In our example the lower bound on x1 is 0 which is the same as the def
120. 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 C Java and NET class libraries offering an API that includes modeling facilities to allow the programmer to embed CPLEX optimizers in C Java or NET applications Table 1 lists the files that contain the libraries Table 1 Concert Technology Libraries Microsoft Windows UNIX C ilocplex lib libilocplex a concert lib libconcert a Java cplex jar cplex jar ILOG CPLEX dll NET Ct ILOG CONCERT dl11 The ILOG Concert Technology libraries make use of the Callable Library described next The 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 cplex 1ib and cplex d11 on Windows platforms and in 1ibcplex a libcplex so and libcplex si on UNIX platforms In this manual the phrase CPLEX Component Libraries is used to refer equally to any of these libraries While all of the libraries are callable the term CPLEX Callable Library as used here refers specifically to the C library Compatible Platforms ILOG CPLEX is available on Windows and UNIX platforms The programming inte
121. ion model 2 a 33 lt x C tQ lt 5 g C5 5 go 9 Oo roy lt The 11oCplex class implements the ILOG Concert Technology interface for creating variables and constraints It also provides functionality for solving Mathematical Programing MP problems and accessing solution information Compiling ILOG CPLEX Applications in ILOG Concert Technology When compiling a Java program that uses ILOG Concert Technology you need to inform the Java compiler where to find the file cplex jar containing the ILOG CPLEX Concert ILOG CPLEX 9 0 GETTING STARTED 91 COMPILING 92 ILOG CPLEX APPLICATIONS IN ILOG CONCERT TECHNOLOGY Technology class library To do this you add the cplex jar file to your classpath This is most easily done by passing the command line option classpath path to cplex Jjar to the Java compiler javac If you need to include other Java class libraries you should add the corresponding jar files to the classpath as well Ordinarily you should also include the current directory to be part of the Java classpath At execution time the same classpath setting is needed Additionally since ILOG CPLEX is implemented via JNI you need to instruct the Java Virtual Machine JVM where to find the shared library or dynamic link library containing the native code to be called from Java This may be done with the command line option Djava library path path to shared library to the java comm
122. ject to X X X3 lt S 20 X 3x x3 lt 30 with these bounds 0 x 40 0 lt x lt Too 0 lt x3 lt Too Before any ILOG CPLEX Callable Library routine can be called your application must call the routine CPXopenCPLEX to get a pointer called env to the ILOG CPLEX environment Your application will then pass this pointer to every Callable Library routine If this routine fails it returns an error code This error code can be translated to a string by the routine CPXgeterrorstring After the ILOG CPLEX environment is initialized the ILOG CPLEX screen indicator parameter CPX PARAM SCRIND is turned on by the routine CPXsetintparam This causes all default ILOG CPLEX output to appear on the screen If this parameter is not set then ILOG CPLEX will generate no viewable output on the screen or in a file At this point the routine setproblemdata is called to create an empty problem object Based on the problem building method selected by the command line argument the application then calls a routine to build the matrix by rows by columns or by nonzeros The routine populatebyrow first calls CPXnewcols to specify the column based problem data such as the objective bounds and variables names The routine CPXaddrows is then called to supply the constraints The routine populatebycolumn first calls CPXnewrows to specify the row based problem data such as the right hand side values and sense of constraints The routine CPXadd
123. jects of class IloNumColumn are handle objects like most other Concert Technology objects The method end must therefore be called to delete the associated implementation object when it is no longer needed However for implicit column ILOG CPLEX 9 0 GETTING STARTED 75 BUILDING AND SOLVING A SMALL LP MODEL IN C 76 expressions where no IloNumColumn object is explicitly created such as the ones used in this example the method end should not be called The column expression is passed as a parameter to the constructor of class IloNumVar For example the constructor IloNumVar obj 1 0 c 0 1 0 c 1 1 0 0 0 40 0 creates a new modeling variable with lower bound 0 0 upper bound 40 0 and by default type ILOFLOAT and adds it to the objective obj with a linear coefficient of 1 0 to the range c 0 with a linear coefficient of 1 0 and to c 1 with a linear coefficient of 1 0 Column expressions can be used directly to construct numerical variables with default bounds 0 IloInfinity and type ILOFLOAT as in the following statement x add obj 2 0 c 0 1 0 c 1 3 0 where IloNumVar does not need to be explicitly written Here the C compiler recognizes that an I1oNumVar object needs to be passed to the add method and therefore automatically calls the constructor IloNumVar IloNumColumn in order to create the variable from the column expression Modeling by Nonzero Elements The last of the three functio
124. k default basismsg Bad basis status break printf s basismsg printf 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 Nn goto TERMINATE printf Maximum bound violation 17 10g1n 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 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 g r O Aseaqiy 91qel1eo ILOG CPLEX 9 0 GETTING STARTED 145 READING A PROBLEM FROM A FILE EXAMPLE LPEX2 C 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 n CPXgeterrorstring env status errmsg fprintf stderr s errmsg return status END main This simple routine frees up the pointer ptr and sets
125. l Modeling by Columns Function populatebycolumn can be viewed as the transpose of populatebyrow While for simple examples like this one population by rows may seem the most straightforward and natural approach there are some models where modeling by column is a more natural or more efficient approach When modeling by columns range objects are created with their lower and upper bound only No expression is given which is impossible since the variables are not yet created Similarly the objective function is created with only its intended optimization sense and without any expression Next the variables are created and installed in the already existing ranges and objective a r E e ie c o 1 N bo ouy2a 1199u09 The description of how the newly created variables are to be installed in the ranges and objective is by means of column expressions which are represented by the class IloNumColumn Column expressions consist of objects of class 11oAddNumVar linked together with operator These 110AddNumVar objects are created using operator of the classes I1o00bjective and IloRange They define how to install a new variable to the invoking objective or range objects For example obj 1 0 creates an IloAddNumVar capable of adding a new modeling variable with a linear coefficient of 1 0 to the expression in ob j Column expressions can be built in loops using operator Column expressions ob
126. l perturbed problem 2s pre Binary format for presolved problem qp Quadratic coefficient matrix file j rew MPS format problem with generic names 5 sav Binary matrix and basis file ni sos Special ordered sets file tre Branch and bound treesave file txt Text solution file vec Vector solution format file File type The BAS format is used for storing basis information and is introduced in Writing Basis Files on page 52 See also Reading Basis Files on page 55 The LP format was discussed in Using the LP Format on page 37 Using this format is explained in Writing LP Files on page 51 and Reading LP Files on page 54 The MPS format is covered in Reading MPS Files on page 55 Reminder All these file formats are documented in more detail in the reference manual ILOG CPLEX File Formats Writing LP Files When you enter the write command the following message appears Name of file to write Enter the problem name example and ILOG CPLEX will ask you to select from a list of options For this example choose LP ILOG CPLEX displays a confirmation message like this ILOG CPLEX 9 0 GETTING STARTED 51 WRITING PROBLEM AND SOLUTION FILES 52 Problem written to file example If you would like to save the file with a different name you can simply use the write command with the new file name as an argument Try this using the name example2 This time you can avoid intermediate prompts by specifying an LP problem typ
127. m then concludes by printing the values that have been obtained in the previous steps and terminates after calling cplex end to free the memory used by the model object the catch method of IloException provides screen output in case of any error conditions along the way The remainder of the example source code is devoted to the details of populating the model object mentioned above and the following three sections provide details on how the methods work ILOG CPLEX 9 0 GETTING STARTED BUILDING AND SOLVING A SMALL LP MODEL IN JAVA Modeling by Rows The method populateByRow creates the model by adding the finished constraints and objective function to the active model one by one It does so by first creating the variables with the method cplex numVarArray Then the minimization objective function is created and added to the active model with the method IloCplex addMinimize The expression that defines the objective function is created by a method IloCplex scalProd that forms a scalar product using an array of objective coefficients times the array of variables Finally each of the two constraints of the model are created and added to the active model with the method 11oCplex addLe For building the constraint expression the methods IloCplex sumand IloCplex prod are used as a contrast to the approach used in constructing the objective function Modeling by Columns While for many examples population by rows may seem most
128. mand ILOG CPLEX 9 0 GETTING STARTED READING A PROBLEM FROM A FILE EXAMPLE LPEX2 C lpex2 example mps d reads the file example mps and solves the problem with the dual simplex optimizer To illustrate the ease of reading a problem the example uses the routine CPXreadcopyprob This routine detects the type of the file reads the file and copies the data into the ILOG CPLEX problem object that is created with a call to CPXcreateprob The user need not be concerned with the memory management of the data Memory management is handled transparently by CPXreadcopyprob After calling CPXopenCPLEX and turning on the screen indicator by setting the CPX PARAM SCRIND parameter to CPX ON the example creates an empty problem object with a call to CPXcreateprob This call returns a pointer 1p to the new problem object Then the data is read in by the routine CPXreadcopyprob After the data is copied the appropriate optimization routine is called based on the command line argument After optimization the status of the solution is determined by a call to CPXget stat The cases of infeasibility or unboundedness in the model are handled in a simple fashion here a more complex application program might treat these cases in more detail With these two cases out of the way the program then calls CPXsolninfo to determine the nature of the solution Once it has been determined that a solution in fact exists then a call to CPXgetobjval is ma
129. mation dual price and reduced cost information as well as other detailed information about the solution can be viewed using the DISPLAY command after a solution is generated Summary The syntax for the help command is help command name ILOG CPLEX 9 0 GETTING STARTED 35 e r O E D 1do eAnoeje1u AOZIWI ENTERING A PROBLEM Entering a Problem 36 Most users with larger problems enter problems by reading data from formatted files That practice is explained in Reading Problem Files on page 53 For now you will enter a smaller problem from the keyboard by using the enter command The process is outlined step by step in these topics Entering the Example Problem on page 36 Using the LP Format on page 37 Entering Data on page 39 Entering the Example Problem As an example this manual uses the following problem Maximize X 2x 3x3 subject to X X x3 lt 20 X 3x5 X3 lt 30 with these bounds 0 x 40 0 lt X2 lt 00 0 lt X3 lt 00 This problem has three variables x x and x3 and two less than or equal to constraints The enter command is used to enter a new problem from the keyboard The procedure is almost as simple as typing the problem on a page At the CPLEX gt prompt type enter A prompt appears on the screen asking you to give a name to the problem that you are about to enter Naming a Problem The problem name may be anything that i
130. mbling the arrays in memory may be a useful enhancement for a production version Choose an Optimizer Once a problem object has been instantiated and populated it can be solved using one of the optimizers provided by the ILOG CPLEX Callable Library The choice of optimizer depends on the problem type LP and QP problems can be solved by e the primal simplex optimizer e the dual simplex optimizer and e the barrier optimizer LP problems can also be solved by e the sifting optimizer and e the concurrent optimizer LP problems with a substantial network can also be solved by a special network optimizer If the problem includes integer variables branch amp cut must be used There are also many different possible parameter settings for each optimizer The default values will usually be the best for linear programs Integer programming problems are more sensitive to specific settings so additional experimentation will often be useful Choosing the best way to solve the problem can dramatically improve performance For more information refer to the sections about tuning LP performance and trouble shooting MIP performance in the ILOG CPLEX User s Manual Observe Good Programming Practices Using good programming practices will save development time and make the program easier to understand and modify A list of good programming practices is provided in the ILOG CPLEX User s Manual Debug Your Program Your prog
131. minimize or maximize on the same line as the objective function but you must separate them by at least one space Variable Names In the example the variables are named simply x1 x2 x3 but you can give your variables more meaningful names such as cars or gallons The only limitations on variable names in LP format are that the names must be no more than 255 characters long and use only the alphanumeric characters a z A Z 0 9 and certain symbols 96 amp 2 9 Any line with more than 510 characters is truncated A variable name cannot begin with a number or combination that cannot be used the letter e or 1 a period and there is one character E alone or followed by a number or another e since this notation is reserved for exponents Thus a variable cannot be named e24 nor e9cats nor eels nor any other name with this pattern This restriction applies only to problems entered in LP format ILOG CPLEX 9 0 GETTING STARTED 37 e r O E D JOZIWNdO 8A1 9e19 U ENTERING A PROBLEM 38 Constraints Once you have entered the objective function you can move on to the constraints However before you start entering the constraints you must indicate that the subsequent lines are constraints by typing subject to or st These terms can be placed alone on a line or on the same line as the first constraint if separated by at least one space Now you can type in the constraints in the follow
132. nd display solution variables In response the list of variable names with the solution value for each variable is displayed like this Variable Name Solution Value x1 40 000000 x2 17 500000 x3 42 500000 To view the slack values of each constraint enter the command display solution slacks ILOG CPLEX 9 0 GETTING STARTED PERFORMING SENSITIVITY ANALYSIS The resulting message indicates that for this problem the slack variables are all zero All slacks in the range 1 2 are 0 To view the dual values sometimes called shadow prices for each constraint enter the command display solution dual The list of constraint names with the solution value for each constraint appears like this Constraint Name Dual Price cl 2 750000 c2 0 250000 Summary Display solution characteristics by entering a command with the syntax display solution identifier e r O E D JOZIWNdO 8A1 9e19 U Performing Sensitivity Analysis Sensitivity analysis of the objective function and right hand side provides meaningful insight about ways in which the optimal solution of a problem changes in response to small changes in these parts of the problem data Sensitivity analysis can be performed on the following objective function right hand side values bounds To view the sensitivity analysis of the objective function enter the command display sensitivity obj For our example ILOG CPLEX displays the f
133. nds with their descriptions appears on the screen like this add add constraints to problem baropt Solve using barrier algorithm change change the problem display display problem solution or parameter settings enter enter a new problem help provide information on CPLEX commands mipopt Solve a mixed integer program netopt solve the problem using network method optimize Solve the problem primopt Solve using the primal method quit leave CPLEX read read problem or basis information from a file set set parameters tranopt Solve using the dual method write write problem or solution info to a file xecute execute a command from the operating system Enter enough characters to uniquely identify commands amp options Commands can be entered partially CPLEX will prompt you for further information or as a whole To find out more about a specific command type help followed by the name of that command For example to learn more about the primopt command type help primopt Typing the full name is unnecessary Alternatively you can try hp The following message appears to tell you more about the use and syntax of the primopt command The PRIMOPT command solves the current problem using a primal simplex method or crosses over to a basic solution if a barrier solution exists Syntax PRIMOPT A problem must exist in memory from using either the ENTER or READ command in order to use the PRIMOPT command Sensitivity infor
134. nformation After solving the model by calling the method solve the results are accessed in the same way as in ilolpexl cpp with the exception of basis information for the variables It is important to understand that not all optimizer options compute basis information and thus it cannot be queried in all cases In particular basis information is not available when the ILOG CPLEX 9 0 GETTING STARTED READING A PROBLEM FROM A FILE EXAMPLE ILOLPEX2 CPP model is solved using the barrier optimizer IloCplex Barrier without crossover parameter I1oCplex BarCrossAlg set to IloCplex NoAlg Querying Quality Measures Finally the program prints the maximum primal infeasibility or bound violation of the solution To cope with the finite precision of the numerical computations done on the computer IloCplex allows some tolerances by which for instance optimality conditions may be violated A long list of other quality measures is available Complete Program The complete program follows You can also view it online in the file ilolpex2 cpp rl m D SSS ASCH en File examples src ilolpex2 cpp Version 9 0 AAA CR Copyright C 1999 2003 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products z Life a N a ee a uu IT 053 Dp ilolpex2 cpp Reading in and optimizing a problem h ek S g To run this
135. ns that can be used to build the model is populatebynonzero It creates objects for the objective and the ranges without expressions and variables without columns Then methods 11o00bjective setCoef and IloRange setCoef are used to set individual nonzero values in the expression of the objective and the range constraints As usual the objective and ranges must be added to the model Complete Program The complete program follows You can also view it online in the file ilolpex1 cpp p Ss SS pS A E a S Xo File examples src ilolpexl cpp Version 9 0 Ju SERE ARRE REA RN A RS A EL ARSS Copyright C 1999 2003 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products RR M C C C C EE V ilolpexl cpp Entering and optimizing a problem Demonstrates different methods for creating a problem The user has to choose the method on the command line PE ilolpexl r generates the problem by adding rows ilolpexl c generates the problem by adding columns yh ilolpexl n generates the problem by adding a list of coefficients finclude lt ilcplex ilocplex h gt ILOG CPLEX 9 0 GETTING STARTED BUILDING AND SoLviNG A SMALL LP MODEL IN C ILOSTLBEGIN static void usage const char progname populatebyrow IloModel model IloNumVarArray var IloRangeArray con populatebycolumn IloModel model Il
136. nsult the ILOG License Manager User s Guide and Reference for further guidance For Windows users if the program has trouble locating cplex90 d11 or ILOG CPLEX d11 make sure the DLL is stored either in the current directory or in a directory listed in your PATH environment variable o 1 gt Q O U E m x The UNIX Makefile or Windows project file contains useful information regarding recommended compiler flags and other settings for compilation and linking Compiling and Linking Your Own Applications The source files for the examples and the makefiles provide guidance for how your own application can call ILOG CPLEX The following chapters give more specific information on the necessary header files for compilation and how to link ILOG CPLEX and Concert Technology libraries into your application Chapter 3 Concert Technology Tutorial for C Users contains information and platform specific instructions for compiling and linking the Concert Technology Library for C users Chapter 4 Concert Technology Tutorial for Java Users contains information and platform specific instructions for compiling and linking the Concert Technology Library for Java users Chapter 5 Concert Technology Tutorial for NET Users offers an example of a C NET application Chapter 6 Callable Library Tutorial contains information and platform specific instructions for compiling and linking the Callable Library ILOG CPL
137. nt name of constraint c3 New name of constraint new3 The constraint c3 now has name new3 or The name of the constraint has been changed The problem can be checked with a display command for example display problem constraints new3 to confirm that the change was made This same technique can also be used to change the name of a variable Changing Sense Next change the sense of the new3 constraint from gt to lt using the sense option of the change command At the CPLEX gt prompt type change sense ILOG CPLEX 9 0 GETTING STARTED 59 CHANGING A PROBLEM 60 ILOG CPLEX prompts you to specify a constraint There are two ways of specifying this constraint if you know the name for example new3 you can enter the name if you do not know the name you can specify the number of the constraint In this example the number is 3 for the new3 constraint Try the first method and type Change sense of which constraint new3 Sense of constraint new3 is ILOG CPLEX tells you the current sense of the selected constraint All that is left now is to enter the new sense which can be entered as or You can also type simply lt interpreted as X or gt interpreted as gt The letters 1 g and e are also interpreted as lt gt and respectively New sense lt or gt or z lt Sense of constraint new3 changed to lt The sense of the constraint has been chan
138. o the comment Step 7 in the file and add these lines to create a method that tells a user how to invoke this application internal static void Usage System Console WriteLine usage LPexl option options r build model row by row options c build model column by column options n build model nonzero by nonzero System Console WriteLine System Console WriteLine System Console WriteLine Y v 3 8 95 o omy 3 Z ma E gt c5 0 o 25 n Q lt Add a command evaluator Go to the comment Step 8 in the file and add these lines to create a switch statement that evaluates the command that a user of your application might enter switch args 0 ToCharArray 1 mo case PopulateByRow cplex var rng break case c PopulateByColumn cplex var rng break case n PopulateByNonzero cplex var rng break default Usage return Solve After you have declared the decision variables and added the constraints and objective function to the model your application is ready to search for a solution Search for a solution Go to Step 9 in the file and add this line to make your application search for a solution if cplex Solve ILOG CPLEX 9 0 GETTING STARTED 113 SOLVE Display the solution Go to the comment Step 10 in the file and add these lines to enable your application to display any solution found in Step 9 double x
139. oNumVarArray var IloRangeArray con populatebynonzero IloModel model IloNumVarArray var IloRangeArray con int main int argc char argv IloEnv env try IloModel model env if argo 2 argv 1 0 LI strchr rcn argv 1 1 NULL A usage argv 0 throw 1 IloNumVarArray var env IloRangeArray con env 2 ao 053 switch il 1 5 9 case rv o ok a populatebyrow model var con 9 break 9 S case c populatebycolumn model var con c e break o Q case oy 2 2 lt populatebynonzero model var con break 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 lt lt Values lt lt vals lt lt endl cplex getSlacks vals con env out lt lt Slacks lt lt vals lt lt endl ILOG CPLEX 9 0 GETTING STARTED 77 BUILDING AND SOLVING A SMALL LP MODEL cplex getDuals vals con env out lt lt Duals lt lt cplex getReducedCosts vals var env out lt lt Reduced Costs Y lt lt cplex exportModel 1lpex1 1p catc
140. of other commands Commands can be carried out incrementally or all in one line from the CPLEX gt prompt Whenever a parameter 1s set to a new value ILOG CPLEX inserts a comment in the log file that indicates the new value Setting a Parameter To see the parameters that can be changed type set The parameters that can be changed are displayed with a prompt like this Available Parameters advance set indicator for advanced starting information barrier set parameters for barrier optimization clocktype set type of clock used to measure time defaults set all parameter values to defaults logfile set file to which results are printed lpmethod set method for linear optimization mip set parameters for mixed integer optimization network set parameters for network optimizations output set extent and destinations of outputs preprocessing set parameters for preprocessing qpmethod set method for quadratic optimization read set problem read parameters sifting set parameters for sifting optimization simplex set parameters for primal and dual simplex optimizations threads set default parallel thread count timelimit set time limit in seconds workdir set directory for working files workmem set memory available for working storage in megabytes Parameter to set If you press the return key without entering a parameter name the following message is displayed No parameters changed 56 ILOG CPLEX 9 0 GETTING STARTED
141. ollowing ranges for sensitivity analysis of the objective function OBJ Sensitivity Ranges Variable Name Reduced Cost Down Current Up x1 3 5000 2 5000 1 0000 infinity x2 zero 5 0000 2 0000 3 0000 x3 zero 2 0000 3 0000 infinity ILOG CPLEX displays each variable its reduced cost and the range over which its objective function coefficient can vary without forcing a change in the optimal basis The current value of each objective coefficient is also displayed for reference Objective function ILOG CPLEX 9 0 GETTING STARTED 49 WRITING PROBLEM AND SOLUTION FILES sensitivity analysis is useful to determine how sensitive the optimal solution is to the cost or profit associated with each variable Similarly to view sensitivity analysis of the right hand side type the command display sensitivity rhs For our example ILOG CPLEX displays the following ranges for sensitivity analysis of the right hand side RHS RHS Sensitivity Ranges Constraint Name Dual Price Down Current Up cl 2 7500 36 6667 20 0000 infinity c2 0 2500 140 0000 30 0000 100 0000 ILOG CPLEX displays each constraint its dual price and a range over which its right hand side coefficient can vary without changing the optimal basis The current value of each RHS coefficient is also displayed for reference Right hand side sensitivity information is useful for determining how sensitive the optimal solution and resource values are to the availability of those re
142. ols store the current number of rows and columns respectively cur numcols CPXgetnumcols env 1p cur numrows CPXgetnumrows env lp Retrieve basis if one is available if solntype CPX BASIC SOLN cstat 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 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 n goto TERMINATE status CPXgetx env lp x 0 cur numcols 1 if status fprintf stderr Failed to obtain primal solution in goto TERMINATE Write out the solution for j 0 j lt cur numcols j printf Column d Value 17 109 j x j if cstat NULL switch cstat j case CPX AT LOWER ILOG CPLEX 9 0 GETTING STARTED READING A PROBLEM FROM A FILE EXAMPLE LPEX2 C 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 brea
143. om a file Adding Interactively Type the add command then enter the new constraint on the blank line After validating the constraint the cursor moves to the next line You are in an environment identical to that of the enter command after having issued subject to At this point you may continue to ILOG CPLEX 9 0 GETTING STARTED 57 CHANGING A PROBLEM add constraints or you may type bounds and enter new bounds for the problem For the present example type end to exit the add command Your session should look like this add Enter new constraints and bounds end terminates xl 2x2 3x3 gt 50 end Problem addition successful When the problem is displayed again the new constraint appears like this display problem all Maximize obj x1 2 x2 3 x3 Subject To Gus een x2 x3 20 C214 XT SE RIZO x3 lt 30 C3 x1 2 x2 3 x3 gt 50 Bounds 0 lt x1 lt 40 All other variables are gt 0 end Adding from a File Alternatively you may read in new constraints and bounds from a file If you enter a file name after the add command ILOG CPLEX will read a file matching that name The file contents must comply with standard ILOG CPLEX LP format ILOG CPLEX does not prompt for a file name if none is entered Without a file name interactive entry is assumed Summary The general syntax for the add command is add or add filename Changing a Problem 58 The enter and add commands allow
144. on endl env end g et le gt O Oo c o D L2 6bo ouy23 Wadu0y Note The construction of the environment comes before the try catch clause In case of an exception env end must still be called To protect against failure during the construction of the environment another t xy catch clause may be added If code other than Concert Technology code is used in the part of that sample denoted by all other exceptions will be caught with the statement catch Doing so is good practice as it assures that no exception is unhandled Building and Solving a Small LP Model in C A complete example of building and solving a small LP model can now be presented This example demonstrates General Structure of an ILOG CPLEX Concert Technology Application on page 74 ILOG CPLEX 9 0 GETTING STARTED 73 BUILDING AND SOLVING A SMALL LP MODEL IN C 74 Modeling by Rows on page 75 Modeling by Columns on page 75 Modeling by Nonzero Elements on page 76 Example ilolpex1 cpp which is one of the example programs in the standard ILOG CPLEX distribution is an extension of the example presented in Introducing ILOG CPLEX It shows three different ways of creating an ILOG Concert Technology LP model how to solve it using 11oCplex and how to access the solution Here is the problem that the example optimizes Maximize X 2x 3x3 subject to X X X3 lt S 20 X
145. ond to the variables var and range constraints rng respectively the methods will write to var 0 and rng 0 an array of all the variables and constraints in the model for later access After the model has been created in the cplex object it is ready to be solved by calling cplex solve The solution log will be output to the screen this is because I loCplex prints all logging information to the OutputStream cplex out which by default is initialized to System out You can change this by calling the method cplex setOut In particular you can turn off logging by setting the output stream to nu11 that is by calling cplex setOut null Similarly 11o0Cplex issues warning messages to cplex warning and cplex setWarning can be used to change or turn off the OutputStream that will be used If the solve method finds a solution for the active model it returns true The next section of code accesses the solution The method cplex getValues var 0 returns an array of primal solution values for all the variables This array is stored as double x The values in x are ordered such that x 3 is the primal solution value for variable var 0 j Similarly the reduced costs duals and slack values are queried and stored in arrays dj pi and slack respectively Finally the solution status of the active model and the objective value of the solution are queried with the methods 11oCplex getStatus and IloCplex getObjValue respectively The progra
146. one was found if cplex Solve double x cplex GetValues var 0 double dj cplex GetReducedCosts var 0 double pi cplex GetDuals rng 0 double slack cplex GetSlacks rng 0 cplex Output WriteLine Solution status cplex GetStatus cplex Output WriteLine Solution value cplex ObjValue int ncols cplex Ncols for ant j 0 j lt nicols 3 cplex Output WriteLine Column j Value a x j Reduced cost dj j int nrows cplex Nrows for int i 0 i lt nrows i cplex Output WriteLine Row Sow Slack slack i Pi s pilil cplex End catch ILOG CONCERT Exception e System Console WriteLine Concert exception W e caught The following methods all populate the problem with data for the following linear program Maximize 116 ILOG CPLEX 9 0 GETTING STARTED EXAMPLE LPEX1 CS xl 2 x2 3 x3 Subject To xl x2 x3 lt 20 xl 3 x2 x3 lt 30 m Bounds Q 5 0 lt x1 lt 40 Oo 9 End 3 T using the IMPModeler API So c5 internal static void PopulateByRow IMPModeler model o o O INumVar var o O IRange rng double lb 0 0 0 0 0 0 double ub 40 0 System Double MaxValue System Double MaxValue INumVar x model NumVarArray 3 lb ub var 0 x double objvals
147. p routines CPXwriteprob can be called at any time after CPXcreateprob has created the 1p pointer The label TERMINATE is used as a place for the program to exit if any type of failure occurs or if everything succeeds In either case the problem object represented by 1p is released by the call to CPX reeprob and any memory allocated for solution arrays is freed The application then calls CPXcloseCPLEX it tells ILOG CPLEX that all calls to the Callable Library are complete If an error occurs when this routine is called then a call to CPXgeterrorstringis needed to determine the error message since CPXcloseCPLEX causes no screen output Complete Program The complete program follows You can also view it online in the file 1pex1 c Jen taces toan ue coc eeu erii eon LUE cane e AU AEE ero erede en uL opens i E File examples src lpexl c A Version 9 0 Ay RAE REC Ep Copyright C 1997 2003 by ILOG All Rights Reserved EL Permission is expressly granted to use this example in the course of developing applications that use ILOG products YSL oe et eS ee at ache Ann eine ES tn ene E a es lpexl c Entering and optimizing a problem Demonstrates different methods for creating a problem The user has to choose the method on the command line lpexl r generates the problem by adding rows lpexl c generates the problem by adding columns lpexl n generates the problem by adding a list
148. ractive Optimizer and 36 1pex1 c 128 lpexl cs 109 LPex1 java 97 standard notation for 10 problem object creating 123 modifying 123 problem types solved by CPLEX 10 Q QCP description 10 QP applicable algorithms 81 description 10 solving pure 81 GETTING STARTED Quadratic Programming QP problem see QP quit Interactive Optimizer command 63 quitting ILOG CPLEX 63 Interactive Optimizer 63 R range constraint 75 adding to a model 96 read Interactive Optimizer command 53 54 55 avoiding prompts for options 54 basis files and 55 file type options 53 syntax 55 reading file format for 53 LP files 54 model from file 80 82 MPS files 55 problem files 53 138 reduced cost accessing in Interactive Optimizer 48 accessing in Java 97 removing bounds 60 representing optimization problem 74 re solving 47 RHS see right hand side right hand side RHS changing coefficient 61 sensitivity analysis 50 154 root LP solving 81 S SAV file format 148 saving problem files 50 solution files 50 scalProd Java method 99 sense changing in Interactive Optimizer 59 ILOG CPLEX 9 0 INDEX sensitivity analysis performing 49 153 set Interactive Optimizer command 56 advance 47 available parameters 56 defaults 57 logfile 47 simplex 46 basisinterval 52 syntax 57 setOut Concert method 98 setRootAlgorithm method IloCplex class 82 setting parameters 56 88 parameters to default 57 see also changing setWarning Conc
149. ram may not run properly the first time you build it Learn to use a symbolic debugger and other widely available tools that support the creation of error free code Use ILOG CPLEX 9 0 GETTING STARTED BUILDING AND SOLVING A SMALL LP MODEL IN C the list of debugging tips provided in the ILOG CPLEX User s Manual to find and correct problems in your Callable Library application Test Your Application Once an application works correctly it still may have errors or features that inhibit execution speed To get the most out of your application be sure to test its performance as well as its correctness Again the ILOG CPLEX Interactive Optimizer can help Since the Interactive Optimizer uses the same routines as the Callable Library it should take the same amount of time to solve a problem as a Callable Library application Use the CPXwriteprob routine with the SAV format to create a binary representation of the problem object then read it in and solve it with the Interactive Optimizer If the application sets optimization parameters use the same settings with the Interactive Optimizer If your application takes significantly longer than the Interactive Optimizer performance within your application can probably be improved In such a case possible performance inhibitors include fragmentation of memory unnecessary compiler and linker options and coding approaches that slow the program without causing it to give incorrect results U
150. reate 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 case r status populatebyrow env lp break Yar case c status populatebycolumn env lp break case n ILOG CPLEX 9 0 GETTING STARTED 131 g r O 2 Aseaqiy aqe BUILDING AND SoLviNG A SMALL LP MODEL IN C 132 status populatebynonzero env 1p break if status fprintf stderr Failed to populate problem Wn goto TERMINATE Optimize the problem and obtain solution status CPXlpopt env lp if status Y 1 fprintf stderr Failed to optimize LP n goto TERMINATE 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 lp x double malloc cur numcols sizeof double slack double malloc cur numrows sizeof double dj double malloc cur numcols sizeof double pi double malloc cur numrows sizeof double if x NULL slack NULL dj NULL pi NULL EE status CPXERR NO MEMORY fprintf stderr Could not alloc
151. reateprob It is destroyed when you call CPX reeprob ILOG CPLEX allows you to create more than one problem object although typical applications will use only one Each problem object is referenced by a pointer returned by CPXcreateprob and represents one specific problem instance All Callable Library functions except parameter setting functions and message handling functions require a pointer to a problem object Populating the Problem Object The problem object instantiated by CPXcreateprob represents an empty problem that contains no data it has zero constraints zero variables and an empty constraint matrix This empty problem object must be populated with data This step can be carried out in several ways The problem object can be populated by assembling arrays of data and then calling CPXcopylp to copy the data into the problem object For example see Building and Solving a Small LP Model in C on page 127 Alternatively you can populate the problem object by sequences of calls to the routines CPXnewcols CPXnewrows CPXaddcols CPXaddrows and CPXchgcoeflist these routines may be called in any order that is convenient For example see Adding Rows to a Problem Example lpex3 c on page 147 If the data already exist in a file using MPS format or LP format you can use CPXreadcopyprob to read the file and copy the data into the problem object For example see Reading a Problem from a File Example lpex2 c on page 138
152. rface works the same way and provides the same facilities on all platforms ILOG CPLEX 9 0 GETTING STARTED 11 WHAT 12 Is ILOG CPLEX Installation Requirements If you have not yet installed ILOG CPLEX on your platform please consult Chapter 1 Setting Up ILOG CPLEX It contains instructions for installing ILOG CPLEX Optimizer Options This manual explains how to use the LP algorithms that are part of ILOG CPLEX The QP QCP and MIP problem types are based on the LP concepts discussed here and the extensions to build and solve such problems are explained in the LOG CPLEX User s Manual Some users may not have access to all algorithms Such users should consult their ILOG account manager or the ILOG support web site to determine to which algorithms they have access Default settings will result in a call to an optimizer that is appropriate to the class of problem you are solving However you may wish to choose a different optimizer for special purposes An LP or QP problem can be solved using any of the following CPLEX optimizers Dual Simplex Primal Simplex Barrier and perhaps also the Network Optimizer if the problem contains an extractable network substructure Pure network models are all solved by the Network Optimizer QCP models are all solved the Barrier optimizer MIP models are all solved by the Mixed Integer Optimizer which in turn may invoke any of the LP or QP optimizers in the course of its computation
153. ribution Verifying Installation on UNIX On a UNIX system go to the subdirectory examples machine libformat that matches your particular platform and in it you will find a file named Makefile Execute one of the examples for instance 1pex1 c by doing make lpexl lpex1 r fthis example takes one argument either r c or n If your interest is in running one of the C examples try make ilolpexl ilolpex1 r this is the same as 1pex1 and takes the same arguments If your interest is in running one of the Java examples try make LPexl class java Djava library path bin platform classpath lib cplex jar LPexl r ILOG CPLEX 9 0 GETTING STARTED USING THE COMPONENT LIBRARIES Any of these examples should return an optimal objective function value of 202 5 Verifying Installation on Windows On a Windows machine you can follow a similar process using the facilities of your compiler interface to compile and then run any of the examples A project file for each example is provided in a format for Microsoft Visual Studio 6 and Visual Studio NET In Case of Errors If an error occurs during the make or compile step then check that you are able to access the compiler and the necessary linker loader files and system libraries If an error occurs on the next step when executing the program created by make then the nature of the error message will guide your actions If the problem is in licensing co
154. rk flow The example solves this problem in two steps 1 The ILOG CPLEX Network Optimizer is used to solve Minimize c x subject to Hx d I lt x lt u 2 The constraints Ax b are added to the problem and the dual simplex optimizer is used to solve the new problem starting at the optimal basis of the simpler network problem The data for this problem consists of the network portion using variable names beginning with the letter A and the complicating constraints using variable names beginning with the letter A The example first calls CPXopenCPLEX to create the environment and then turns on the ILOG CPLEX screen indicator CPX PARAM SCRIND Next it sets the simplex display level CPX_PARAM_SIMDISPLAY to 2 to indicate iteration by iteration output so that the g r O 2 1e1q17 91qel1eo ILOG CPLEX 9 0 GETTING STARTED 147 ADDING ROWS TO A PROBLEM EXAMPLE LPEX3 C 148 progress of each iteration of the hybrid optimizer can be observed Setting this parameter to 2 is not generally recommended the example does so only for illustrative purposes The example creates a problem object by a call to CPXcreateprob Then the network data is copied via a call to CPXcopylp After the network data is copied the parameter CPX PARAM LPMETHOD is set to CPX_ALG_NET and the routine CPX1popt is called to solve the network part of the optimization problem using the network optimizer The objective value of this problem is retri
155. rning Concert method 98 Windows building Callable Library applications 121 dynamic loading 122 installing CPLEX 26 Microsoft Visual C compiler 122 Microsoft Visual C IDE 121 testing CPLEX in Concert Technology 67 verifying installation 29 write Interactive Optimizer command 50 51 file type options 51 syntax 53 writing basis files 52 file format for 51 LP files 51 model to file 80 problem files 50 solution files 50 X xecute Interactive Optimizer command 63 syntax 63 xxx file format 52 GETTING STARTED
156. roblem starting from the optimal basis of the network problem The dual simplex method is highly effective in such a case because this basis remains dual feasible after the slacks artificial variables of the added constraints are initialized as basic Notice that the 0 values in the data are omitted in the example program ILOG CPLEX makes extensive use of sparse matrix methods and although ILOG CPLEX correctly handles any explicit zero coefficients given to it most programs solving models of more than modest size benefit in terms of both storage space and speed if the natural sparsity of the model is exploited from the very start Before the model is solved the network optimizer is selected by setting the RootAlg parameter to the value IloCplex Network as shown in example ilolpex2 cpp The ILOG CPLEX 9 0 GETTING STARTED 87 g r e ie c o o N bo ouy2a W e 70 MODIFYING AN OPTIMIZATION PROBLEM EXAMPLE ILOLPEX3 CPP 88 simplex display parameter IloCplex SimDisplay is set so that the simplex algorithm issues logging information as it executes Setting ILOG CPLEX Parameters IloCplex provides a variety of parameters that allow you to control the solution process They can be categorized as Boolean integer numerical and string parameters and are represented by the enumeration types IloCplex BoolParam IloCplex IntParam IloCplex NumParam and I1oCplex StringParam respec
157. ros on page 100 S 9 qa Example LPex1 java is an extension of the example presented in Entering the Example 2 3 Problem on page 36 2 E gt o Maximize X 2x 3x3 93 vs subject to X X X3 lt 20 e X 3x x3 lt 30 with these bounds 0 lt x lt 40 0 lt X2 lt 00 0 lt X3 lt 00 After an initial check that a valid option string was provided as a calling argument the program begins by enclosing all executable statements that follow in a try catch pair of ILOG CPLEX 9 0 GETTING STARTED 97 BUILDING AND SOLVING A SMALL LP MODEL IN JAVA 98 statements In case of an error ILOG CPLEX Concert Technology will throw an exception of type IloException which the catch statement then processes In this simple example an exception triggers the printing of a line stating Concert exception e caught where e is the specific exception First create the model object cp1ex by executing the following statement IloCplex cplex new IloCplex At this point the cplex object represents an empty model that is a model with no variables constraints or other content The model is then populated in one of several ways depending on the command line argument The possible choices are implemented in the methods e populateByRow e populateByColumn e populateByNonzero All these methods pass the same three arguments The first argument is the cplex object to be populated The second and third arguments corresp
158. s allowed as a file name in your operating system If you decide that you do not want to enter a new problem just press the lt return gt key without typing anything The CPLEX gt prompt will reappear without causing any action The same can be done at any CPLEX gt prompt If you do not want to complete the command simply press the return key For now type in the name example at the prompt Enter name for problem example The following message appears Enter new problem end on a separate line terminates and the cursor is positioned on a blank line below it where you can enter the new problem ILOG CPLEX 9 0 GETTING STARTED ENTERING A PROBLEM You can also type the problem name directly after the ent ex command and avoid the intermediate prompt Summary The syntax for entering a problem is enter problem name Using the LP Format Entering a new problem is basically like typing it on a page but there are a few rules to remember These rules conform to the ILOG CPLEX LP file format and are documented in the reference manual JLOG CPLEX File Format tutorial The problem should be entered in the following 1 Objective Function 2 Constraints 3 Bounds Objective Function s LP format appears throughout this order Before entering the objective function you must state whether the problem is a minimization or maximization For this example you type maximize xl 2x2 3x3 You may type
159. s for creating a problem The user has to choose the method on the command line LPexl r generates the problem by adding constraints LPexl c generates the problem by adding variables LPexl n generates the problem by adding expressions using ILOG CONCERT using ILOG CPLEX public class LPexl internal static void Usage System Console WriteLine usage LPexl option System Console WriteLine options r build model row by row System Console WriteLine options c build model column by column System Console WriteLine options n build model nonzero by nonzero public static void Main string args if args Length 1 args 0 ToCharArray Q0 0 Usage return try Create the modeler solver object Cplex cplex new Cplex INumVar var new INumVar 1 IRange rng new IRange 1 Evaluate command line option and call appropriate populate method The created ranges and variables are returned as element 0 of arrays var and rng switch args 0 ToCharArray 1 ILOG CPLEX 9 0 GETTING STARTED 115 EXAMPLE LPEX1 CS case r PopulateByRow cplex var rng break case c PopulateByColumn cplex var rng break case n PopulateByNonzero cplex var rng break default Usage return write model to file cplex ExportModel lpex1l 1p solve the model and display the solution if
160. satisfiedLinkError 93 error handling compiler 67 license manager 68 linker 68 programming errors 72 runtime errors 73 testing installation 29 67 example adding rows to a problem 147 entering a problem 36 entering and optimizing a problem in C 127 entering and optimizing a problem in C 109 ilolpex2 cpp 82 ilolpex3 cpp 86 lpex1 c 127 lpexl cs 109 lpex2 c 138 lpex3 c 147 modifying an optimization problem 86 reading a problem file 138 reading a problem from a file 82 running Callable Library 121 running Component Libraries 28 running Concert Technology 67 running from standard distribution 121 solving a problem 45 exception handling 73 executing operating system commands 63 exportModel method GETTING STARTED IloCplex class 80 expression column 75 F False 96 feasible solution 96 file format read options 53 write options 51 file name extension 52 54 80 G getCplexStatus 97 getCplexStatus method IloCplex class 72 getDuals method IloCplex class 75 getObjValue method IloCplex class 72 getReducedCosts method IloCplex class 75 getSlacks method IloCplex class 75 getStatus 96 getStatus method IloCplex class 72 75 getValue method IloCplex class 72 getValues method IloCplex class 75 getting see accessing greater than equal to constraints add to a model 96 H handle class definition 69 empty handle 70 handling ILOG CPLEX 9 0 INDEX errors 72 126 exceptions 73 help In
161. se the Examples The ILOG CPLEX Callable Library is distributed with a variety of examples that illustrate the flexibility of the Callable Library The C source of all examples is provided in the standard distribution For explanations about the examples of quadratic programming problems QPs mixed integer programming problems MIPs and network flows see the ILOG CPLEX User s Manual Explanations of the following examples of LPs appear in this manual lpex1 c illustrates various ways of generating a problem object lpex2 c demonstrates how to read a problem from a file optimize it via a choice of several means and obtain the solution lpex3 c demonstrates how to add rows to a problem object and reoptimize It is a good idea to compile link and run all of the examples provided in the standard distribution Building and Solving a Small LP Model in C The example 1pex1 c shows you how to use problem modification routines from the ILOG CPLEX Callable Library in three different ways to build a model The application in the example takes a single command line argument that indicates whether to build the g r O 2 Keq 91qel1eo ILOG CPLEX 9 0 GETTING STARTED 127 BUILDING AND SOLVING A SMALL LP MODEL IN C 128 constraint matrix by rows columns or nonzeros After building the problem the application optimizes it and displays the solution Here is the problem that the example optimizes Maximize X 2x 3x3 sub
162. sources ILOG CPLEX can also display lower bound sensitivity ranges with the command display sensitivity lb and upper bound sensitivity with the command display sensitivity ub Summary Display sensitivity analysis characteristics by entering a command with the syntax display sensitivity identifier Writing Problem and Solution Files 50 The problem or its solution can be saved by using the write command This command writes the problem statement or a solution report to a file The tutorial example continues in the topics Selecting a Write File Format on page 51 Writing LP Files on page 51 Writing Basis Files on page 52 Using Path Names on page 52 ILOG CPLEX 9 0 GETTING STARTED WRITING PROBLEM AND SOLUTION FILES Selecting a Write File Format When you type the write command in the Interactive Optimizer ILOG CPLEX displays a menu of options and prompts you for a file format like this File Type Options bas INSERT format basis file bin Binary solution file dpe Binary format for dual perturbed problem dua MPS format of explicit dual of problem emb MPS format of embedded network iis Irreducibly inconsistent set LP format lp LP format problem file E min DIMACS min cost network flow format of embedded network 2 mps MPS format problem file 2 mst MIP start file net CPLEX network format of embedded network E ord Integer priority order file S O ppe Binary format for prima
163. splay problem names variables 2 3 ILOG CPLEX 9 0 GETTING STARTED 43 DISPLAYING A PROBLEM Displaying Constraints To view a single constraint within the matrix use the command and the constraint number For example type the following display problem constraints 2 The second constraint appears c2 xl 3 x2 4 x3 lt 30 Displaying the Objective Function When you want to display only the objective function you must enter its name obj by default or an index number of 0 display problem constraints Display which constraint name s 0 Maximize obje EL 72 HZ 3x3 Displaying Bounds To see only the bounds for the problem type the following command don t forget the hyphen display problem bounds The result is 0 lt x1 lt 40 All other variables are gt 0 Summary The general syntax of the display command is display option option2 identifier identifier2 Displaying a Histogram of NonZero Counts For large models it can sometimes be helpful to see summaries of nonzero counts of the columns or rows of the constraint matrix This kind of display is known as a histogram There are two commands for displaying histograms one for columns one for rows display problem histogram c display problem histogram r 44 ILOG CPLEX 9 0 GETTING STARTED SOLVING A PROBLEM For the small example in this tutorial the column histogram looks like this Column counts excluding fixed var
164. ssion in a loop which is what is typically needed in more complex applications Interface IloLinearNumExpr is an extension of I1oNumExpr and thus can be used anywhere an expression can be used As mentioned before expressions can be used to create constraints or an objective function for a model Here is how to create a minimization objective for the above expression IloObjective obj cplex minimize expr ILOG CPLEX 9 0 GETTING STARTED 95 THE ANATOMY OF AN ILOG CONCERT TECHNOLOGY APPLICATION 96 In addition to creating an objective IloCplex must be instructed to use it in the model it solves This is done by adding the objective to IloCplex via cplex add obj Every modeling object that is to be used in a model must be added to the IloCplex object The variables need not be explicitly added as they are treated implicitly when used in the expression of the objective More generally every modeling object that is referenced by another modeling object which itself has been added to 11oCplex is implicitly added to IloCplex as well There is a shortcut notation for creating and adding the objective to 11oCplex cplex addMinimize expr Since the objective is not otherwise accessed it does not need to be stored in the variable obj Adding constraints to the model is just as easy For example the constraint x 0 x 1 x 2 lt 20 0 can be added by calling cplex addle cplex sum cplex negative x 0 x 1 x 2
165. t env CPXopenCPLEX amp status If an error occurs the status value indicates the reason for T 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 env NULL char errmsg 1024 fprintf stderr Could not open CPLEX environment Nn CPXgeterrorstring env status errmsg fprintf stderr s errmsg goto TERMINATE Turn on output to the screen ILOG CPLEX 9 0 GETTING STARTED ADDING ROWS TO A PROBLEM EXAMPLE LPEX3 C Status CPXsetintparam env CPX PARAM SCRIND CPX ON if status fprintf stderr Failure to turn on screen indicator error d n status goto TERMINATE status CPXsetintparam env CPX PARAM SIMDISPLAY 2 if status fprintf stderr Failed to turn up simplex display level n goto TERMINATE Create the problem lp CPXcreateprob env amp status chvatal if lp NULL fprintf stderr Failed to create subproblemin status 1 goto TERMINATE Copy network part of problem status CPXcopylp env lp COLSORIG ROWSSUB CPX MIN Hcost Hrhs Hsense Hmatbeg Hmatcnt Hmatind Hmatval Hlb Hub NULL if status 4 fprintf stderr CPXcopylp failed n
166. t call ILOG CPLEX Building Callable Library Applications on Win32 Platforms Building an ILOG CPLEX application using Microsoft Visual C Integrated Development Environment or the Microsoft Visual C command line compiler are explained here Microsoft Visual C IDE To make an ILOG CPLEX Callable Library application using Visual C first create or open a project in the Visual C Integrated Development Environment IDE Project files are provided for each of the examples found in the directory examples msvc6 lt libformat gt and examples msvc6 lt libformat gt For details on the build process refer to the information file msvc html which is found in the top of the installed ILOG CPLEX directory structure Note The distributed application must be able to locate 1LOG CPLEX d11 at run time ILOG CPLEX 9 0 GETTING STARTED 121 g r O E 2 Aseaqiy aqe How ILOG CPLEX WORKS Microsoft Visual C Command Line Compiler If the Visual C command line compiler is used outside of the IDE the command should resemble the following example The example command assumes that the file cplex90 1ib is in the current directory with the source file 1pex1 c and that the line in the source file include lt ilcplex cplex h gt correctly points to the location of the include file or else has been modified to do so or that the directories containing these files have been added to the environment variables LIB and INCLUDE
167. t hand side of constraint 1 to be 25 0 a user could could enter the following but for this tutorial do not enter this now change rhs 1 25 0 Deleting Another option to the change command is delete This option is used to remove an entire constraint or a variable from a problem Return the problem to its original form by removing the constraint you added earlier Type change delete ILOG CPLEX 9 0 GETTING STARTED 61 CHANGING A PROBLEM ILOG CPLEX displays a list of delete options Delete Options constraints delete range of constraints variables delete range of variables equality delete range of equality constraints greater than delete range of greater than constraints less than delete range of less than constraints At the first prompt specify that you want to delete a constraint Deletion to make constraints At the next prompt enter a constraint name or number or a range as you did when you used the display command Since the constraint to be deleted is named new3 enter that name Delete which constraint s new3 Constraint 3 deleted Check to be sure that the correct range or number is specified when you perform this operation since constraints are permanently removed from the problem Indices of any constraints that appeared after a deleted constraint will be decremented to reflect the removal of that constraint The last message indicates that the operation is complete The problem can now be checked
168. t you to save your problem ILOG CPLEX 9 0 GETTING STARTED 63 QuiTTING ILOG CPLEX 64 ILOG CPLEX 9 0 GETTING STARTED Concert Technology Tutorial for C Users This tutorial shows you how to write C programs using CPLEX with Concert Technology In this chapter you will learn about 9 9 9 9 0 4 The Design of CPLEX in Concert Technology on page 66 Compiling and Linking ILOG CPLEX in Concert Technology Applications on page 67 The Anatomy of an ILOG Concert Technology Application on page 68 g r e e c o 1 N Building and Solving a Small LP Model in C on page 73 Writing and Reading Models and Files on page 80 Selecting an Optimizer on page 81 Reading a Problem from a File Example ilolpex2 cpp on page 82 Modifying and Reoptimizing on page 86 Modifying an Optimization Problem Example ilolpex3 cpp on page 86 ILOG CPLEX 9 0 GETTING STARTED 65 Bojouu 9 1192u02 THE DESIGN OF CPLEX IN CONCERT TECHNOLOGY The Design of CPLEX in Concert Technology 66 A clear understanding of C objects is fundamental to using ILOG Concert Technology with ILOG CPLEX to build and solve optimization models These objects can be divided into two categories 1 Modeling objects are used to define the optimization problem Generally an application creates multiple modeling objects to specify one optimization problem Those objects are grouped into an I1oModel object represent
169. teractive Optimizer command 34 syntax 35 histogram 44 ILM see ILOG License Manager IloAddNumVar class 75 IloAlgorithm Exception class 73 IloAlgorithm Status enumeration 75 IloColumn and method 100 IloCplex class add modeling object 96 addLe method 99 addMinimize method 99 Concert Technology 66 exportModel method 80 getCplexStatus method 72 getDuals method 75 getObjValue method 72 getReducedCosts method 75 getSlacks method 75 getStatus method 72 75 getValue method 72 getValues method 75 importModel method 80 82 Java 91 numVarArray method 99 prod method 99 scalProd method 99 setParam method 81 setRootAlgorithm method 82 solve method 72 74 82 86 solving with 71 sum method 99 IloCplex Algorithm enumeration 81 IloCplex BoolParam enumeration 88 IloCplex Exception class 73 IloCplex IntParam enumeration 88 IloCplex NumParam enumeration 88 IloCplex StringParam enumeration 88 IloEnv 68 IloEnv class 68 GETTING STARTED 161 INDEX end method 69 oException class 73 IloExpr class 71 IloExtractable class 69 ILOG License Manager ILM 28 ILOG LICENSE FILE environment variable 28 loLinearNumExpr 95 IloMinimize function 70 IloModel class add method 70 71 column method 100 extractable 69 numVar method 100 role in Concert 66 IloNumArray class 75 IloNumColumn class 75 IloNumExpr 95 IloNumExpr class 95 IloNumVar class 76 columns and 76 reading files and 80 role in Concert Technolog
170. teractive features of ILOG CPLEX there is a direct approach to this task from the Callable Library This section modifies the example 1pex1 c on page 127 to show how to perform sensitivity analysis with routines from the Callable Library To begin make a copy of 1pex1 c and edit this new source file Among the declarations for example immediately after the declaration for dj insert these additional declarations double lowerc NULL upperc NULL double lowerr NULL upperr NULL g r O Aseaqiy 91qel1eo ILOG CPLEX 9 0 GETTING STARTED 153 PERFORMING SENSITIVITY ANALYSIS At some point after the call to CPX1popt for example just before the call to CPXwriteprob perform sensitivity analysis on the objective function and on the right hand side coefficients by inserting this fragment of code upperc double malloc cur numcols sizeof double lowerc double malloc cur numcols sizeof double status CPXobjsa env lp 0 cur numcols 1 lowerc upperc If status f fprintf stderr Failed to obtain objective sensitivity n goto TERMINATE printf nObjective coefficient sensitivity n for j 0 j lt cur numcols j printf Column d Lower 10g Upper 10g n j lowerc 3 upperc j upperr double malloc cur_numrows sizeof double lowerr double malloc cur numrows sizeof double status CPXrhssa env lp 0 cur numrows 1
171. the Callable Library routines required The test may also uncover any flaws in procedure logic before you invest significant development effort Trying the ILOG CPLEX Interactive Optimizer is an easy way to determine the best optimization procedure and parameter settings Assemble the Data You must decide which approach to populating the problem object is best for your application Reading an MPS or LP file may reduce the coding effort but can increase the run time and disk space requirements of the program Building the problem in memory and then calling CPXcopylp avoids time consuming disk file reading Using the routines CPXnewcols CPXnewrows CPXaddcols CPXaddrows and CPXchgcoeflist can lead to modular code that may be more easily maintained than if you assemble all model data in one step Another consideration is that if the Callable Library application reads an MPS or LP formatted file usually another application is required to generate that file Particularly in the case of MPS files the data structures used to generate the file could almost certainly be used ILOG CPLEX 9 0 GETTING STARTED 125 z r O 2 Aseaqiy aqe CREATING A SUCCESSFUL CALLABLE LIBRARY APPLICATION 126 to build the problem defining arrays for CPXcopylp directly The result would be less coding and a faster more efficient application These observations suggest that formatted files may be useful when prototyping your application while asse
172. the simplex method where to begin the next optimization Basis files usually correspond to the result of some previous optimization and help to speed re optimization They are particularly helpful when you are dealing with very large problems if small changes are made to the problem data Writing Basis Files on page 52 showed you how to save a basis file for the example after it was optimized For this tutorial first read the example 1p file Then read this basis file by typing the following command read example bas The message of confirmation Basis example bas read indicates that the basis file was successfully read If the advanced basis indicator is on this basis will be used as a starting point for the next optimization and any new basis created during the session will be used for future optimizations If the basis changes during a session you can save it by using the write command Summary The general syntax for the read command is read filename file format ILOG CPLEX 9 0 GETTING STARTED 55 e r O E D JOZIWNdO 3A1 9819 U SETTING ILOG CPLEX PARAMETERS or read filename file extension where file_extension corresponds to one of the allowed file formats Setting ILOG CPLEX Parameters ILOG CPLEX users can vary parameters by means of the set command This command is used to set ILOG CPLEX parameters to values different from their default values The procedure for setting a parameter is similar to that
173. time and get maximum performance from your programs 1 Prototype the Model 2 Identify the Routines to be Called 3 Test Procedures in the Application 4 Assemble the Data 5 Choose an Optimizer 6 Observe Good Programming Practices 7T Debug Your Program 8 Test Your Application 9 Use the Examples Prototype the Model Create a small version of the model to be solved An algebraic modeling language is sometimes helpful during this step ILOG CPLEX 9 0 GETTING STARTED CREATING A SUCCESSFUL CALLABLE LIBRARY APPLICATION Identify the Routines to be Called By separating the application into smaller parts you can easily identify the tools needed to complete the application Part of this process consists of identifying the Callable Library routines that will be called In some applications the Callable Library is a small part of a larger program In that case the only ILOG CPLEX routines needed may be for problem creation optimizing obtaining results In other cases the Callable Library is used extensively in the application If so Callable Library routines may also be needed to modify the problem set parameters determine input and output messages and files query problem data Test Procedures in the Application Itis often possible to test the procedures of an application in the ILOG CPLEX Interactive Optimizer with a small prototype of the model Doing so will help identify
174. tion o ooooooo 68 Constructing the Environment lloEnv llli Ih 68 Creating a Model lloModel 00 0 RII n 69 Solving the Model llo0Cplex o ooooococcocrcocro ttt eens 71 Querying Results cocer c Rev IVO p Lu Eu P beue es 72 Flandling Err rs 2 erc a NE POUR EODD E Fed epa 72 Building and Solving a Small LP Model in C llle 73 General Structure of an ILOG CPLEX Concert Technology Application 74 Modeling by Rows ede bove Abide a la bis 75 Modeling by Col mrs tere ons ele Mae peed ee Ae Ma ee IRE e eru Pe Ru AE Ere Rm 75 Modeling by Nonzero Elements coococccccn tenes 76 Complete Progra esere neiere hh mms 76 Writing and Reading Models and Files 0 00 eee eee eee eee eee eee 80 ILOG CPLEX 9 0 GETTING STARTED 5 CONTENTS Chapter 4 Chapter 5 Selecting an Optimizer 0 cece e n n nnn 81 Reading a Problem from a File Example ilolpex2 cpp lessen 82 Reading the Model from a File a n 0 cece RII 82 Selecting the Optimizer o oooooococooccor m n 82 Accessing Basis Information oooooocooocooo e 82 Querying Quality Measures ooocoocococ s eee 83 Complete Program abu it Wires CUI 83 Modifying and Reoptimizing sees IRI III III 86 Modifying an Optimization Problem Example ilolpex3 cpp oooooooooomooo 86 Setting ILOG CPLEX Parameters oococccoccco rn 88 Modifying an
175. tion in a problem Each decision variable has a domain of possible values The constraints are limits or restrictions on combinations of values for these decision variables The model may also contain an objective an expression that can be maximized or minimized The third stage is to use the classes of ILOG Concert Technology for NET users to solve the problem Solving the problem consists of finding a value for each decision variable while simultaneously satisfying the constraints and maximizing or minimizing an objective if one is included in the model In these tutorials you will describe model and solve a simple problem that also appears elsewhere in C C and Java versions of this manual e Building and Solving a Small LP Model in C on page 127 e Building and Solving a Small LP Model in C on page 73 e Building and Solving a Small LP Model in Java on page 97 Describe The first step is for you to describe the problem in natural language and answer basic questions about the problem What is the known information in this problem That is what data is available What is the unknown information in this problem That is what are the decision variables What are the limitations in the problem That is what are the constraints on the decision variables What is the purpose of solving this problem That is what is the objective function ILOG CPLEX 9 0 GETTING STARTED 107 DESCRIBE Describe 108 Note
176. tively Modifying an Optimization Problem After the simple model is solved and the resulting objective value is passed to the output channel cplex out the remaining constraints are created and added to the model At this time the model has already been extracted to cplex As a consequence whenever the model is modified by adding a constraint this addition is immediately reflected in the cplex object via notification Starting from a Previous Basis Before solving the modified problem example i1olpex3 cpp sets the optimizer option to IloCplex Dual as this is the algorithm that can generally take best advantage of the optimal basis from the previous solve after the addition of constraints Complete Program The complete program follows You can also view it online in the file ilolpex3 cpp VUE cc A SS Se O umi File examples src ilolpex3 cpp Version 9 0 A A Sa er I ere Copyright C 1999 2003 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products Ju puc up A RO REOR TII RES ilolpex3 cpp example of adding constraints to solve a problem Modified example from Chvatal Linear Programming Chapter 26 minimize c x subject to Hx d Ax b l lt x lt u where H 1 01 0 1 0 0 0 d 3 ILOG CPLEX 9 0 GETTING STARTED MODIFYING AN OPTIMIZATION PROBLEM
177. to a model 96 continuous variable representing 70 CPLEX compatible platforms 11 Component Libraries 11 description 10 directory structure 26 installing 26 licensing 28 problem types 10 quitting 63 setting up 25 starting 34 technologies 11 cplex command 34 cplex jar location 91 cplex log file 47 CPXaddcols routine 123 125 128 CPXaddrows routine 123 125 128 148 CPXboundsa routine 154 CPXchgcoeflist routine 123 125 128 CPXcloseCPLEX routine 123 129 139 148 CPXcopylp routine 123 124 125 126 129 148 CPXcreateprob routine 123 139 148 CPXfreeprob routine 123 129 139 148 CPXgeterrorstring routine 128 129 C C C E C C C C PXgetobjval routine 148 PXlpopt routine 128 148 154 PXmsg routine 122 PXnewcols routine 123 125 128 PXnewrows routine 123 125 128 PXopenCPLEX routine 122 128 139 147 PXreadcopyprob routine 123 139 PXsetintparam routine 128 ILOG CPLEX 9 0 INDEX CPXsolution routine 128 148 CPXwriteprob routine 127 129 148 154 creating algorithm object 71 74 automatic log file 47 binary problem representation 127 constraint 75 environment 147 environment object 68 74 model Concert Technology 95 model I 1oModel 69 model objects 74 objective function 75 80 optimization model 69 70 problem files 50 problem object 123 148 SOS 80 variable 80 D data entering 39 entry options 13 deleting constraints 61 problem options 62 vari
178. to use CPXgeterrorstring For other CPLEX routines the errors will be seen if the CPX PARAM SCRIND indicator is set to CPX ON Lf status 4 char errmsg 1024 fprintf stderr Could not close CPLEX environment n CPXgeterrorstring env status errmsg fprintf stderr s errmsg g r O E 2 return status Aseaqiy 91qel1eo ILOG CPLEX 9 0 GETTING STARTED 133 BUILDING AND SOLVING A SMALL LP MODEL IN C 134 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 static void usage char progname fprintf stderr Usage s XWMn progname fprintf stderr where X is one of the following options An fprintf stderr t generate problem by row n fprintf stderr G generate problem by column Wn fprintf stderr n generate problem by nonzero n fprintf stderr Exiting n END usage These functions all populate the problem with data for the following linear program Maximize obj xl 2 x2 3 x3 Subject To Gir IN e ok 3 C2 X 3 MZ ks Bounds 0 lt x1 lt 40 End a7 define NUMROWS 2 define NUMCOLS 3 define NUMNZ 6 lt 20 lt 30 To populate by row we first create the columns and then add the rows static int populatebyrow CPXENVptr en
179. u know how to compile link and execute programs written in a high level language The 18 ILOG CPLEX 9 0 GETTING STARTED WHAT S IN THIS MANUAL Callable Library is written in the C programming language while Concert Technology is available for users of C Java and the NET framework 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 What s in This Manual Chapter 1 Setting Up ILOG CPLEX tells how to install CPLEX Chapter 2 Interactive Optimizer Tutorial explains step by step how to use the Interactive Optimizer how to start it how to enter problems and data how to read and save files how to modify objective functions and constraints and how to display solutions and analytical information Chapter 3 Concert Technology Tutorial for C Users describes the same activities using the classes in the C version of the CPLEX Concert Technology Library Chapter 4 Concert Technology Tutorial for Java Users describes the same activities using the classes in the Java version of the CPLEX Concert Technology Library Chapter 5 Concert Technology Tutorial for NET Users describes the same activities using NET facilities Chapter 6 Callable Library Tutorial describes the same activities using the routines in the ILOG CPLEX Callable Library All tutorials use examples that are delivered with the stand
180. uA uw G0 de 0 0 Q Ll 0 1 0r 50 0 a 0 1 0 C 00 20 OF Oct 0 ob del Aco 2 1 2 l1 2l 2 hear 203 152 d c 9 1 4 2 8 2 8 l1 0 0 0 0 0 0 0 u 50 50 50 50 50 50 50 Treat the constraints with A as the complicating constraints EXAMPLE 0 1 0 4 1 3 1 75 g oye em 3e 1 2 12 3 0 50 and the constraints with H as the simple problem The idea is to solve the simple problem first constraints for the complicating constraints include lt ilcplex ilocplex h gt ILOSTLBEGIN int main IloEnv try IloModel model env env IloNumVarArray x env 8 and then add the chvatal 0 50 model add IloMinimize env 9 x 0 x 1 4 x 2 2 x 3 model add x 0 model add x 0 x 1 model add x 1 model add model add IloCplex cplex model cplex setParam IloCplex SimDisplay cplex setParam IloCplex RootAlg cplex solve cplex out 8 x 4 2 x 5 8 x 6 12 x 71 x 2 x 4 x 3 x 2 x 5 x 6 x 3 x5 x 7 x 4 x 6 x 7 2 IloCplex Network After network optimization lt lt cplex getObjValue model add 2 x 0 1 x 1 Ze 4 1 x I5 model add 1 x 0 3 x 1 l xp4 2 5 cplex setParam IloCplex RootAlg cplex solve ILOG CPLEX 9 0 v objective is lt lt endl 2x EZ
181. ub objvals 11 07 2 0 3 0 model Add model Maximize model ScalProd x objvals rng rng rng rng rng new IRange 2 0 model AddRange System Double MaxValue 20 0 1 model AddRange System Double MaxValue 30 0 0 Expr model Sum model Prod 1 0 x 0 1 Expr 0 model Prod 1 0 x 1 model Prod 1 0 x 21 model Sum model Prod 1 0 x 0 model Prod 3 0 x 1 model Prod 1 0 x 21 ILOG CPLEX 9 0 GETTING STARTED Callable Library Tutorial This tutorial shows how to write programs that use the ILOG CPLEX Callable Library In this chapter you will learn about The Design of the ILOG CPLEX Callable Library on page 119 Compiling and Linking Callable Library Applications on page 120 How ILOG CPLEX Works on page 122 Creating a Successful Callable Library Application on page 124 Building and Solving a Small LP Model in C on page 127 Reading a Problem from a File Example lpex2 c on page 138 Adding Rows to a Problem Example lpex3 c on page 147 9 9 9 9 9 9 Performing Sensitivity Analysis on page 153 The Design of the ILOG CPLEX Callable Library Figure 6 1 shows a picture of the ILOG CPLEX world The ILOG CPLEX Callable Library together with the ILOG CPLEX database make up the ILOG CPLEX core The core becomes associated with your application through Callable Library routines The g O 2 Aseaqry aqe ILOG CPLEX 9 0 GETTING STARTED
182. unction is created only with its intended optimization sense and without any expression Next the variables are created and installed in the existing ranges and objective These newly created variables are introduced into the ranges and the objective by means of column objects which are implemented in the class IColumn Objects of this class are created with the methods Cplex Column and can be linked together with the method IColumn And to form aggregate IColumn objects ILOG CPLEX 9 0 GETTING STARTED 111 3 9 95 o omy 3 Z ma E gt c5 0 o Ro 0 Q lt MODEL 112 An IColumn object created with the method 1Cplex Column contains information about how to use this column to introduce a new variable into an existing modeling object For example if obj is an IObjective object cplex Column obj 2 0 creates an IColumn object containing the information to install a new variable in the expression of the IObjective object obj with a linear coefficient of 2 0 Similarly for an IRange constraint rng the method call cplex Column rng 1 0 creates an IColumn object containing the information to install a new variable into the expression of rng as a linear term with coefficient 1 0 In short when you use a modeling by column approach new columns are created and installed as variables in all existing modeling objects where they are needed To do this with ILOG Concert Technology you create an IColumn object for every model
183. v CPXLPptr lp int status 0 ILOG CPLEX 9 0 GETTING STARTED BUILDING AND SoLviNG A SMALL LP MODEL IN C double obj NUMCOLS double lb NUMCOLS double ub NUMCOLS char colname NUMCOLS int rmatbeg NUMROWS int rmatind NUMNZ double rmatval NUMNZ double rhs NUMROWS char sense NUMROWS char rowname NUMROWS CPXchgobjsen env lp CPX MAX Problem is maximization Now create the new columns First populate the arrays obj 0 1 0 obj 1 2 0 obj 2 3 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 CPXnewcols env lp NUMCOLS obj lb ub NULL colname if status goto TERMINATE Now add the constraints rmatbeg 0 0 rowname 0 cl rmatind 0 0 rmatind 1 1 rmatind 2 2 sense 0 L rmatval 0 1 0 rmatval 1 1 0 rmatval 2 1 0 rhs 0 20 0 rmatbeg 1 3 rowname 1 c2 rmatind 3 0 rmatind 4 1 rmatind 5 2 sense 1 L rmatval 3 1 0 rmatval 4 3 0 rmatval 5 1 0 rhs 1 30 0 status CPXaddrows env lp 0 NUMROWS NUMNZ rhs sense rmatbeg rmatind rmatval NULL rowname if status goto TERMINATE TERMINATE return status END populatebyrow To populate by column we first create the rows and then add the columns g r
184. va application an ILOG CPLEX application is implemented as a method of a class In this discussion the method will be the static main method The first task is to create an IloCplex object It is used to create all the modeling objects needed to represent the model For example an integer variable with bounds O and 10 is created by calling cplex intVar 0 10 where cplex is the IloCplex object Since Java error handling in ILOG CPLEX uses exceptions you should include the ILOG Concert Technology part of an application in a try catch statement All the exceptions thrown by any ILOG Concert Technology method are derived from IloException Thus I1oException should be caught in the catch statement In summary here is the structure of a Java application that calls ILOG CPLEX import ilog concert import ilog cplex static public class Application static public main String args try 1 IloCplex cplex new IloCplex create model and solve it catch IloException e System err println Concert exception caught e ILOG CPLEX 9 0 GETTING STARTED THE ANATOMY OF AN ILOG CONCERT TECHNOLOGY APPLICATION Create the Model The 11oCplex object provides the functionality to create an optimization model that can be solved with 11oCplex The interface functions for doing so are defined by the ILOG Concert Technology interface 11oModeler and its extension IloMPModeler These interfaces define the constructor
185. ws Now go to the comment Step 4 in that file and add these lines to create a method to populate the empty model with data by rows internal static void PopulateByRow IMPModeler model INumVar var IRange rng double lb 0 0 0 0 0 0 double ub 40 0 System Double MaxValue System Double MaxValue INumVar x model NumVarArray 3 lb ub var 0 x double objvals 1 0 2 0 3 0 model AddMaximize model ScalProd x objvals rng 0 new IRange 2 rng 0 0 model AddLe model Sum model Prod 1 0 x 0 model Prod 1 0 x 1 model Prod 1 0 x 2 20 0 rng 0 1 model AddLe model Sum model Prod 1 0 x 0 model Prod 3 0 x 1 model Prod 1 0 x 2 30 0 Those lines populate the model with data specific to this particular example However you can see from its use of the interface IMPModeler how to add ranged constraints to a model IMPModeler is the Concert Technology interface typically used to build math programming MP matrix models You will see its use again in Step 5 and Step 6 ILOG CPLEX 9 0 GETTING STARTED MODEL Populate the model by columns Go to the comment Step 5 in the file and add these lines to create a method to populate the empty model with data by columns internal static void PopulateByColumn IMPModeler model INumVar var IRange rng IObjective obj model AddMaximize rng 0 new IRange 2 rng 0 0 mo
186. y 3 3 modeling interfaces lloCplex hi 2 o lt c5 25 Le A EL um LS a o vo lt CPLEX database Figure 4 1 A View of ILOG CPLEX in ILOG Concert Technology ILOG CPLEX 9 0 GETTING STARTED 93 THE ANATOMY OF AN ILOG CoNcERT TECHNOLOGY APPLICATION Figure 4 1 illustrates the design of ILOG Concert Technology and how a user program uses it ILOG Concert Technology defines a set of interfaces for modelling objects Such interfaces do not actually consume memory this is the reason the box in the figure has a dotted outline When a user creates an ILOG Concert Technology modelling object using ILOG CPLEX an object is created in the ILOG CPLEX database that implements the interface defined by ILOG Concert Technology However a user application never accesses such objects directly but only communicates with them through the interfaces defined by ILOG Concert Technology The only ILOG Concert Technology objects directly created and accessed by a user are objects from class 11oCplex This class implements two interfaces IloModeler and IloMPModeler that allow you to create modelling objects The class 11oCplex also provides methods to solve models and query solutions The Anatomy of an ILOG Concert Technology Application 94 To use the ILOG CPLEX Java interfaces you need to import the appropriate packages into your application This is done with the lines import ilog concert import ilog cplex As for every Ja
187. y 70 role in model 95 IloObjective class 70 75 80 role in model 95 setCoef method 76 IloRange class casting operator for 75 example 71 reading from file 80 role in Concert Technology 70 role in model 95 setCoef method 76 setExpr method 100 IloSemiContVar class 80 I1loSOS1 class 80 I10SOS2 class 80 importModel method IloCplex class 80 82 infeasible 97 installing CPLEX 25 to 29 testing installation 28 see also testing installation integer parameter 88 integer variable 162 ILOG CPLEX 9 0 optimizer used 126 representing in model 70 Interactive Optimizer 33 to 63 command formats 34 commands 35 description 11 example model 14 quitting 63 starting 34 see also individual Interactive Optimizer commands invalid encrypted key 93 iteration log 46 47 J Java Native Interface IND 91 Java Virtual Machine JVM 92 javamake for Windows 92 L libformat 92 licensing CPLEX 28 linear optimization 10 Linear Programming LP problem see LP linker error messages 68 using with CPLEX 67 linking applications 29 Callable Library applications 120 Concert Technology applications 67 Concert Technology library files 29 CPLEX library files 29 log file adding to 56 cplex log 47 creating 47 iteration log 46 47 LP creating a model 13 node 81 problem format 10 GETTING STARTED root 81 solving a model 13 solving pure 81 LP file format 37 reading 54 writing 51
188. you to build a problem from the keyboard but they do not allow you to change what you have built You make changes with the change command The change command can be used for Changing Constraint or Variable Names Changing Sense Changing Bounds and Removing Bounds ILOG CPLEX 9 0 GETTING STARTED CHANGING A PROBLEM Changing Coefficients Deleting entire constraints or variables Start out by changing the name of the constraint that you added with the add command In order to see a list of change options type change The elements that can be changed are displayed like this Change options bounds change bounds on a variable E coefficient change a coefficient El delete delete some part of the problem name change a constraint or variable name 9 objective change objective function value E e problem change problem type S lt qpterm change a quadratic objective term Q 2 rhs change a right hand side or network supply demand value a 9 sense change objective function or a constraint sense type change variable type 3 E O Change to make Changing Constraint or Variable Names Enter name at the Change to make prompt to change the name of a constraint Change to make name The present name of the constraint is c3 In the example you can change the name to new3 to differentiate it from the other constraints using the following entries Change a constraint or variable name c vel 6 Prese

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