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IBM ILOG AMPL CPLEX 12.2 User`s Guide

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1. 00 eee cece e eee eee eee 71 Directives to Manage the Solution Pool 20 c cece eee eee eee eee 71 Directives for Controlling Output 0 0 cece eee eee 73 Common DifficultieS i 00 00 44 csc ceed wee ee ee ieee eee Vee edie ees 74 Running Out of Memory 0 2 0 0 74 IBM ILOG AMPL V12 2 USER S GUIDE Chapter 8 Chapter 9 Failure To Prove Optimality 0 0 0 ccc o 75 Difficult MIP Subproblems 0 0 0 00 c tenet eee 75 Defined Suffixes for CPLEX 0000 c cece eee eee 77 Algorithmic Control a I EA eed wie dan Ae aE 77 Sensitivity Ranging e eieren A ee eee ba een tera is 80 Diagnosing InfeasibilitieS 0 0 cee eee eee 81 Direction of Unboundedness 200 eee eee 83 CPLEX Status Codes in AMPL oococcooccc eee eee 85 Solve Codes ii ART ne ane AP eae Siete a 85 Basis StatUS su i wcci eee ieee erie A ee 89 So eae RA NA eB AS NN as Dares me aes BE ets 93 IBM ILOG AMPL V12 2 USER S GUIDE 5 IBM ILOG AMPL V12 2 USER S GUIDE 3 1 4 1 6 1 6 2 6 3 6 4 7 1 7 2 7 3 7 4 7 5 8 1 9 1 9 2 A 1 List of Tables Auxiliary Elle ees ii AA A A G aA A a a 21 AMPL Option Names for Command Line Switches 0c c see eee eee eee eee eee 25 Settings for the dependency Directive oocococccncncananna eee eee eee eeneee 42 Settings for the advance Directive 0c cece eee eee eee eee eee eee eee ee eee 44 Settings for the pgradient Directive 0 cc
2. ampl suffix priority IN integer gt 0 lt 9999 ampl suffix direction IN integer gt 1 lt 1 ampl let i in ORIG j in DEST ampl Use i j priority amp1 sum p in PROD demand j p ampl let Use GARY FRE direction 1 ampl solve CPLEX 11 0 0 optimal integer solution objective 235625 446 simplex iterations 64 branch and bound nodes Indeed CPLEX now requires fewer nodes 64 and fewer simplex iterations 446 to reach optimality While this is not a dramatic improvement larger cases where directing branch and bound in this manner makes the difference between unsolvability and finding the solution in a few minutes are well known The lazy suffix is used to designate constraints which should be handled separately from the rest of the constraints in a mixed integer program Lazy constraints are constraints which are essential to defining the feasible region of the mixed integer program but that a user knows are unlikely to be violated Thus a reasonable way to handle these constraints is to apply them in a lazy way that is only as necessary Each time a potential integer solution is found it is checked against the lazy constraints If all the constraints are satisfied the integer solution is accepted IBM ILOG AMPL V12 2 USER S GUIDE If any of the lazy constraints are not satisfied the potential integer solution is rejected and the constraints which were not satisfied are added to the problem a
3. 82 The following example shows how IIS finding might be applied to the infeasible diet problem from chapter 2 of the AMPL book After solve detects that there is no feasible solution it is repeated with the iisfind directive ampl model diet mod ampl data diet2 dat ampl option solver cplexamp ampl solve CPLEX 11 0 0 infeasible problem 7 iterations 7 in phase I ampl option cplex options iisfind 1 ampl solve CPLEX 11 0 0 iisfind 1 CPLEX 11 0 0 infeasible problem 0 iterations Returning iis of 7 variables and 2 constraints suffix iis symbolic OUT option iis table 0 non not in the iis Y low at lower bound 2 fix fixed 3 upp at upper bound 4 mem member 5 pmem possible member 6 plow possibly at lower bound 7 pupp possibly at upper bound 8 bug You can use display to look at the iis values that have been returned ampl display _varname _var iis _conname _con iis _varname _var iis _conname _con iis 1 Buy BEEF upp diet A non 2 Buy CHK low diet B1 non 3 Buy FISH low diet B2 mem 4 Buy HAM upp diet c non 5 Buy MCH upp diet NA mem 6 Buy MTL upp diet CAL non 7 Buy SPG non z 8 Buy TUR low This information indicates that the IIS consists of four upper and three lower bounds on the variables plus the constraints on B2 and on NA in the diet Together these restrictions have no f
4. This alternative has no known advantages and is supplied for completeness only symmetry i default 1 This directive controls the amount of symmetry breaking CPLEX should use The default of 1 tells CPLEX to choose Set i 0 to turn off symmetry breaking and i 1 2 3 for increasing amounts of symmetry breaking effort Directives for Algorithmic Control 60 CPLEX has default values for the algorithmic control directives that often work well for solving a wide range of mixed integer programs However it is sometimes necessary to specify alternative values for one or more of the following directives to improve solution times You can view each of these directives as corresponding to a particular decision faced at each step in the branch amp cut procedure To be specific imagine that an LP QP QCP subproblem has just been solved The sequence of decisions and the corresponding directives are then as follows Branch next from which node in the tree backtrack nodesel Branch by constraining which fractional variable at the selected node mip priorities ordertype varselect refer to the discussion on setting priorities by variable in Algorithmic Control on page 77 IBM ILOG AMPL V12 2 USER S GUIDE Investigate which of a fractional variable s two resulting branches first branch refer to the discussion on setting branching preference by variable in Algorithmic Control on page 77 Solve the resulting new sub
5. default 0 Directs CPLEX to compute and return dual variable values for solutions in the solution pool when the value of the option is 1 Dual variable values are not computed for solutions in the pool when the value of the option is 0 poolintensity i default 0 This directive tells CPLEX how much effort to use in generating additional solutions with larger values specifying more effort The default of 0 is considered to be the value 1 if the populate directive is not also specified and 2 if it is Values of 3 and 4 can be quite time consuming value 4 directs CPLEX to enumerate all solutions that is to try all possible combinations of the integer variables which can also be quite memory intensive since there can be a large number of solutions poolreplace i default 0 This directive specifies the policy for replacing solutions in the solution pool if more than poolcapacity solutions are generated i 0 keeps only the newest solutions i 1 keeps the solutions with the best objective values and i 2 keeps the solutions that are most diverse poolstub f The directive specifies the stub for solution files in the MIP solution pool The solutions that remain in the solution pool after some are replaced if more than poolcapacity solutions are found are written to files f amp 1 f amp n where n is the number of solutions in the solution pool That is file names are obtained by appending 1 2 nto f The value of n is return
6. solution but also increases the chance of a convergence failure in the algorithm and consequently may result in no solution at all Therefore caution is advised in deviating from the default setting For LPs and QPs that is when all the constraints are linear see the comptol directive Directives for Improving Stability CPLEX is highly robust and has been designed to avoid problems such as degenerate stalling and numerical inaccuracy that can occur in the simplex algorithm However some linear programs can benefit from adjustments to the following directives if difficulties are encountered numericalemphasis i default 0 This directive lets you indicate to CPLEX that it should emphasize precision in numerically difficult or unstable problems with consequent performance trade offs in time and memory When set to its nondefault value of 1 CPLEX will choose tactics that emphasize numerical stability Try setting this directive before trying any of the other settings in this section doperturb il default 0 perturbation r default 1 0e 6 perturblimit i2 default 0 The simplex algorithm tends to make very slow progress when it encounters solutions that are highly degenerate in the sense of having many basic variables lying at one of their bounds rather than between them When CPLEX detects degenerate stalling it automatically introduces a perturbation that expands the bounds on every variable by a small amount thereby creating a
7. workfiledir f This directive lets you indicate to CPLEX that it should conserve memory where possible When you set this parameter to its nondefault value of 1 CPLEX will choose tactics such as data compression or disk storage for some of the data computed by the simplex barrier and MIP optimizers Of course conserving memory may impact performance in some models Also while solution information will be available after optimization certain computations that require a basis that has been factored for example for the computation of the basis condition number may be unavailable The workfilelim directive specifies the maximum amount of RAM that may be used for the Cholesky factorization of the barrier optimizer before files are used for the remainder of memory needs The default is 128 which means CPLEX will use 128 megabytes of RAM before using disk space These temporary barrier files are created in the directory specified by the value of the workfiledir directive If no value is specified the directory specified by the TMPDIR on UNIX or TMP on Windows environment variable is used If TMPDIR or TMP are not set either the current working directory is used Temporary barrier files are deleted automatically when CPLEX terminates normally threads i default 0 This directive specifies a global thread limit that is a default thread count for the parallel MIP parallel barrier and concurrentopt optimizers The value 0 tells CPLEX to use as
8. you to set up different options for each solver you use and to switch among them by simply choosing the appropriate solver with the option solver command For example ampl option cplex options relax scale 1 Solver options consist of an identifier alone or an identifier followed by an sign and a value Some solvers treat uppercase and lowercase versions of an option identifier as equivalent while others are sensitive to case so that RELAX is not the same as relax for example Solver option settings can easily become long enough to stretch over more than one line In such cases you can either continue a single quoted string by placing a character at the end of each line as in ampl option cplex options crash 0 dual ampl feasibility 1 0e 8 scale 1 ampl lpiterlim 100 Or you can write a series of individually quoted strings which will be concatenated automatically by AMPL as in ampl option cplex options crash 0 dual ampl feasibility 1 0e 8 scale 1 ampl lpiterlim 100 If you use the latter approach be sure to include spaces at the beginning or end of the individual strings so that the identifiers will be separated by spaces when all of the strings are concatenated 18 IBM ILOG AMPL V12 2 USER S GUIDE Often you will want to add solver options to the set you are currently using If you simply type a command such as option solver_ options new options however you will overwrite the existing opt
9. 1 ampl display solve result num solve result solve result num 0 solve _ result solved ampl option solve result table option solve result_table 0 solved 100 solved 200 infeasible 300 unbounded 400 limit 500 failure 1 i IBM ILOG AMPL V12 2 USER S GUIDE 85 86 The session log shows that the built in AMPL parameter solve_result_numis 1 initially and parameter solve_result is The solve invocation resets these parameters however so that they describe CPLEX s status at the end of its run the solve_result_num parameter by a numeric code and solve_result by a message string In the example shown solve_result_numis set to 0 and solve_result to solved indicating normal termination The AMPL option solve_result_table lists the valid combinations of solve _result_num and solve_result for CPLEX These combinations should be interpreted as shown below Table 9 1 Interpretation of Numeric Result Codes Number String Interpretation 0 99 solved optimal solution found 100 199 solved optimal solution indicated but error likely 200 299 infeasible constraints cannot be satisfied 300 399 unbounded objective can be improved without limit 400 499 limit stopped by a limit such as on iterations 500 599 failure stopped due to solver error Status ranges are normally used to control algorithmic flow in AMPL scripts where solve_result_numcan be tested to distinguish among cases that must b
10. 10 Install IBM ILOG AMPL by means of the installation program provided to you through a download or other medium The variety of installation programs available correspond to the different operating systems on which IBM ILOG AMPL is available For detailed system requirements of these installations see the topic DSR at http www 01 ibm com software integration optimization ampl index html Remember that most distributions will operate properly only on the specific platform and operating system version for which they were intended If you upgrade your operating system you may need to obtain a new distribution All AMPL installations include cplexamp cplexamp exe on Windows the CPLEX solver for AMPL This combined distribution is known as the AMPL CPLEX system Note that cplexamp may not be licensed for a few users with unsupported solvers However most AMPL installations will include the use of cplexamp Usage Notes The CPLEX solver for AMPL is named cplexamp cplexamp exe on Windows This version of AMPL will use this solver by default Older versions of the CPLEX solver for AMPL were simply named cplex cplex exe on Windows Some users of that version may have specified the solver in their model or run files like this option solver cplex If you have models that contain settings like this you will encounter errors or the old version of the solver might be invoked There are two ways to fix this Ideally you should
11. Mathematical Programming 2nd edition Saving temporary files AMPL deletes the temporary problem n1 and solution so1 files after a solver is finished so no permanent record of the solution is kept unless you save the output yourself for example using display with redirection as illustrated above To override the deletion of temporary files you can use the AMPL write command For example C gt ampl ampl model steel mod data steel dat ampl write bsteel ampl solve CPLEX 11 0 0 optimal solution objective 192000 2 iterations 0 in phase I ampl quit The first letter b in the filename portion of the write command is interpreted specially as explained below If you now display the files in the current directory with a command such as dir steel you will find the problem file steel n1 and the solution file steel sol To later view the solution values you would use the solution command For example C gt ampl ampl model steel mod data steel dat ampl solution steel sol CPLEX 11 0 0 optimal solution objective 192000 2 iterations 0 in phase I ampl display Make Make bands 6000 coils 1400 ampl quit You must include the model and data statements as shown above so that AMPL knows the definitions of symbolic names like Make But solution then retrieves the earlier results from steel sol without running a solver IBM ILOG AMPL V12 2 USER S GUIDE if you use b
12. also apply to mixed integer QP models MIQP In cases where the nature of QP dictates different behavior from a directive usually the result is that the directive is ignored and default behavior remains in effect An example of this would be the dual directive to specify that CPLEX solves the explicit dual formulation for QP the default primal formulation will be used anyway In almost every case such differences will result in best performance and will require no user intervention Quadratic Constraints A model containing one or more quadratic constraints of the form T ax x Ox lt r is called a Quadratically Constrained Program QCP and can be solved using the CPLEX barrier algorithm Linear constraints may also be present in a QCP and a positive semi definite quadratic term in the objective function is permitted If discrete variables are present then the model is termed Mixed Integer QCP or MIQCP The Q matrix for each quadratic constraint must be positive semi definite just as for a quadratic objective function to ensure that the feasible space remains convex Most of the comments regarding CPLEX features in section Quadratic Programs above also pertain to QCP with the additional observation that only the barrier optimizer applies to continuous models that have any quadratic constraints and therefore barrier is also the only choice for subproblem solution of MIQCP models IBM ILOG AMPL V12 2 USER S GUIDE 31 Sp
13. as the first character of the filename portion of the write command AMPL uses a compact and efficient binary format for the problem and solution files If you use g instead AMPL writes the files in an ASCII format that may be easier to transmit electronically over systems like the Internet In technical support and consulting situations IBM may ask you to send a file using this format If you use m AMPL writes the problem in MPS format and the filename ends in mps for example steel mps This is described further in Using MPS File Format on page 22 Creating Auxiliary Files AMPL can create certain human and program readable auxiliary files that help relate the various set variable constraint and objective names used in your AMPL model to the column and row indices that are written to the problem file and seen by the solver This is particularly valuable when the AMPL presolve phase actually eliminates variables and constraints before the problem is sent to the solver To create the auxiliary files you set the AMPL option auxfiles to a string of letters denoting the combination of auxiliary files you would like produced and then use the write command to create and save the auxiliary files along with the problem n1 file For example the command ampl option auxfiles cr will cause the write command to create auxiliary files containing the names of the variables columns and constraints rows as sent to the solver The tabl
14. branch amp cut algorithm which is to deliver proved optimal solutions if given enough time the setting merely changes some internal strategies and tactics along the way and represents a way for the user to express his or her aims in a way that is separate from the model formulation A setting of 4 indicates emphasis on hidden feasibles With this setting the MIP optimizer works hard to find high quality feasible solutions that are otherwise very difficult to find Use this setting when you more are interested in a good feasible solution than a provably optimal solution and when feasibility emphasis has difficulty finding solutions of acceptable quality IBM ILOG AMPL V12 2 USER S GUIDE 61 62 Table 7 2 recapitulates the settings of this parameter Table 7 2 Settings for the mipemphasis Directive Setting Effect O default Balance optimality and feasibility 1 Emphasize feasibility over optimality 2 Emphasize optimality over feasibility 3 Emphasize moving best bound 4 Emphasize hidden feasibles auxrootthreads i default 0 This directive tells CPLEX how many threads to use during root node processing for auxiliary tasks that is non solving tasks The number of threads for auxiliary tasks must be at least one less than the total number of threads available to CPLEX At the default value of i 0 CPLEX chooses how many threads to use for auxiliary tasks backtrack r default 0 9999 bbinterv
15. can be specified for each variable by setting its direction suffix to a value between 1 and 1 Variables not assigned a suffix value get a default value of zero A negative value indicates a preference for branching down and a positive value indicates a preference for branching up IBM ILOG AMPL V12 2 USER S GUIDE 77 78 For variables with direction at zero the branching direction is determined by the branching related directives described in Directives for Algorithmic Control on page 60 Each time that CPLEX must choose a fractional valued integer variable on which to branch it gives preference to the fractional variables that have the highest priority value A judicious choice of priorities any number between 0 and 9999 is valid can guide the search in a way that reduces the number of nodes generated For example let us consider a model drawn from pages 446 447 of the AMPL book ampl model models multmip3 mod ampl data models multmip3 dat ampl solve CPLEX 11 0 0 optimal integer solution objective 235625 601 simplex iterations 91 branch and bound nodes Note that CPLEX takes 91 nodes and 601 simplex iterations to find the optimal integer solution Now let us provide CPLEX with branching priorities for all variables as well as a preferred branching direction for a single variable Note that before we re run CPLEX we set mipstartvalue to discard the existing solution ampl option cplex options mipstartvalue 0
16. change these lines to option solver cplexamp IBM ILOG AMPL V12 2 USER S GUIDE If that is not practical you can copy the file cplexamp to cplex If you do the latter you must remember to copy it again the next time you upgrade cplexamp Installed Files UNIX systems amplcplexuserguidel22 pdf bin lt system gt ampl bin lt system gt cplexamp examples licenses Windows Systems amplcplexuserguide122 pdf bin lt system gt ampl exe bin lt system gt ampltabl d1l bin lt system gt cplex122 d11 bin lt system gt cplexamp exe bin lt system gt exhelp32 exe examples licenses Examples models looping industries industries finance industries logistic industries product industries purchase industries schedule User s manual for IBM ILOG AMPL AMPL The CPLEX solver for AMPL Directory of examples see Examples below Files describing the license terms User s manual for IBM ILOG AMPL AMPL Table handlers CPLEX DLL used by cplexamp exe The CPLEX solver for AMPL Utility program invoked by AMPL for DOS shells Directory of examples see Examples below Files describing the license terms Sample AMPL models Most of these correspond to examples in the AMPL book More information on some of the examples is provided in the readme file in this directory Advanced sample AMPL models A description of each is provided in the readme file in this directory More samples The industr
17. contain at most one from and one to phrase and these phrases may not specify optional coefficients In the case of linear programs that are mostly defined in terms of node and arc declarations but that have some side constraints defined by subject to declarations the benefit is highly dependent on problem structure it is best to try experimenting with both i 0 and i 1 parallelmode i default 0 This directive sets the type of parallelism used by CPLEX Multiple runs of the same problem with the same settings will get identical solution paths with deterministic mode but not with opportunistic mode Opportunistic mode can be faster than deterministic mode due to less synchronization among the threads The default automatic setting allows CPLEX to choose between deterministic and opportunistic mode depending on the threads directive If the threads directive is set to its automatic setting the default CPLEX chooses deterministic mode If the threads directive is set to one CPLEX runs sequentially in deterministic mode in a single thread Otherwise if the threads directive is set to a value greater than one CPLEX chooses opportunistic mode The value i 1 is used to set deterministic mode and the value i 1 is used to set opportunistic mode relax This directive instructs CPLEX to ignore any integrality restrictions on the variables The resulting linear program is solved by whatever algorithm the above directives specify maximize min
18. different but closely related problem Generally CPLEX can make faster progress on this less constrained problem once optimality is indicated the perturbation is removed by resetting the bounds to their original values The value of r determines the size of the perturbation If you receive messages from CPLEX indicating that the linear program has been perturbed more than once r is probably too large reduce it to a level where only one perturbation is required The default doperturb value of i1 0 selects CPLEX s automatic perturbation strategy If an automatic perturbation occurs early in the solution process consider setting i1 1 to select perturbation at the outset This alternative will save the time of first allowing the IBM ILOG AMPL V12 2 USER S GUIDE 49 optimization to stall before activating the perturbation mechanism but is useful only rarely for extremely degenerate problems The perturblimit parameter governs the number of stalled iterations CPLEX allows before perturbing the problem The default value of i2 0 causes CPLEX to determine this number based on the characteristics of the particular problem being solved Setting 12 to a positive integer value identifies a specific number of stalled iterations to tolerate before perturbing the problem feasibility r1 default 1 0e 6 markowitz r2 default 0 01 optimality r3 default 1 0e 6 If a problem is making slow progress through Phase I or repeatedly becomes infeasibl
19. however aggregation may also increase the number of nonzero constraint coefficients resulting in more work at each simplex iteration The default setting of i2 10 usually makes a good tradeoff between reduction in size and increase in nonzeros but you may want to experiment with lower values if CPLEX reports that many aggregations have been made If CPLEX consistently reports that no aggregations can be performed on the other hand you can set il to O to turn off the aggregation routine and save memory and processing time To request a report of the number of aggregations see the prestats directive later in this section dependency i default 1 By default 1 1 CPLEX chooses automatically when to use dependency checking This parameter offers several settings that make it possible for a user to control dependency checking more precisely Table 6 1 shows you the possible settings of the parameter that controls dependency checking and indicates their effects Table 6 1 Settings for the dependency Directive Setting Effect 1 default automatic let CPLEX choose when to use dependency checking 0 turn off dependency checking 1 turn on only at the beginning of preprocessing 2 turn on only at the end of preprocessing 3 turn on at the beginning and at the end of preprocessing predual i default 0 By default after presolving the problem CPLEX decides whether to solve the primal or dual problem based on which
20. invoked and the problem is infeasible The feasopt and feasoptobj directives tell CPLEX to relax constraints and bounds to find a feasible solution The iisind directive tells CPLEX to try to refine the conflict among the constraints and bounds to a smaller set of constraints and bounds These directives can also be applied to integer programs conflictdisplay i default 1 This directive controls the amount of output during conflict refinement Set i 0 for no output i 1 for summary output and i 2 for a detailed display feasopt i default 0 Whether to find a feasible point for a relaxed problem when the problem is infeasible With the default setting of 0 no feasible point is found Set i 1 to find a feasible point and i 2 to find an optimal feasible point among all those that require only as much relaxation as is needed to find the first feasible point feasoptobj i default 1 This directive sets the objective to use in measuring minimality of a relaxation Set i 1 for minimizing the sum of the relaxations of constraints and bounds Set i 2 for minimizing the number of constraints and bounds that must be relaxed Set i 3 to minimize the sum of squares of the required relaxations of constraints and bounds iisfind i default 0 When i 1 for an infeasible problem CPLEX returns an irreducible infeasible subset IIS of the constraints and variable bounds By definition members of an IIS have no feasible solution but dropping any one of them permi
21. many threads as are allowed by the license when the parallelmode directive is 1 A value of 0 when parallelmode is 0 or 1 tells CPLEX to use as many threads as possible subject to maintaining a deterministic algorithm A positive value for i specifies that i threads should be used netopt i default 1 CPLEX incorporates an optional heuristic procedure that looks for pure network constraints in your linear program If this procedure finds sufficiently many such constraints CPLEX applies its fast network simplex algorithm to them Then if there are also non network constraints CPLEX uses the network solution as a start for solving the whole LP by the general primal or dual simplex algorithm whichever you have chosen The default value of i 1 invokes the network identification procedure if and only if your model uses node and arc declarations and CPLEX sets up the primal formulation as discussed above Setting i 0 suppresses the procedure while i 2 requests its use in all cases You can have CPLEX display the number of network nodes constraints and arcs variables that it has extracted by setting the prestats directive described with the preprocessing options below to 1 CPLEX s network simplex algorithm can achieve dramatic reductions in optimization time for pure network linear programs defined entirely in terms of node and arc declarations IBM ILOG AMPL V12 2 USER S GUIDE For a pure network LP every arc declaration must
22. narrowly focused search also often results in faster individual node processing times Overall efficiency is sometimes worse than with best bound node selection since each branch is exhaustively searched to the deepest level before fathoming it in favor of better branches Another memory conserving strategy is to use strong branching variable selection using the varselect directive When using strong branching substantial computational effort is made at each node to determine the best branching variable As a result many fewer nodes are generated reducing the overall demand on memory Often strong branching is faster as well as using less memory On some problems the automatic generation of cuts results in excessive use of memory with little benefit in speed In such cases it is expedient to turn off cut generation by setting the covers and cliques directives to 1 Failure To Prove Optimality One frustrating aspect of the branch amp cut technique for solving MIP problems is that the solution process can continue long after the best solution has been found In these situations the branch amp cut tree is being exhaustively searched in an effort to guarantee that the current integer feasible solution is indeed optimal Remember that the branch amp cut tree may be as large as 2 nodes where n equals the number of binary variables A problem containing only 30 binary variables could produce a tree having over 1 billion nodes If no oth
23. node file is written to disk Compressing the file 1 3 adds computation time but allows more efficient use of memory When the nodefile directive instructs CPLEX to write nodes to a node file the workfilelim directive specifies the maximum size of RAM to be consumed before writing to disk takes place Although node files are designed for efficiency the speed of RAM is always superior to that of disk and you should take advantage of what memory your computer has The default value of 128 a reasonable value for most computers means that 128 megabytes of RAM will be devoted to storing the tree and requirements beyond that will begin to go to files on disk A related directive is treememl im described below which serves to place a limit on the total size of the tree The default value of the treememlim directive is effectively infinity which means CPLEX will continue to write nodes to disk until it solves the problem or exhausts available disk space or encounters some other limit Disk node files are created in the temporary directory specified by the value of the workfiledir directive If no value is specified the directory specified by the TMPDIR on UNIX or TMP on Windows environment variable is used If TMPDIR or TMP are not set either the current working directory is used Node files are deleted automatically when CPLEX terminates normally ordertype i default 0 CPLEX can automatically generate certain priority orders which de
24. paramfileprm f2 These directives are used to import the settings contained in either the 1 or 2 files The 1 file uses AMPL directive names and the 2 file is a CPLEX PRM file tunefix 1 This directive tells CPLEX which parameters to keep fixed during the tuning algorithm The tuning algorithm starts with all parameters at their default values except those specified in 1 1 is a list of directives and values either enclosed in single or double quotes or separated by commas with no white space if more than one The list 1 is combined with any settings from the tunefixfile directive Example tunefix mipgap 0 tunefixfile f The name of a file with AMPL directives which CPLEX should leave fixed during the tuning algorithm The tuning algorithm starts with all parameters at their default values except those specified in The set of parameters in is combined with any settings from the tunefix directive tunedisplay i default 1 This directive controls the amount of output from the tuning algorithm No output is produced when i 0 A minimal amount is produced when i 1 The parameters being tried are printed when i 2 and full logs are printed when i 3 IBM ILOG AMPL V12 2 USER S GUIDE tunerepeat i default 1 CPLEX can tune on several variations of the problem The variations are obtained by permuting the rows and columns of the problem Tuning on several variations may give more robust tuning results tunetime r default 1
25. problem it determines it can solve faster Setting i 1 explicitly instructs CPLEX to solve the dual problem while setting it to 1 explicitly instructs CPLEX to solve the primal problem Regardless of the problem CPLEX solves internally it still reports primal solution values This is often a useful technique for problems with more constraints than variables prereduce i default 3 This directive determines whether primal reductions dual reductions or both are performed during preprocessing By default CPLEX performs both Set this directive to 0 to prevent all reductions 1 to only perform primal reductions and 2 to only perform dual reductions IBM ILOG AMPL V12 2 USER S GUIDE While the default usually suffices performing only one kind or the other may be useful when diagnosing infeasibility or unboundedness presolve i default 1 Prior to invoking any simplex algorithm CPLEX applies transformations that reduce the size of the linear program without changing its optimal solution In this presolve phase constraints that involve only one non fixed variable are removed either the variable is fixed and also dropped for an equality constraint or a simple bound for the variable is recorded for an inequality Each inequality constraint is subjected to a simple test to determine if there exists any setting of the variables within their bounds that can violate it if not it is dropped as nonconstraining Further iterative tests at
26. simplex 3 Network simplex 4 Barrier 5 Sifting The default strategy chooses the algorithm by using an internal heuristic based on the type of subproblem Typically CPLEX will use the dual simplex method when the problem is linearly constrained and the barrier method when it is a quadratically constrained program For linear programming subproblems the default settings usually perform well but other strategies may significantly reduce the time per node except for the quadratically constrained case where barrier is the only available choice These settings do not significantly affect the number of nodes that must be visited during the search When the Barrier algorithm is used to solve subproblems i1 4 by default 12 1 CPLEX uses primal simplex for the crossover In certain cases dual simplex may be faster When the subproblems are quadratically constrained programs CPLEX does not perform a crossover so this directive has no effect IBM ILOG AMPL V12 2 USER S GUIDE mipcuts i default 0 cliquecuts il default 0 covercuts i2 default 0 disjcuts i3 default 0 flowcuts i4 default 0 flowpathcuts i5 default 0 fraccuts i6 default 0 gubcuts i7 default 0 impliedcuts i8 default 0 mcfcuts i9 default 0 mircuts i10 default 0 zerohalfcuts i11 default 0 Integer programming solve times can often be improved by generating new constraints or cuts based on polyhedral considerations These additional constraints tighte
27. the objective offered by each candidate for leaving variable Steepest edge pricing involves an extra initialization cost but its extra cost per iteration is much less in the dual simplex algorithm than in the primal Thus if you find that your problems solve faster using the dual simplex you should consider experimenting with the steepest edge procedures e The standard procedure i 2 and the variant in slack space i 3 have similar computational costs often their overall performance is similar as well though one or the other can be advantageous for particular applications e The variant using unit initial norms i 4 is a compromise that sidesteps the initialization cost it is most likely to be advantageous for relatively easy problems that have a low number of iterations or time per iteration pricing i default 0 To promote efficiency when using reduced cost pricing in primal simplex CPLEX considers only a subset of the nonbasic variables as candidates to enter the basis The default of i 0 selects a heuristic that dynamically determines the size of the candidate list taking 46 IBM ILOG AMPL V12 2 USER S GUIDE problem dimensions into account You can manually set the size of this list to i gt 0 but only very rarely will this improve performance refactor i default 0 This directive specifies the number of iterations between refactorizations of the basis matrix At the default setting of i 0 CPLEX automatically calcul
28. the one below for CPLEX C gt cplexamp steel AMPL solver options In this example the first argument steel matches the filename after the initial letter b in the AMPL write command The AMPL argument tells the solver that it is receiving a problem from AMPL This may optionally be followed by any solver options you need for the problem using the same syntax used with the option solver_options command but omitting the outer quotes for example crash 1 relax Assuming that the solver runs successfully to completion it will write a solution file steel sol in this case You can then restart AMPL and read in the results with the solution command as outlined earlier C X gt ampl ampl model steel mod data steel dat ampl solution steel sol Using MPS File Format 22 MPS file format originally developed decades ago for IBM s Mathematical Programming System is a widely recognized format for linear and integer programming problems Although it is a standard supported by many solvers and modeling systems including AMPL MPS file format is neither compact nor easy to read and understand AMPL s binary file format is a much more efficient way for modeling systems and solvers to communicate Also MPS file format cannot be used for nonlinear problems and not all MPS compatible solvers support exactly the same format particularly for mixed integer problems IBM ILOG AMPL V12 2 USER S GUIDE AMPL does have the ability to tran
29. the status of INForUNBD that is infeasible or IBM ILOG AMPL V12 2 USER S GUIDE 59 unbounded Re solving with presolve turned off allows CPLEX to determine whether the problem is infeasible or unbounded sosl i default 1 An optimization problem containing restrictions that at most one of a specified group of variables can take a nonzero value is a form of discrete optimization that can be handled by an equivalent mixed integer program When i is at its default value of 1 this conversion is performed using a structure known as a special ordered set of type 1 If i is changed to 0 the conversion is made instead to an equivalent formulation using multiple binary variables sos2 i default 1 An optimization problem containing piecewise linear terms may have to be converted to an equivalent mixed integer program as explained in Piecewise linear Programs on page 30 When i is at its default value of 1 this conversion results in only one extra variable per piecewise linear breakpoint All of the extra variables associated with a particular piecewise linear term are marked as belonging together so that CPLEX s branch amp cut procedure knows to treat them specially Variables so marked have come to be known as a special ordered set of type 2 whence the name sos2 for this directive When i is changed to 0 from its default of 1 the conversion creates a larger number of variables but does not employ the special ordered set feature
30. write out vec file named 2 IBM ILOG AMPL V12 2 USER S GUIDE 51 52 singular i default 10 CPLEX will attempt to repair the basis matrix up to i times when it finds evidence that the matrix is singular Once this limit is exceeded CPLEX terminates with the current basis set to the best factorizable basis that has been found timelimit r default 1 0e 75 CPLEX stops after r seconds of computation time and returns its current solution whether or not it has determined that the solution is optimal IBM ILOG AMPL V12 2 USER S GUIDE Directives for Controlling Output When invoked by solve CPLEX normally returns just a few lines to your screen to summarize its performance The following directives let you choose a greater amount of output which may be useful for monitoring the progress of a long run or for comparing the effects of other directives on the detailed behavior on CPLEX s algorithms Output normally comes to the screen but it may be redirected to a file by specifying solve gt filename bardisplay i default 0 The default choice of i 0 produces a minimal few lines of output from CPLEX summarizing the results of a barrier method run When i 1 a log line recording the barrier iteration number primal and dual objective values and infeasibility information is displayed after each barrier iteration When i 2 additional information about the barrier run is provided This level of output is occasionally useful f
31. 0000 This directive limits the time per tuning trial This directive is meaningful only if r is less than the value of the time directive IBM ILOG AMPL V12 2 USER S GUIDE 35 36 IBM ILOG AMPL V12 2 USER S GUIDE Using CPLEX for Continuous Optimization CPLEX Algorithms for Continuous Optimization For problems with linear constraints CPLEX employs either a simplex method or a barrier method to solve the problem Refer to a linear programming textbook for more information on these algorithms Four distinct methods of optimization are incorporated in the CPLEX package A primal simplex algorithm that first finds a solution feasible in the constraints Phase I then iterates toward optimality Phase II A dual simplex algorithm that first finds a solution satisfying the optimality conditions Phase I then iterates toward feasibility Phase II A network primal simplex algorithm that uses logic and data structures tailored to the class of pure network linear programs A primal dual barrier or interior point algorithm that simultaneously iterates toward feasibility and optimality optionally followed by a primal or dual crossover routine that produces a basic optimal solution see below CPLEX normally chooses one of these algorithms for you but you can override its choice by the directives described below IBM ILOG AMPL V12 2 USER S GUIDE 37 The default algorithm when your computer has more than on
32. 26 L 26 ostr 26 P 26 S 26 s 26 sn 26 T 26 t 26 v 26 T temporary files directory 23 saving 20 termination messages 86 text editor using 13 text file predefined commands 26 threads directive 40 time to find solution 54 to read problem 54 to write solution 54 timelimit IBM ILOG AMPL directive 52 71 timing directive 54 74 treememlim directive 71 troubleshooting common difficulties 74 tunedisplay directive 34 tunefile directive 34 tunefileprm directive 34 tunefix directive 34 tunefixfile directive 34 tunerepeat directive 35 tunetime directive 35 U unbdd suffix 83 up suffix 80 uppercutoff directive 70 upperobj directive 51 usage notes 10 user cuts 64 79 V varselect directive 69 version directive 54 V12 2 USER S GUIDE 101 W workfiledir directive 40 66 workfilelim directive 40 66 write command 20 21 writebasis directive 51 writevector directive 51 102 IBM ILOG AMPL V12 2 USER S GUIDE
33. 30 R RAM requirement for linear programs 38 readbasis directive 51 readvector directive 51 refactor directive 47 relax optimality 69 relax directive 41 relobjdiff directive 70 repairtries directive 67 repeatpresolve directive 59 resolve directive 59 rinsheur directive 67 round directive 68 S save output 20 saving temporary files 20 scale directive 43 search directives for stopping and starting 71 sensitivity directive 53 siftopt 100 IBM ILOG AMPL directive 39 simplex algorithm basic solution 38 directives 44 singular directive 52 solution display information 20 save output 20 saving a solution 20 solution command 20 solution file ASCII format 21 binary format 21 temporary 19 solutionlim directive 71 solve codes 85 86 solver add solver options 19 choosing 17 display solution information 20 execute outside AMPL 22 interface 17 multiline options 18 options 18 problem files 19 set initial values 19 solution files 19 specify options 18 use of initial values 19 sosl directive 60 sos2 directive 60 stability directives for improving 49 startalgorithm directive 68 starting directives 50 stopping directives 50 strongcand directive 68 V12 2 USER S GUIDE strongit directive 68 submipnodelim directive 69 suffix bestnode 79 current 80 direction 77 down 80 iis 81 priority 77 unbdd 83 up 80 switches Cn 25 command line 25 en 25 f
34. CPLEX 000 e cece eee 29 Piecewise linear Programs 0 0 ect eee 30 Quadratic Programs ep esiae A ee 30 Quadratic Constraints cocida a ee 31 Specifying CPLEX Directives 00 eee e eee eee 32 Directives for Handling Infeasible Problems 00sec ween eee eee eee 33 Directive for TUNING 1 2 a ei c ee eee eee eee eee eee eee eee een aE 34 Using CPLEX for Continuous Optimization 0 00 cece eee eee 37 CPLEX Algorithms for Continuous Optimization o oooonororommmmomm 37 Directives for Problem and Algorithm Selection 0000e cece eee eee eee 38 Directives for Preprocessing 0 e seen eee eee eee eee 41 Directives for Controlling the Simplex Algorithm 00 0c e cece eee eee 44 Directives for Controlling the Barrier Algorithm 00 eee eee eee eee eee 47 Directives for Improving Stability 2 2 0 0 cece eee eee 49 Directives for Starting and Stopping cece eee eee eee eee 50 Directives for Controlling Output 00 0 c eee eee eee 53 Using CPLEX for Integer Programming 0200e sees eee eee 55 CPLEX Mixed Integer AlgorithM ooooocccncconoan eee eee 55 Directives for Preprocessing 00 c cece eee eee eee eee eee 57 Directives for Algorithmic Control 0 0 cece eee eee eee eee 60 Directives for Relaxing Optimality o oooooooncroorananan eee 69 Directives for Halting and Resuming the Search
35. Codes and Termination Messages Continued Number 540 541 542 550 551 552 553 554 555 556 557 558 559 560 561 562 563 570 Message at termination Diagonal QP Hessian has elements of the wrong sign QP Hessian has diag elements of the wrong sign QP Hessian is not positive definite problem has nonquadratic nonlinear constraints problem has a nonlinear objective problem has nonlinear integer variables problem has integer variables and a quadratic objective problem has unlinearized piecewise linear terms problem has a quadratic objective involving division by 0 nonlinear objective without CPLEX Barrier option for QPs CPLEX MIP option needed to handle piecewise linear terms quadratic constraint involves division by zero bug no quadratic terms in nonlinear constraint error in cplex_options surprise return from a CPLEX routine perhaps a driver bug constraint is not convex quadratic logical constraint is not an indicator constraint CPLEX licensing problem Following optimization CPLEX also returns an individual status for each variable and constraint This feature is intended mainly for reporting the basis status of variables after a linear program is solved either by the simplex method or by an interior point barrier method followed by a crossover routine In addition to the variables declared by var statements in an AMPL model solvers also define slack or artificial variables that are associated with c
36. O O O Y N PA O Figure 7 1 CPLEX Mixed Integer Algorithm the Search Tree There is a subproblem at each node of the tree and each node is explored by solving the associated subproblem IBM ILOG AMPL V12 2 USER S GUIDE 55 56 The algorithm starts with just a top or root node whose associated subproblem is the relaxation of the integer program the LP that results when all integrality restrictions are dropped If this relaxation happened to have an integer solution then it would provide an optimal solution to the integer program Normally however the optimum for the relaxation has some fractional valued integer variables Additional constraints called cutting planes are added to the subproblem These cutting planes tighten the feasible region Also heuristic algorithms for finding integer solutions are applied using the information from the solution of the subproblem A fractional variable is then chosen for branching and two new subproblems are generated each with more restrictive bounds for the branching variable For example if the branching variable is binary or 0 1 one subproblem will have the variable fixed at zero the other node will have it fixed at one In the search tree the two new subproblems are represented by two new nodes connected to the root Most likely each of these subproblems also has fractional valued integer variables in which case the branching process must be repeated successive branchings p
37. V12 2 USER S GUIDE ordertype directive 66 out of memory 22 output directives for controlling 71 73 directives for controlling output 53 P parallelmode directive 41 paramfile directive 34 paramfileprm directive 34 persistent option settings 26 perturbation directive 49 perturblimit directive 49 pgradient directive 44 piecewise linear programs transformation 30 polishafter_absmipgap directive 67 polishafter_intsol directive 67 polishafter_mipgap directive 67 polishafter_time directive 67 polishtime directive 67 poolagap directive 72 poolcapacity directive 72 pooldualdirective 72 poolgap directive 72 poolintensity directive 72 poolreplace directive 72 IBM ILOG AMPL poolstub directive 72 populate directive 72 populatelim directive 73 predual directive 42 preprocessing directives 41 directives integer programs only 57 prereduce directive 42 prerelax directive 59 presolve directive 43 presolvenode directive 59 prestats directive 43 pretunefile directive 34 pretunefileprm directive 34 pricing directive 46 primal directive 39 primal simplex algorithm 37 primal dual barrier algorithm 37 primalopt directive 39 priorities directive 67 priority suffix 77 probe directive 59 probetime directive 59 problem file ASCII format 21 binary format 21 problem files 19 V12 2 USER S GUIDE 99 Q gcpconvergetol directive 49 quadratic programming
38. al il default 7 nodeselect i2 default 1 These directives determine the criterion for choosing the next node from which to branch once a feasible integer solution has been found Depending on whether i2 is set to 1 2 or 3 CPLEX associates a value with each node and chooses a node based on these values For i2 1 a node s value is the bound on the integer optimum that is given by solving the LP subproblem at that node For 12 2 or i2 3 a node s value is an estimate of the best integer objective that can be achieved by branching from that node estimates of node objective values are derived from so called pseudocosts which are in turn derived from the solutions to the LP subproblems Settings 2 and 3 differ regarding the exact nature of the estimated objective Depending on the value at the current most recently created active node CPLEX either branches from that node or else backtracks to the node that has the best bound 12 1 or best estimate 12 2 or i2 3 among all active nodes When used in conjunction with best estimate node selection 12 2 the bbinterval setting 11 controls the interval for selecting the best bound node Decreasing this interval may be useful when best estimate finds good solutions but makes little progress moving the bound Conversely increasing 11 may help when the best estimate node selection does not find any good integer solutions The backtracking decision is made by comparing the value bound or estima
39. ap 69 mipinterval 73 mipkappa 74 mipsearch 65 mipstartstatus 58 mipstartvalue 58 migcpstrat 65 mircuts 65 netfind 47 netopt 40 nodefile 66 nodelim 71 nodeselect 62 objdifference 70 optimality 50 ordering 48 ordertype 66 parallelmode 41 paramfile 34 paramfileprm 34 perturbation 49 perturblimit 49 pgradient 44 polishafter absmipgap 67 polishafter_intsol 67 polishafter mipgap 67 polishafter_time 67 polishtime 67 poolagap 72 poolcapacity 72 pooldual 72 poolintensity 72 poolreplace 72 poolstub 72 populate 72 V12 2 USER S GUIDE 95 populatelim 73 predual 42 prereduce 42 prerelax 59 presolve 43 presolvenode 59 prestats 43 pretunefile 34 pretunefileprm 34 pricing 46 primal 39 primalopt 39 priorities 67 probe 59 probetime 59 qcpconvergetol 49 readbasis 51 readvector 51 refactor 47 relax 41 relobjdiff 70 repairtries 67 repeatpresolve 59 resolve 59 rinsheur 67 round 68 scale 43 sensitivity 53 siftopt 39 singular 52 solutionlim71 sos1 60 sos2 60 startalgorithm 68 strongcand 68 strongit 68 submipnodelim 69 threads 40 timelimit 52 71 timing 54 74 treememlim 71 tunedisplay 34 tunefile 34 tunefileprm 34 tunefix 34 96 IBM ILOG AMPL tunefixfile 34 tunerepeat 35 tunetime 35 uppercutoff 70 upperobj 51 varselect 69 version 54 workfiledir 40 66 workfilelim 40 66 writebasis 51 writevector 51 directives algorithmic control 60 append additional CPLEX directives 33 control barrier al
40. ates a refactorization frequency by a heuristic formula You can determine the frequency that CPLEX is using by setting the display directive described below to 1 Since each update to the factorization uses more memory CPLEX may reduce the factorization frequency if memory is low In extreme cases the basis may have to be refactored every few iterations and the algorithm will be very slow Given adequate memory CPLEX s performance is relatively insensitive to changes in refactorization frequency For a few extremely large difficult problems you may be able to improve performance by reducing i from the value that CPLEX chooses netfind i default 1 This directives governs the method used by the CPLEX network optimizer to extract a network from the linear program The value of i influences the size of the network extracted potentially reducing optimization time The default value i 1 extracts only the natural network from the problem CPLEX then invokes its network simplex method on the extracted network In some cases CPLEX can extract a larger network by multiplying rows by 1 reflection scaling and rescaling constraints and variables so that more matrix coefficients are plus or minus 1 Setting the netfind directive to 2 enables reflection scaling only while setting it to 3 allows reflection scaling and general scaling Directives for Controlling the Barrier Algorithm Several key strategies of the barrier algorithm can be changed t
41. ation to a linear program can be done if the following conditions are met Any piecewise linear term in a minimized objective must be convex its slopes forming an increasing sequence as in lt lt 1 1 3 5 5 1 0 1 5 3 gt gt x j Any piecewise linear term in a maximized objective must be concave its slopes forming a decreasing sequence as in lt lt 1 3 1 5 0 5 0 25 gt gt x 3 Any piecewise linear term in the constraints must be either convex and on the left hand side of a lt constraint or equivalently the right hand side of a constraint or else concave and on the left hand side of a constraint the right hand side of a lt constraint In all other cases the transformation is to a mixed integer program AMPL automatically performs the appropriate conversion sends the resulting linear or mixed integer program to CPLEX and converts the solution into user defined variables The conversion has the effect of adding a variable to correspond to each linear piece when the above rules are not satisfied additional integer variables and constraints must also be introduced Quadratic Programs This user guide provides but a brief description of quadratic programming In effect it is assumed that you are familiar with the area Interested users may wish to consult a good reference such as Practical Optimization by Gill Murray and Wright Academic Press 1981 for more details A mathematical description of a q
42. blems or greater than r2 for minimization problems As a result any solution returned by CPLEX will have an optimal value at least as large as rl or as small as r2 This feature can be useful in conjunction with other limits on the search but too high a value of r1 or too low a value of r2 may result in no integer solution being found objdifference r1 default 0 0 relobjdiff r2 default 0 0 This directive automatically updates the cutoff to more restrictive values Normally the incumbent integer solution s objective value is used as the cutoff for subsequent nodes When r1 gt 0 the cutoff is instead the incumbent s value r1 if minimizing or r1 if maximizing This forces the mixed integer optimization to ignore integer solutions that are not at least r1 better than the one found so far As a result there tend to be fewer nodes generated and the algorithm terminates more quickly but the true integer optimum may be missed if its objective value is within rl of the best integer objective found If r1 0 r2 is used to adjust the objective function value during the optimization For a maximization problem r2 times the absolute value of the objective function value is added to the best feasible objective value obtained so far Similarly if the objective is to be minimized r2 times the absolute value is subtracted from the best so far feasible objective value Subsequent nodes are ignored if their linear relaxations have optimal values w
43. blems where otherwise CPLEX will not find a solution heuristicfreq i default 0 Use the heuristicfreg directive to specify the frequency with which CPLEX applies a heuristic at the nodes This can help find solutions missed using other settings The default value i 0 instructs CPLEX to use internal logic to decide when to apply the heuristic To suppress application of the heuristic at all nodes let i 1 To specify the node frequency with which CPLEX applies the heuristic set i to a positive integer IBM ILOG AMPL V12 2 USER S GUIDE 63 lazy i default 3 This directive tells CPLEX how to treat constraints with the lazy suffix At the default value constraints with lazy suffix of 1 are treated as lazy constraints and those with lazy suffix of 2 are treated as user cuts When the value is 0 all constraints with the lazy suffix are treated as ordinary constraints When the value is 1 those with suffix of 1 are treated as lazy constraints and all others are ordinary constraints and when the value is 2 those with suffix of 2 are treated at user cuts and all others are treated as ordinary constraints mipalgorithm il default 0 mipcrossover i2 default 1 This directive specifies the algorithm or combination of algorithms that CPLEX will apply to solve the LP subproblem at each branch amp cut node The recognized values of i1 are Table 7 3 Settings for the mipcrossover Directive 0 Automatic 1 Primal simplex 2 Dual
44. c eee eee 45 Dual Pricing Indicator dgradient 2 cece eee eee eee eee eee eee 46 Values of the AMPL Option send_statuSeS 20 eee 59 Settings for the mipemphasis Directive 06 c eee eee eee eee 62 Settings for the mipcrossover Directive 2 06 c eee eee eee eee 64 Settings for the round Directive 2 20 c ee eee eee eee eee eee eee 68 Settings for the startalgorithm Directive 0 cece eee eee eee 68 Settings for the lazy Directive ooooooocnccocrnnana eee eee eee eee eee ee eee 79 Interpretation of Numeric Result Codes 0c eee eee eee eee 86 Solve Codes and Termination Messages 2 00 eee e eee eee eee eee eens 86 CPLEX SYNONYMS esos cece ss eee eee a A eae Cee eee RE ae eee ee ce ee ee oes 91 IBM ILOG AMPL V12 2 USER S GUIDE 7 IBM ILOG AMPL V12 2 USER S GUIDE Welcome to AMPL Welcome to IBM ILOG AMPL a comprehensive powerful algebraic modeling language for problems in linear nonlinear and integer programming AMPL is based upon modern modeling principles and utilizes an advanced architecture providing flexibility most other modeling systems lack AMPL has been proven in commercial applications and is successfully used in demanding model applications around the world AMPL helps you create models with maximum productivity By using AMPL s natural algebraic notation even a very large complex model can often be stated in a concise often less than one page understandable form As
45. d display information about the condition number often called kappa of the basis matrix in subproblem solves At the default value of i 0 no kappa values are computed or displayed At the value i 1 kappa values are sampled and at the value i 2 a kappa value is computed for every subproblem Computing kappa values is additional work and thus will increase the solve time but usually this increase is not signficant timing i default 0 This directive can be used to display a summary of processing times It works the same for integer programming as for linear programming as described in Using CPLEX for Continuous Optimization on page 37 Common Difficulties 74 The following discussion addresses the difficulties most often encountered in solving integer programs with CPLEX Running Out of Memory The most common difficulty when solving MIP problems is running out of memory This problem arises when the branch amp cut tree becomes so large that insufficient memory is available to solve an LP subproblem As memory gets tight you may observe warning messages while CPLEX attempts to navigate through various operations within limited memory If a solution is not found shortly the solutions process will be terminated with an error termination message The tree information saved in memory can be substantial CPLEX saves a basis for every unexplored node When utilizing the best bound or best estimate method of node selection the list o
46. e during Phase II numerical difficulties have arisen Adjusting the algorithmic tolerances controlled by these directives may help Decreasing the feasibility tolerance increasing the optimality tolerance and or increasing the Markowitz tolerance will typically improve numerical behavior The feasibility tolerance r1 gt 0 specifies the degree to which a linear program s basic variables may violate their bounds You may wish to lower r1 after finding an optimal solution if there is any doubt that the solution is truly optimal but if it is set too low CPLEX may falsely conclude that the problem has no feasible solution Valid values for r1 lie between 1e 9 and 0 1 The Markowitz threshold r2 lt 1 influences the order in which variables are eliminated during basis factorization Increasing r2 may yield a more accurate factorization and consequently more accurate computations during iterations of the simplex algorithm Too large a value may produce an inefficiently dense factorization however Valid values for r2 lie between 0 0001 and 0 99999 The optimality tolerance r3 gt 0 specifies how closely the optimality or dual feasibility conditions must be satisfied for CPLEX to declare an optimal solution Valid values for r3 lie between 1e 9 and 0 01 Directives for Starting and Stopping 50 Normally CPLEX uses an internal procedure to determine a starting point for the simplex algorithm then iterates to optimality The following directives o
47. e in a file with the run extension You can then type C gt ampl steel mod steel dat steel run which accomplishes the same thing as C X gt ampl ampl include steel mod ampl include steel dat ampl include steel run ampl quit C gt IBM ILOG AMPL V12 2 USER S GUIDE If you intend to load several files and solve a problem but you want to type a few interactive commands in the middle of the process type the character in place of a filename AMPL processes the files on the command line from left to right when it encounters the symbol it displays the amp1 prompt and accepts commands until you type end For example you could type C gt ampl steel mod steel dat steel run ampl let avail 50 ampl end This will solve the problem as before but with the parameter avail set to 50 instead of 40 the value specified in steel dat To start AMPL load a model and data file and wait for your interactive commands type C gt ampl steel mod steel dat IBM ILOG AMPL V12 2 USER S GUIDE 15 16 IBM ILOG AMPL V12 2 USER S GUIDE AMPL Solver Interaction Choosing a Solver AMPL s solver interface supports linear nonlinear and mixed integer models with no built in size limitations This interface is rich enough to support many of the features used by advanced solvers to improve performance and solution accuracy such as piecewise linear constructs representation of network problem
48. e LP subproblems at the nodes of the branch and bound tree By default CPLEX decides automatically Set i 1 to force node presolve Set i 2 to also probe on integer infeasible variables at the nodes Set i 1 to prevent any node presolve The default setting usually works best probe i default 0 This directive controls whether CPLEX should perform probing before solving the MIP Probing can lead to dramatic reductions in the problem size but can also consume large amounts of time By default 0 CPLEX automatically decides whether to perform probing To disable probing set i 1 To enable probing set it to a value of 1 2 or 3 A larger value results in an increased level of probing More probing can lead to greater reductions in problem size but also significant increases in probing time probetime i default le 75 This directive limits the amount of time in seconds spent probing repeatpresolve i default 1 This directive tells CPLEX whether to re apply presolve with or without cuts to a MIP model after processing at the root is otherwise complete The default of i 1 lets CPLEX choose Set i 1 to represolve without the generated cuts and set i 2 to represolve using the generated cuts Set i 3 to represolve with the generated cuts and allow new cuts Set i 0 to prohibit represolve resolve i default 1 This directive at its default value i 1 tells CPLEX to solve the problem again with presolve turned off after CPLEX has returned
49. e below shows the types of auxiliary files that can be created and the letter you use to request them via the AMPL option auxfiles Table 3 1 Auxiliary Files Letter Extension Description a adj adjustment to objective for example to compensate for fixed variables eliminated by presolve c col AMPL names of the variables columns sent to the solver f fix names of variables fixed by presolve and the values to which they are fixed a row AMPL names of the constraints rows sent to the solver s slc names of slack constraints eliminated by presolve because they can never be binding u unv names of variables dropped by presolve because they are never used in the problem instance IBM ILOG AMPL V12 2 USER S GUIDE 21 Running Solvers Outside AMPL With the write and solution commands you can arrange to execute your solver outside the AMPL session You might want to do this if you receive an out of memory message from your solver not from AMPL itself When the solver is invoked from within AMPL a fair amount of memory is already used for the AMPL Modeling System program code and for data structures created by AMPL for its own use in memory If you execute the solver alone it can use all available memory To run your solver separately first use AMPL to create a problem file C gt ampl ampl model steel mod data steel dat ampl write bsteel ampl quit Then run your solver with a command like
50. e handled in different ways It is occasionally useful however to make fine distinctions among different solver termination conditions All valid solve codes with the corresponding termination message from CPLEX are listed in the table below Table 9 2 Solve Codes and Termination Messages Number Message at termination O optimal solution 1 primal has unbounded optimal face 2 optimal integer solution 3 optimal integer solution within mipgap or absmipgap 100 best solution found primal dual feasible 110 optimal with unscaled infeasibilities 111 integer optimal with unscaled infeasibilities IBM ILOG AMPL V12 2 USER S GUIDE Table 9 2 Solve Codes and Termination Messages Continued Number Message at termination 200 infeasible problem 201 infeasible with phase II singularities 202 infeasible with phase singularities 204 converged dual feasible primal infeasible 205 converged primal and dual infeasible 206 best solution found primal infeasible 207 best solution found primal dual infeasible 208 infeasible or unbounded in presolve 209 integer infeasible or unbounded in presolve 210 infeasible problem found by dualopt dunbdd returned 220 integer infeasible 300 unbounded problem 301 converged primal feasible dual infeasible 302 best solution found dual infeasible 310 unbounded problem found by primalopt unbdd returned 320 integer unbounded ray 400 phase II objective limit exceeded 401 phase ll iteration limit 402 phase
51. e processor or core and the threads and parallelmode directives are at their default values is a deterministic variant of the concurrentopt algorithm which is described below For problems with quadratic constraints only the barrier method is used and there is no crossover algorithm The simplex algorithm maintains a subset of basic variables or a basis equal in size to the number of constraints A basic solution is obtained by solving for the basic variables when the remaining nonbasic variables are fixed at appropriate bounds Each iteration of the algorithm picks a new basic variable from among the nonbasic ones steps to a new basic solution and drops some basic variable at a bound The coefficients of the variables form a constraint matrix and the coefficients of the basic variables form a nonsingular square submatrix called the basis matrix At each iteration the simplex algorithm must solve certain linear systems involving the basis matrix For this purpose CPLEX maintains a factorization of the basis matrix which is updated during most iterations and is occasionally recomputed The sparsity of a matrix is the proportion of its elements that are not zero The constraint matrix basis matrix and factorization are said to be relatively sparse or dense according to their proportion of nonzeros Most linear programs of practical interest have many zeros in all the relevant matrices and the larger ones tend also to be the sparser T
52. e solution but will usually be slower overall to reach the optimal integer solution A pseudocost rule i1 2 estimates the worsening of the objective that will result by forcing each fractional variable to an adjacent integer and uses these degradations in an internal heuristic for choosing a variable to branch on This setting tends to be most effective when the problem embodies complex tradeoffs and the dual variables have an economic interpretation Strong branching i 3 considers several different branches by actually solving subproblems for different choices of branching variable The variable yielding the best results is then chosen Strong branching requires more time for each node but usually fewer nodes to solve the problem This strategy works especially well on binary problems where the number of binary variables is significantly greater than the number of rows It is also useful when memory is limited creating fewer nodes requires less memory Pseudo reduced costs i 4 are related to pseudocosts i 2 but are less expensive to compute They may therefore be advantageous on models whose LP relaxation contains many hundreds or thousands of fractional variables that are potentially to be branched upon Directives for Relaxing Optimality In dealing with a difficult integer program you may need to settle for a good solution rather than a provably optimal one The following directives offer various ways of weakening the optimali
53. e specific characteristics of the linear programs you are solving and must be determined through experimentation pgradient i default 0 This directive governs the primal simplex algorithm s choice of a pricing procedure that determines which variable is selected to enter the basis at each iteration Your choice is 44 IBM ILOG AMPL V12 2 USER S GUIDE likely to make a substantial difference to the tradeoff between computational time per iteration and the number of iterations As a rule of thumb if the number of iterations to solve your linear program exceeds three times the number of constraints you should consider experimenting with alternative pricing procedures The recognized values of i are as follows Table 6 3 Settings for the pgradient Directive 1 Reduced cost pricing Hybrid reduced cost devex pricing Devex pricing Steepest edge pricing Steepest edge pricing in slack pace A OU N O Full pricing The reduced cost procedures are sophisticated versions of the pricing rules most often described in textbooks The devex and steepest edge alternatives employ more elaborate computations which can better predict the improvement to the objective offered by each candidate variable for entering the basis Compared to the default of i 0 the less compute intensive reduced cost pricing i 1 may be preferred if your problems are small or easy or are unusually dense say 20 to 30 nonzeros per column Converse
54. e two directives impact strong branching see varsel directive below The strongcand directive controls the size of the candidate list for strong branching The strongit parameter limits the number of iterations performed on each branch in strong branching The default setting of i2 0 which allows CPLEX to determine the iteration parameter will generally suffice You can use low values of i1 and i2 if the time per strong branching node appears excessive you may reduce the time per node yet still maintain the performance Conversely if the time per node is reasonable but CPLEX makes limited progress consider increasing the values IBM ILOG AMPL V12 2 USER S GUIDE submipnodelim default 500 The submipnodel im directive restricts the number of nodes searched during application of the RINS heuristic and the processing of MIP start values varselect i default 0 Once a node has been selected for branching this directive determines how CPLEX chooses a fractional valued variable to branch on By default i 0 the choice is made by an internal heuristic based on the problem and its progress The maximum infeasibility rule 1 chooses the variable with the largest fractional part This forces larger changes earlier in the tree but it tends to disregard the objective function in doing so The minimum infeasibility rule i 1 chooses the variable with the smallest fractional part This may lead more quickly to a first integer feasibl
55. easible solution but dropping any one of them will permit a solution to be found to the remaining ones Of course in our example we shouldn t actually drop the lower bounds on IBM ILOG AMPL V12 2 USER S GUIDE the Buy variable we could end up with negative values However we could reduce certain lower bounds to zero Direction of Unboundedness For an unbounded linear program one that effectively has a minimum objective value of Infinity or a maximum of Infinity the solution is characterized by a feasible point together with a direction of unboundedness from that point On return from CPLEX the values of the variables define the feasible point The direction of unboundedness is given by an additional value associated with each variable through the associated solver defined suffix unbdd An application of the direction of unboundedness can be found in our example of Benders decomposition applied to a transportation location problem One part of the decomposition scheme is a subproblem obtained by fixing the variables Build i which indicate the warehouses that are to be built to trial values build i When all values build i are set to zero no warehouses are built and the primal subproblem is infeasible As a result the dual formulation of the subproblem which always has a feasible solution is unbounded When this dual problem is solved from the AMPL command line CPLEX returns the direction of unboundedness i
56. ecifying CPLEX Directives 32 In many instances you can successfully apply CPLEX by simply specifying a model and data setting the solver option to cplex and typing solve For larger linear programs and especially the more difficult integer programs however you may need to pass specific options also referred to as directives to CPLEX to obtain the desired results To give directives to CPLEX you must first assign an appropriate character string to the AMPL option called cplex_options When CPLEX is invoked by solve it breaks this string into a series of individual directives Here is an example ampl model diet mod ampl data diet dat ampl option solver cplexamp ampl option cplex options crash 0 dual ampl feasibility 1 0e 8 scale 1 ampl lpiterlim 100 ampl solve CPLEX 11 0 0 crash 0 dual feasibility le 08 scale 1 lpiterlim 100 CPLEX 11 0 0 optimal solution objective 88 2 1 iterations 0 in phase I CPLEX confirms each directive it will display an error message if it encounters one that it does not recognize CPLEX directives consist of an identifier alone or an identifier followed by an sign and a value a space may be used as a separator in place of the You may store any number of concatenated directives in cplex_options The example above shows how to type all the directives in one long string using the character to indicate that the string continues on the next line Alternatively yo
57. ed in suffix npool on the problem populate i default 0 This directive tells CPLEX to run its populate algorithm in order to generate more solutions When i 0 only the usual MIP optimization is run When i 1 populate is run after MIP optimization When i 2 populate is run instead of MIP optimization IBM ILOG AMPL V12 2 USER S GUIDE populatelim i default 20 Limits the number of solutions added to the solution pool by the populate algorithm Directives for Controlling Output When invoked by solve CPLEX normally returns just a few lines to your screen to summarize its performance The following directives let you choose more output which may be useful for monitoring the progress of a long run or for comparing the effects of other directives on the behavior of the branch amp cut algorithm Output normally comes to the screen but may be redirected to a file by specifying solve gt filename mipdisplay i1 default 0 mipinterval i2 default 0 The default of 11 0 produces a minimal few lines of output from CPLEX summarizing the results of the run When i1 1 a single log line is displayed for every integer solution found The information includes the number of nodes processed and the objective values of the best integer solution found so far and of the best unprocessed node subproblem The optimal value lies between these two When i1 2 a more detailed log line is displayed once every i2 nodes as well as for each node w
58. ememlim r default 1 0e75 The total size of the branch amp cut tree is limited to r megabytes Directives to Manage the Solution Pool CPLEX can store multiple solutions for integer programs in a solution pool The poolstub directive must be specified in order to display and query the solution pool its value is used to recover the solutions For example to display all the solutions in the pool use these commands in AMPL option cplex options poolstub somename solve New problem suffix npool should be returned If it s positive we can examine the solutions for i in 1 Current npool solution somename i amp sol display _varname _var IBM ILOG AMPL V12 2 USER S GUIDE 71 72 CPLEX will add all the solutions it finds during the usual branch and cut algorithm to the pool with the default settings of the solution pool parameters The populate and poolintensity directives can be used to increase the number of solutions added to the pool poolagap r1 default 1e75 poolgap r2 default 1e75 These directives restrict solutions added to the pool based on their objective values relative to the best solution value currently in the pool Solutions will be added to the solution pool when best solution solution lt r1 or best solution solution 1 0 best solution lt r2 poolcapacity i default 2100000000 Specifies the number of solutions to keep in the solution pool pooldual i
59. er stopping criteria have been set the process might continue until the search is complete or your computer s memory is exhausted In general you should set at least one limit on the number of nodes processed number of improved solutions found or total processing time using the CPLEX directives given above Setting limits ensures that the tree search will terminate in reasonable time You can then inspect the solution and if necessary re run the problem using different directive settings Consider some of the shortcuts described above for improving performance particularly those for relaxing optimality They may provide you with an optimal or very nearly optimal solution even though a proof of optimality would require more computer resources than you have available Difficult MIP Subproblems Certain classes of MIP problems occasionally produce very difficult subproblems The subproblems may be dual degenerate Or an alternative algorithm such as primal simplex or barrier may perform better with the particular model IBM ILOG AMPL V12 2 USER S GUIDE 75 76 If the subproblems are dual degenerate consider setting mipalgorithm to choose primal simplex for solving subproblems If the subproblems are taking many iterations per node to solve consider setting dgradient to use a stronger dual pricing algorithm Most often one would use dual steepest edge pricing In cases where the barrier algorithm is selected to solve the initia
60. esktop you can use AMPL s shell command to invoke an editor from within AMPL You can use any editor that saves files in ASCII format Windows command line DOS users can use edit or notepad and UNIX users vi or emacs If you are using edit under DOS for instance you can type ampl shell edit steel dat Use editor menus and commands to edit your file then save it and exit the editor At the ampl prompt you can type new AMPL commands such as ampl reset data ampl data steel dat Note that editing a file in a text editor does not affect your AMPL session until you explicitly reload the edited file as shown above Running AMPL in Batch Mode 14 If you have previously developed a model and its data and would like to solve it and display the results automatically you can create a file containing the commands you would like AMPL to execute and specify that file at the command line when you run AMPL For example you might create a file called steel run containing the commands model steel mod data steel dat option solver cplexamp solve display Make gt steel ans Note that this assumes that steel run is in the same directory as the model and data files and that AMPL can be found on the path You can then run AMPL as follows C gt ampl steel run A more flexible approach which is a commonly followed convention among AMPL users is to put just the AMPL commands the last three lines in the example abov
61. f unexplored nodes can become very long for large or difficult problems How large the unexplored node list can become is entirely dependent on the actual amount of physical memory available the size of the problem and the solution algorithm selected Certainly increasing the amount of memory available extends the problem solving capability Unfortunately once a problem has failed because of insufficient memory you cannot project how much further the process needed to go or how much memory would be required to ultimately solve it Some parts of the branch amp cut tree can be stored in compressed files either on disk or in memory when the nodefile directive is used Storing part of each node in files will allow more nodes to be explored once the workf ilelim amount of memory has been used See the discussion of the nodefile directive This feature may be especially useful if you use steepest edge pricing for subproblem simplex pricing strategy because the pricing information consumes a lot of memory IBM ILOG AMPL V12 2 USER S GUIDE The best approach to reduce memory usage is to modify the solution process Switching to a higher backtrack parameter value and best estimate node selection strategy or depth first search node selection which is even more extreme often works Depth first search rarely generates a large unexplored node list since CPLEX will be diving deep into the branch amp cut tree rather than jumping around within it This
62. ffixes apply to the constant value or right hand side Details on CPLEX defined suffixes are provided in Defined Suffixes for CPLEX on page 77 IBM ILOG AMPL V12 2 USER S GUIDE 53 54 timing i default 0 When this directive is changed to 1 from its default value of 0 a summary of processing times is displayed to standard output Input 0 06 CPU 0 06 Wall Solve 6 42 CPU 6 42 Wall Output 0 05 CPU 0 05 Wall Input is the time that CPLEX takes to read the problem from a file that has been written by AMPL Solve is the time that CPLEX spends trying to solve the problem Output is the time that CPLEX takes to write the solution to a file for AMPL to read CPU values provide processor time whereas Wa11 values provide elapsed time Setting i 2 writes the timing information to standard error and setting i 3 directs the information to both the standard output and the standard error The latter two options are only interesting for UNIX CPLEX for AMPL users version This directive causes the display of the CPLEX version being used to solve the problem IBM ILOG AMPL V12 2 USER S GUIDE Using CPLEX for Integer Programming CPLEX Mixed Integer Algorithm For problems that contain integer variables CPLEX uses a branch amp cut approach The optimizing algorithm maintains a hierarchy of related linear programming subproblems referred to as the search tree and usually visualized as branching downward O N o o Yo N
63. gorithm 47 control output 53 71 73 control simplex algorithm 44 CPLEX directives 32 CPLEX directives for linear programs 38 halt and resume search 71 improving stability 49 infeasible problems 41 preprocessing 41 preprocessing integer programs only 57 relax optimality 69 select algorithm 38 starting and stopping 50 store multiple 32 disjcuts directive 65 display command 20 doperturb directive 49 down suffix 80 dual directive 39 dual pricing indicator 46 dual simplex algorithm 37 dualopt directive 39 dualthresh directive 39 V12 2 USER S GUIDE E eachcutlim directive 58 editing using a text editor 13 end AMPL session 13 F feasibility directive 50 feasopt directive 33 feasoptobj directive 33 file creating auxiliary 21 load several files 15 predefined commands 26 temporary directory 23 file directive 53 flowcuts directive 65 flowpathcuts directive 65 fpheur directive 63 fraccand directive 58 fraccuts directive 65 fracpass directive 58 G global thread limit 40 gubcuts directive 65 H heuristicfreq IBM ILOG AMPL directive 63 iis suffix 81 lisfind directive 33 impliedcuts directive 65 infeasible problems directives 41 installation 10 integer programs 29 integrality directive 70 L launching AMPL 13 lazy directive 64 78 linear programs 29 CPLEX solution method 37 logfile directive 53 lowercutoff directive 70 lowerobj directive 51 l
64. gramming 2nd edition as well as the integer programs described in Chapter 20 Integer programs may be pure all integer variables or mixed some integer and some continuous variables integer variables may be binary taking values O and 1 only or may have more general lower and upper bounds For the network linear programs described in Chapter 15 CPLEX also incorporates an especially fast network optimization algorithm The barrier algorithmic option to CPLEX though originally designed to handle linear programs also allows the solution of a special class of nonlinear problems namely quadratic programs QPs as described later in this section However CPLEX does not solve general non QP nonlinear programs For instance if you attempt to solve the following nonlinear problem described in Chapter 18 of the AMPL book CPLEX will generate an error message ampl model models nltransd mod ampl data models nltrans dat ampl option solver cplexamp ampl solve at0 nl contains a nonlinear objective ampl IBM ILOG AMPL V12 2 USER S GUIDE 29 30 This restriction applies if your model uses any function of variables that AMPL identifies as not linear even a function such as abs or min that shares some properties of linear functions Piecewise linear Programs CPLEX does solve piecewise linear programs as described in Chapter 17 if AMPL transforms them to problems that CPLEX solvers can handle The transform
65. he amount of RAM memory required by CPLEX grows with the size of the linear program which is a function of the numbers of variables and constraints and the sparsity of the coefficient matrix The factorization of the basis matrix also requires an allocation of memory the amount is problem specific depending on the sparsity of the factorization When memory is limited CPLEX automatically makes adjustments that reduce its requirements but that usually also reduce its optimization speed The CPLEX directives in the following subsections apply to the solution of linear programs including network linear programs The letters i and r denote integer and real values respectively Directives for Problem and Algorithm Selection 38 CPLEX consults several directives to decide how to set up and solve a linear program that it receives The default is to apply the dual simplex method to the linear program as given substituting the network variant if the AMPL model contains node and arc declarations The following discussion indicates situations in which you should consider experimenting with alternatives IBM ILOG AMPL V12 2 USER S GUIDE dualthresh i default 32000 primal dual Every linear program has an equivalent opposite linear program the original is customarily referred to as the primal LP and the equivalent as the dual For each variable and each constraint in the primal there are a corresponding constraint and variable respective
66. here an integer solution is found A indicates lines of where an integer solution is found When i1 3 CPLEX also prints information on node cut and node presolve The LP iteration log for the root node 11 4 and for all subproblems 11 5 can also be displayed The default value of i2 0 produces log information at relatively high frequency during the early stages of the solve and displays log lines at progressively longer intervals as the algorithm continues In other words CPLEX displays information frequently in the beginning and progressively less often as it works When i2 is positive a value of i2 1 gives a complete picture of the branch amp cut process which may be instructive for small examples With a larger choice of i2 this setting can be very useful for evaluating the progress of long runs the log line includes a count of the number of active nodes this count gives an indication of the rate at which the search tree is growing or shrinking in memory With a negative value of i2 CPLEX varies how often it prints log lines It prints them more frequently when the value is close to zero and less frequently as the value is set further below 0 The frequency also depends on progress in the solve with log lines printed at higher frequency at the beginning of the solve and with decreasing frequency as the solve progresses IBM ILOG AMPL V12 2 USER S GUIDE 73 mipkappa i default 0 This directive tells CPLEX to collect an
67. hrough CPLEX directives If you are repeatedly solving a class of linear programs that requires substantial computer time experimentation with alternative strategies can be worthwhile baralg il default 0 The automatically determined choice of barrier algorithm i1 0 is usually the fastest However on primal or dual infeasible problems the infeasibility estimate start algorithm 11 1 or the infeasibility constant start algorithm i1 2 may improve numerical stability possibly at the cost of speed Setting i1 3 selects the standard barrier algorithm bargrowth r default le 12 This directive is used to detect unbounded optimal faces At higher values the barrier algorithm will be less likely to conclude that the problem has an unbounded optimal face but more likely to have numerical difficulties if the problem does have an unbounded face Any positive number is acceptable input IBM ILOG AMPL V12 2 USER S GUIDE 47 48 barcorr i default 1 CPLEX may perform centering corrections if it encounters numerical difficulties during the barrier method optimization By default i 1 the barrier solver automatically computes an estimate for the maximum number of centering corrections done at each iteration If the automatic estimate is computed to be 0 setting the value to a positive integer may improve the numerical stability of the algorithm probably at the expense of computation time barobjrange r default le 20 This directive se
68. ibed in the Continuous Optimization section but it also makes some changes for the branch amp cut algorithm notably using node files When experimenting with these possibilities it is also a good idea to include directives that set stopping criteria and display informative output these are described in the next two subsections If you consistently fail to receive any useful solution in response to the solve command after a reasonable amount of time and are in doubt as to how to proceed consult the troubleshooting tips at the end of this section Directives for Preprocessing All of the preprocessing directives described in Using CPLEX for Continuous Optimization are also applicable to problems that specify integer valued variables The following directives control additional preprocessing steps that are applicable to certain mixed integer programs only aggcutlim i default 3 This directive controls the number of constraints that can be aggregated for generating flow cover and mixed integer rounding cuts In most cases the default setting of 3 will be satisfactory Set it to 0 to prevent any aggregation boundstr i default 1 Bound strengthening tightens the bounds on variables in mixed integer programs This may enable CPLEX to fix the variable and remove it from consideration during the branch amp cut algorithm By default i 1 CPLEX automatically decides whether to perform bound strengthening This reduction usually improves perf
69. icular number of passes mipstartstatus i1l default 1 mipstartvalue i2 default 1 These directives control how existing MIP solution information is used by CPLEX The default value of i1 1 tells CPLEX to use incoming variable and constraint statuses Incoming statuses can be ignored by setting i1 0 Note however that mipstartstatus is normally overridden by the AMPL option send_statuses which can take on the following values IBM ILOG AMPL V12 2 USER S GUIDE Table 7 1 Values of the AMPL Option send_statuses 0 gt gt send no solver status values 1 default gt gt send statuses if there are no integer variables 2 gt send statuses even if there are integer variables By default 12 1 variable values are checked to see if they provide an integer feasible solution before the problem is optimized If an integer feasible solution is found the objective function value is used as a cutoff during branch amp cut To ignore existing values set i2 0 prerelax i default 1 Setting i 1 invokes the CPLEX presolve for the linear program associated with the initial relaxation of a mixed integer program All other presolve settings apply Sometimes additional reductions can be made beyond any previously performed MIP presolve reductions The default setting of i 1 lets CPLEX decide whether or not it should presolve the relaxation presolvenode i default 0 The presolvenode directive determines how CPLEX applies its presolve to th
70. ies directory is sub divided into industry specific subdirectories The models have been brought together from a variety of sources Together they provide a palette of AMPL models that you may use as a starting point for your projects IBM ILOG AMPL V12 2 USER S GUIDE 11 12 IBM ILOG AMPL V12 2 USER S GUIDE Using AMPL Running AMPL If you have added the AMPL installation directory to the search path you can run AMPL from any directory Otherwise run AMPL by moving to the AMPL directory and typing amp1 at the shell prompt At the amp1 prompt you can type any AMPL language statement or any of the commands described in Section A 14 of the book AMPL A Modeling Language for Mathematical Programming 2nd edition To end the session type quit at the amp1 prompt Using a Text Editor Generally you will edit your model and data both expressed using AMPL language statements in a text editor and type commands at the amp1 prompt to load your model and data solve a problem and inspect the results Although you could type in the statements of a model at the amp1 prompt AMPL does not include a built in text editor so you cannot use AMPL commands to edit the statements you have previously entered Microsoft Windows users on PCs and XWindows users on UNIX systems should open separate windows for editing files and running AMPL IBM ILOG AMPL V12 2 USER S GUIDE 13 If you cannot open multiple windows on your d
71. imize While AMPL completely specifies the problem and its objective sense it is possible to change the objective sense after specifying the model The two directives instruct CPLEX to set the objective sense to be minimize or maximize respectively Directives for Preprocessing Prior to applying any simplex algorithm CPLEX modifies the linear program and initial basis in ways that tend to reduce the number of iterations required The following directives select and control these preprocessing features aggregate il default 1 aggfill i2 default 10 When i1 is left at its default value of 1 CPLEX looks for constraints that possibly after some rearrangement define a variable x in terms of other variables two variable constraints of the form x y b constraints of the form x j yj where x appears in less than i2 other constraints Under certain conditions both x and its defining equation can be eliminated from the linear program by substitution In CPLEX s terminology each such elimination is an aggregation of the linear program When i1 is 1 CPLEX decides how many passes to perform Set i1 IBM ILOG AMPL V12 2 USER S GUIDE 41 to 0 to prevent any such aggregations Set i1 to a positive integer to specify the precise number of passes Aggregation can yield a substantial reduction in the size of some linear programs such as network flow LPs in which many nodes have only one incoming or one outgoing arc If i2 gt 2
72. ion settings To avoid this problem you can use AMPL s notation for options the symbol Soption_name is replaced by the current value of option_name To add an optimality tolerance to the CPLEX options in the above example you would write ampl option cplex options cplex options ampl optimality 1 0e 8 Initial Variable Values and Solvers Some optimizers including most nonlinear solvers but excluding simplex based linear solvers make use of initial values for the decision variables as a starting point in their search for an optimal solution A good choice of initial values can greatly speed up the solution process in some cases Moreover in nonlinear models with multiple local optima the optimal solution reported by the solver may depend on the initial values for the variables AMPL passes initial values for decision variables and dual values if available to the solver You can set initial values using the syntax in the var declaration of your AMPL model When you solve a problem two times in a row the final values from the first solver invocation become the initial values for the second solver invocation unless you override this behavior with statements in your AMPL model In nonlinear models with multiple local optima this can cause some solvers to report a different solution on the second invocation Simplex based solvers typically discard initial values However they can use basis status information if available Ba
73. iteration limit 403 phase ll time limit 404 phase time limit 405 primal objective limit reached 406 dual objective limit reached 410 node limit with no integer solution 411 time limit with no integer solution IBM ILOG AMPL V12 2 USER S GUIDE 87 Table 9 2 Solve Codes and Termination Messages Continued Number 412 413 420 421 422 423 424 500 501 502 503 504 505 506 507 508 509 510 511 512 520 521 523 530 531 Message at termination treememory limit with no integer solution node file limit with no integer solution mixed integer solutions limit node limit with integer solution time limit with integer solution treememory limit with integer solution node file limit with integer solution unrecoverable failure aborted in phase II aborted in phase aborted in barrier dual infeasible aborted in barrier primal infeasible aborted in barrier primal and dual infeasible aborted in barrier primal and dual feasible aborted in crossover solution found numerical difficulties solution found inconsistent equations unrecoverable failure with no integer solution aborted no integer solution out of memory no tree no integer solution unrecoverable failure with integer solution aborted integer solution exists out of memory no tree solution may exist bug problem has no variables bug Error return from named CPLEX routine 88 IBM ILOG AMPL V12 2 USER S GUIDE Basis Status Table 9 2 Solve
74. its models are easy to understand debug and modify AMPL also makes maintaining models easy Using this Guide This brief guide describes starting up AMPL reading a model and supplying data and solving optimizing the model using IBM ILOG CPLEX Chapters 2 4 cover issues such as using command line options and environment variables and using AMPL on different operating systems Later chapters provide a detailed description of CPLEX directives This guide does not teach you the AMPL language To learn and effectively use the features of the AMPL language you should have a copy of the book AMPL A Modeling Language for Mathematical Programming 2nd edition by Robert Fourer David M Gay and Brian W IBM ILOG AMPL V12 2 USER S GUIDE 9 Kernighan copyright 2003 publisher Thomson Brooks Cole ISBN number 0 534 38809 4 This book includes a tutorial on AMPL and optimization modeling models for many classical problems such as production transportation blending and scheduling discussions of modeling concepts such as linear nonlinear and piecewise linear models integer linear models and columnwise formulations and a reference section Additional information can be found at the AMPL website at www ampl com AMPL is continuously undergoing development with updated language features and capabilities The official reference for the language is the AMPL book which is naturally revised less frequently Installing AMPL
75. l LP relaxation it may be useful to apply it to the subproblems as well However since the barrier algorithm cannot currently use a basis nor any other form of advanced start it will usually need to outperform the simplex solvers quite significantly on the subproblems before performance improves It is beneficial to set the barrier algorithm option to settings 1 or 2 Either of these nondefault choices is better at detecting infeasibility a frequent characteristic of MIP subproblems IBM ILOG AMPL V12 2 USER S GUIDE Defined Suffixes for CPLEX The most common use of AMPL suffixes is to represent solver result values that correspond to variables constraints and other model components Yet only the most standard kinds of results such as reduced costs given by X rc where X is a variable name and slacks given by C slack where C is a constraint name are covered by the built in suffixes To allow for solver specific optimization results AMPL permits solvers to define new suffixes and to associate solution result information with them Similarly users can also define suffixes to control the solver User defined suffixes understood by CPLEX and suffixes defined by CPLEX are described in this section Algorithmic Control For each integer variable in a problem CPLEX recognizes a preferred branching direction and a branching priority specified by the following two suffixes direction priority Branching direction preference
76. lls CPLEX what type of tree search to use With the value of 0 CPLEX will decide based on problem characteristics With a value of 1 traditional branch and bound search is used and with a value of 2 dynamic search is used migcpstrat default 0 This directive applies when the integer program has quadratic constraints that is when the problem is an MIQCP CPLEX can either solve a linear program at each node of the branch and bound tree which is faster but only gives an approximate solution to the underlying quadratically constrained program QCP and thus will usually require more nodes or CPLEX can solve a QCP The default value of 0 allows CPLEX to decide which strategy to IBM ILOG AMPL V12 2 USER S GUIDE 65 66 use based on problem characteristics A value of 1 directs CPLEX to solve a QCP at each node and a value of 2 directs CPLEX to solve an LP nodefile i default 1 workfilelim r default 128 workfiledir f The list of unprocessed nodes in the branch amp cut tree typically dominates CPLEX s memory usage when solving integer programs A setting of 0 for the nodefile directive causes CPLEX to store all nodes in physical memory The default value of 1 creates a compressed version of the node file in memory Writing nodes to disk i 2 3 enables CPLEX to process more nodes before running out of memory This is typically more efficient than relying on the operating system s generic swapping procedure If i 2 an uncompressed
77. ly if you have more difficult problems which take many iterations to complete Phase I consider using devex pricing i 1 Each iteration may consume more time but the lower number of total iterations may lead to a substantial overall reduction in time Do not use devex pricing if your problem has many variables and relatively few constraints however as the number of calculations required per iteration in this situation is usually too large to afford any advantage If devex pricing helps you may wish to try steepest edge pricing i 2 This alternative incurs a substantial initialization cost and is computationally the most expensive per iteration but may dramatically reduce the number of iterations so as to produce the best results on exceptionally difficult problems The variant using slack norms i 3 is a compromise that sidesteps the initialization cost it is most likely to be advantageous for relatively easy problems that have a low number of iterations or time per iteration Full reduced cost pricing i 4 is a variant that computes a reduced cost for every variable and selects as entering variable one having most negative reduced cost or most positive as appropriate Compared to CPLEX s standard reduced cost pricing i 1 full reduced cost pricing takes more time per iteration but in rare cases reduces the number of iterations more than enough to compensate This alternative is supplied mainly for completeness as it is proposed in
78. ly in the dual Thus when the number of constraints is much larger than the number of variables in the primal the dual has a much smaller basis matrix and CPLEX may be able to solve it more efficiently The primal and dual directives instruct CPLEX to set up the primal or the dual formulation respectively The dualthresh directive makes a choice the dual LP if the number of constraints exceeds the number of variables by more than i and the primal LP otherwise autoopt dualopt baropt primalopt siftopt concurrentopt The autoopt directive instructs CPLEX to select an appropriate algorithm to solve the problem You can specify a particular algorithm by the dualopt baropt and primalopt directives which invoke dual simplex barrier and primal simplex methods respectively The autoopt directive will most frequently select the dual simplex method The two simplex variants use similar basis matrices but employ opposite strategies in constructing a path to the optimum Any of the algorithms can be applied regardless of whether the primal or the dual LP is set up as explained above in general the six combinations of primalopt dualopt baropt and primal dual perform differently Consider trying the barrier method or the primal simplex method if CPLEX s dual simplex method reports problems in its display or if you simply wish to determine whether another algorithm will be faster Few linear programs exhibit poor numerical performance in both
79. many textbook discussions of the simplex algorithm dgradient i default 0 This directive governs the dual simplex algorithm s choice of a pricing procedure that determines which variable is selected to leave the basis at each iteration Your choice is IBM ILOG AMPL V12 2 USER S GUIDE 45 likely to make a substantial difference to the tradeoff between computational time per iteration and the number of iterations As a rule of thumb if the number of iterations to solve your linear program exceeds three times the number of constraints you should consider experimenting with alternative pricing procedures The dual pricing indicator allows you to indicate devex pricing Table 6 4 lists the valid settings for this directive Table 6 4 Dual Pricing Indicator dgradient Setting Effect 0 Let CPLEX determine automatically 1 Standard dual pricing 2 Steepest edge pricing 3 Steepest edge pricing in slack space 4 Steepest edge pricing unit initial norms 5 Devex pricing These settings can be further described as follows The default value 1 0 lets CPLEX choose a dual pricing procedure through an internal heuristic based on problem characteristics Standard dual pricing i 1 described in many textbooks selects as leaving variable one that is farthest outside its bounds The three steepest edge alternatives employ more elaborate computations which can better predict the improvement to
80. n the United States other countries or both Other company product or service names may be trademarks or service marks of others Python is a registered trademark of the Python Software Foundation MATLABO is a registered trademark of The MathWorks Inc IBM ILOG CPLEX acknowledges use of the dtoa routine of the gdtoa package available at http www netlib org fp The author of this software is David M Gay All Rights Reserved Copyright C 1998 1999 by Lucent Technologies Permission to use copy modify and distribute this software and its documentation for any purpose and without fee is hereby granted provided that the above copyright notice appears in all copies and that both that the copyright notice and this permission notice and warranty disclaimer appear in supporting documentation and that the name of Lucent or any of its entities not be used in advertising or publicity pertaining to distribution of the software without specific written prior permission LUCENT DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS IN NO EVENT SHALL LUCENT OR ANY OF ITS ENTITIES BE LIABLE FOR ANY SPECIAL INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE DATA OR PROFITS WHETHER IN AN ACTION OF CONTRACT NEGLIGENCE OR OTHER TORTIOUS ACTION ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE end of license te
81. n 1 do not treat unavailable functions of constant arguments as variable P presolve 0 turn off AMPLs presolve phase S substout 1 use defining equations to eliminate variables L linelim 1 fully eliminate variables with linear defining equations so model is recognized as linear T gentimes 1 show time to generate each model component t times 1 show time taken in each model translation phase ostr outopt str set problem file format b g m and stub name to display more possibilities use 0 S randseed use current time for random number seed sn randseed n use n for random number seed V version display the AMPL software version number If you type amp1 at the shell prompt AMPL will display a summary list of all the command line switches On some UNIX shells is a special character so you may need to use with double quotation marks Persistent Option Settings 26 If you have many option settings or other commands that you would like performed each time AMPL starts you may create a text file containing these commands in AMPL language syntax Then set the environment variable name OPTIONS_IN to the pathname of this text file For example on a Windows PC you should type C gt set OPTIONS IN c amplinit txt If you are using a C shell on a UNIX machine you would type something like setenv OPTIONS IN ijr amplinit txt AMPL reads the file referred to by OPTIONS_IN and executes any command
82. n and CPLEX will crush an advanced basis or starting vector supplied by the user If this parameter is set to 1 or 2 CPLEX uses advanced starting information when optimization is initiated If you anticipate the advanced basis to be a close match for your problem so that relatively few iterations will be needed or if you are unsure then setting 1 is a good choice because it avoids some overhead processing 9 If you anticipate that the simplex optimizer will require many iterations even with the advanced basis or 1f the model is large and preprocessing typically removes much from the model then setting 2 may yield a faster solution by giving you the advantages of preprocessing However in such cases you might also consider not using the advanced basis by setting this parameter to 0 instead on the grounds that the basis may not be giving you a helpful starting point after all Setting 2 may also be effective for MIPs in which the percentage of integer constraints is low It may also reduce the solution time of fixed MIPs crash i default 1 This directive governs CPLEX s procedure for choosing an initial basis except when the basis is read from a file as specified by the directive readbasis described below A value of i 0 causes the objective to be ignored in choosing the basis whereas values of 1 and 1 select two different heuristics for taking the objective into account The best setting for your purposes will depend on th
83. n the expected way ampl model trnlocld mod ampl data trnlocl dat ampl problem Sub Supply Price Demand Price ampl Dual Ship Cost Dual Ship ampl let i in ORIG build i 0 ampl option solver cplexamp ampl option cplex options presolve 0 ampl solve CPLEX 11 0 0 presolve 0 CPLEX 11 0 0 unbounded problem 30 iterations 0 in phase I variable unbdd returned suffix unbdd OUT IBM ILOG AMPL V12 2 USER S GUIDE 83 The suffix message indicates that unbdd has been created automatically You can use this suffix to display the direction of unboundedness which is quite simple in this case ampl display Supply Price unbdd Supply Price unbdd A eel 6 1 11 1 16 1 21 1 2 4 Tag 12 1 7 1 22 1 3 1 8 1 LS dl 18 1 23 1 4 1 9 1 14 1 19 1 24 1 Bel 10 E TB 1 20 1 25 1 ampl display Demand Price unbdd Demand _Price unbdd A3 1 A6 1 A8 1 A9 1 B2 1 B4 1 i IBM ILOG AMPL V12 2 USER S GUIDE Solve Codes CPLEX Status Codes in AMPL When CPLEX returns control to AMPL after a solve command built in AMPL parameters and an AMPL option provide information on the outcome of the optimization as shown ampl model oil mod ampl data oil dat ampl option solver cplexamp ampl display solve result num solve result solve _result_num 1 solve result ampl solve CPLEX 11 0 0 optimal solution objective 12 20834324 37 iterations 0 in phase
84. n the feasible region reducing the number of fractional variables to choose from when CPLEX needs to select a branching variable CPLEX can generate cuts based on different combinatorial constructs corresponding to the directives listed above By default CPLEX decides whether to generate cuts Typically the default setting yields the best performance To disable a particular family of cuts set its directive to 1 To enable moderate cut generation set the appropriate directive to 1 To enable aggressive cut generation set it to 2 To set all these classes of cuts to one common value for instance 1 to disable all cuts use the directive mipcuts Cuts directives are applied in the order in which they are encountered so for instance mipcuts 1 fraccuts 2 first turns off all cuts and then turns fractional cuts back on The reverse case of fraccuts 2 mipcuts 1 results in all cuts being disabled as though the fraccuts 2 directive is not present Using more aggressive cut generation causes CPLEX to make more passes through the problem to generate cuts The disjcuts cliquecuts and covercutsdirective also supports a setting of 3 for very aggressive cut generation option mip priorities vl il v2 i2 From CPLEX 7 0 onwards the mip_priorities option has been superseded by the priority suffix Please refer to Algorithmic Control on page 77 for a discussion of setting priorities by individual variable mipsearch default 0 This directive te
85. nates for some reason other than a proved optimum such as a time limit or other limit the bestnode suffix in comparison with the solution value may provide some indication of the quality of the solution or the nearness of a proof of optimality IBM ILOG AMPL V12 2 USER S GUIDE 79 Sensitivity Ranging 80 When the sensitivity directive described in Directives for Controlling Output on page 53 is included in CPLEX s option list classical sensitivity ranges are computed and are returned in the following three suffixes Current down Up Let us illustrate the use of these suffixes using an example model from Section 4 3 of the AMPL book ampl model steelT mod ampl data steelT dat ampl option solver cplexamp ampl option cplex options sensitivity ampl solve CPLEX 11 0 0 sensitivity CPLEX 11 0 0 optimal solution objective 515033 18 iterations 1 in phase 1 suffix up OUT suffix down OUT suffix current OUT The three lines at the end show the suffix commands executed by AMPL in response to the results from CPLEX These commands are invoked automatically you do not need to type them For variables suffix current indicates the objective function coefficient in the current problem while down and up give the smallest and largest values of the objective coefficient for which the current simplex basis remains optimal CPLEX returns 1e 20 for down and 1e 20 for up to indicate minus infinity a
86. nd plus infinity respectively ampl display Sell down Sell current amp1 Sell up Sell down Sell current Sell up i bands 1 233 25 1e 20 bands 2 25 4 26 1e 20 bands 3 24 9 27 27 5 bands 4 10 27 29 1 coils 1 29 2857 30 30 8571 coils 2 33 35 1e 20 coils 3 35 2857 37 1e 20 coils 4 35 2857 39 1e 20 i IBM ILOG AMPL V12 2 USER S GUIDE For constraints the interpretation is similar except that it applies to a constraint s constant term the so called right hand side value ampl display time down time current ampl time up time down time current time up 1 37 8071 40 66 3786 2 37 8071 40 47 8571 3 25 32 45 4 30 40 62 5 Diagnosing Infeasibilities For a linear program that has no feasible solution you can ask CPLEX to find an irreducible infeasible subset or IIS of the constraints and variable bounds By definition members of an IIS have no feasible solution but dropping any one of them permits a solution to be found to the remaining ones Clearly knowing the composition of an IIS can help localize the source of the infeasibility The associated suffix is lis You turn on the IIS finder using the isfind option described in Directives for Handling Infeasible Problems on page 33 An associated option iis_table set up and displayed automatically by CPLEX shows the strings that may be associated with iis and gives brief descriptions of what they mean IBM ILOG AMPL V12 2 USER S GUIDE 81
87. o polish and one of these conditions is met polishafter_absmipgap directs CPLEX to start polishing integer solutions after the absolute mixed integer optimality gap reaches r1 polishafter_intsol directs CPLEX to start polishing after finding i1 integer solutions polishafter_mipgap directs CPLEX to start polishing the relative mixed integer optimality gap reaches r2 polishafter_ nodes directs CPLEX to start polishing after processing 12 nodes polishafter time directs CPLEX to start polishing integer solutions after spending r3 in the usual branch amp cut phase polishtime r default 0 0 This directive lets you indicate to CPLEX how much time in seconds to spend after branch amp cut in polishing a solution The default results in no polishing time This parameter is deprecated and will be removed in a future release priorities i default 0 Set i 1 to consider the MIP priorities during variable selection Set i 0 to ignore the priorities repairtries i default 0 This directive lets you indicate to CPLEX whether and how many times it should try to repair an infeasible MIP start that you supplied The directive has no effect if the MIP start you supplied is feasible It has no effect if no MIP start was supplied Set i 1 to prevent repair Set i to any positive integer to limit the number of attempts rinsheur default 0 The rinsheur directive determines how often to apply the relaxation induced neighborhood search heu
88. onstraints Solver statuses for these latter variables are defined in a similar way IBM ILOG AMPL V12 2 USER S GUIDE 89 The major use of solver status values from an optimal basic solution is to provide a good starting point for the next optimization run possibly after a data change You can refer to a variable s solver status by appending sstatus to its name Initially when no problem has yet been solved all variables have the status none After an invocation of a simplex solver the same display lists the statuses of the variables at the optimal basic solution For example consider the following ampl model oil mod ampl data oil dat ampl option solver cplex ampl solve CPLEX 11 0 0 optimal solution objective 12 20834324 37 iterations 0 in phase 1 ampl option sstatus table option sstatus table equ nonbasic at equal lower and upper bounds btw nonbasic between bounds 0 none no status assigned 1 bas basic 2 sup superbasic 3 low nonbasic lt normally lower bound 4 upp nonbasic gt normally upper bound 5 6 t ampl display InCr sstatus InCr sstatus MID C bas W_TEX low i A table of the recognized CPLEX status values is stored in the AMPL option sstatus_table displayed above Numbers and short strings representing status values are given in the first two columns The numbers are mainly for communication between AMPL and CPLEX though you can access them by
89. or diagnosing problems of degeneracy or instability in the barrier algorithm file f1 This directive instructs CPLEX to write a copy of the model it receives for solution into a file named f1 logfile f1 This directive instructs CPLEX to create a log file named 1 that will contain output from the optimization The amount of output in the log file will depend on other directives such as the display directive described above lpdisplay i default 0 The default choice of i 0 produces a minimal few lines of output from CPLEX summarizing the results of the run When i 1 a log line recording the iteration number and the scaled infeasibility or objective value is displayed after each refactorization of the basis matrix Additional information on the operation of the network simplex algorithm is also provided if applicable This is often the appropriate setting for tracking the progress of a long run When i 2 a log line is displayed after each iteration This level of output is occasionally useful for diagnosing problems of degeneracy or instability in the simplex algorithm sensitivity When specified this directive instructs CPLEX to output sensitivity ranges corresponding to the optimal solution For variables the suffix current provides the corresponding objective function coefficient in the current problem and down and up specify the smallest and largest values for which the current basis remains optimal For constraints the su
90. ormance but occasionally takes a long time due to its iterative nature In cases where the time required for bound strengthening outweighs any subsequent reduction in run time disable this feature by setting i 0 To turn on bound strengthening set i 1 coeffreduce i default 2 Coefficient reduction during the presolve phase typically improves CPLEX s performance on integer programs by speeding up the solve times of the LP subproblems solved in the branch and bound algorithm However while coefficient reduction will tighten the LP subproblems occasionally it makes them more difficult to solve So if CPLEX solves an IBM ILOG AMPL V12 2 USER S GUIDE 57 58 integer program in a modest number of nodes but the LP subproblem at each node consumes significant amounts of time solve time may improve by setting i 0 to disable this feature The node count may increase but the savings in time per node may compensate for the increased node count The default setting of i 2 causes CPLEX to perform coefficient reduction whenever possible while i 1 will only reduce coefficients to integer values cutpass i default 0 This directive controls the number of passes CPLEX performs when generating cutting planes for a MIP model By default CPLEX automatically determines the number of passes to perform This setting should suffice for most problems Set the cutpass directive to 1 to stop all cut generation Set it to a positive integer to specify a pa
91. orse that this adjusted value Positive values of r2 usually speed the search but may cause the true optimum to be missed IBM ILOG AMPL V12 2 USER S GUIDE Directives for Halting and Resuming the Search There is usually no need to make exhaustive runs to determine the impact of different search strategies or optimality criteria While you are experimenting consider using one of the directives below to set a stopping criterion in advance In each case the best solution found so far is returned to AMPL As mentioned earlier using break on command line versions of CPLEX for AMPL will return the best known solution for integer programs that means the current incumbent You can arrange to save the entire search tree when CPLEX halts so that the search may be resumed from where it left off Directives for this purpose are also listed below clocktype i default 2 The default setting of clocktype 2 means that CPLEX measures time in terms of elapsed wall clock seconds A setting of 1 means that CPLEX measures time in terms of CPU seconds nodelim i default 2 1e9 The search is terminated after i linear programming subproblems have been solved The default value can vary depending on the hardware solutionlim i default 2 1e9 The search is terminated after i feasible solutions satisfying the integrality requirements have been found timelimit r default 1 0e75 The search is terminated after r seconds of computing time tre
92. ory requirement for linear programs 38 94 IBM ILOG AMPL mixed integer algorithm 55 optimization methods 37 problems handled by CPLEX 29 specifying CPLEX directives 32 crash directive 44 crossover directive 48 current suffix 80 cutpass directive 58 cuts generate 65 polyhedral 65 cutsfactor directive 58 D densecol directive 48 dependency directive 42 devex pricing 46 dgradient directive 45 direction suffix 77 directive absmipgap 69 advance 44 aggcutlim 57 aggfi11 41 aggregate 41 autoopt 39 auxrootthreads 62 backtrack 62 baralg 47 barcorr 48 bardisplay 53 bargrowth 47 bariterlim 51 barobjrange 48 baropt 39 V12 2 USER S GUIDE barstart 48 bbinterval 62 boundstr 57 branch 63 cliquecuts 65 clocktype 51 71 coeffreduce 57 comptol 48 concurrentopt 39 conflictdisplay 33 covercuts 65 crash 44 crossover 48 cutpass 58 cutsfactor 58 densecol 48 dependency 42 dgradient 45 disjcuts 65 doperturb 49 dual 39 dualopt 39 dualthresh 39 eachcutlim 58 feasibility 50 feasopt 33 feasoptobj 33 file 53 flowcuts 65 flowpathcuts 65 fpheur 63 fraccand 58 fraccuts 65 fracpass 58 gubcuts 65 heuristicfreq 63 iisfind 33 impliedcuts 65 integrality 70 lazy 64 78 logfile 53 lowercutoff 70 lowerobj 51 lpdisplay 53 lpiterlim 51 IBM ILOG AMPL markowitz 50 maximize 41 mcfcuts 65 memoryemphasis 40 minimize 41 mipalgorithm 64 mipcrossover 64 mipcuts 65 mipdisplay 73 mipemphasis 61 mipg
93. pdisplay directive 53 lpiterlim directive 51 markowitz directive 50 Markowitz threshold 50 Markowitz tolerance 50 maximize directive 41 mcfcuts directive 65 V12 2 USER S GUIDE 97 memory requirement for linear programs 38 running out 74 memory usage execute solver outside AMPL 22 memoryemphasis directive 40 messages termination 86 minimize directive 41 MIP difficult subproblems 75 mip priorities option 65 mipalgorithm directive 64 mipcrossover directive 64 mipcuts directive 65 mipdisplay directive 73 mipemphasis directive 61 mipgap directive 69 mipinterval directive 73 mipkappa directive 74 mipsearch directive 65 mipstartstatus directive 58 mipstartvalue directive 58 migcpstrat directive 65 mircuts directive 65 N netfind 98 IBM ILOG AMPL directive 47 netopt directive 40 network primal simplex algorithm 37 nodefile directive 66 nodelim directive 71 nodeselect directive 62 nonlinear quadratic programs 29 numeric result codes interpretation 86 O objdifference directive 70 optimality directives for relaxing 69 optimality directive 50 optimization methods available in CPLEX 37 option cautions 25 eexit 25 funcwarn 26 gentimes 26 linelim26 mip priorities 65 outopt 26 presolve 26 randseed 26 substout 26 times 26 version 26 options add options 19 persistent settings 26 preserve settings 27 set options 25 specify solver options 18 ordering directive 48
94. problem by which LP algorithm mipalgorithm Explore rounded subproblem solutions how often heuristicfreg It is often hard to predict which combination of directives will work best Some experimentation is usually required your knowledge of the problem structure may also suggest certain choices of branch amp cut strategy The first directive you may wish to consider is the mipemphasis directive which guides the overall balance between seeking optimality and feasibility by setting many of the other directives to achieve this overall balance mipemphasis i default 0 This directive guides CPLEX s branch amp cut strategy The default of 0 corresponds to a balance between searching for feasible solutions and proving optimality and works well for most users purposes A setting of 1 shifts the emphasis strongly toward finding new feasible solutions and may be an appropriate setting with difficult models for which a proof of optimality is unlikely to be reached anyway A setting of 2 shifts the emphasis slightly more toward the proof of optimality and away from finding new feasibles A setting of 3 shifts the emphasis very aggressively toward the optimality proof by concentrating on moving the best bound value and may be an appropriate setting for models resistant to other solution techniques or when feasible solutions without a proof of optimality are of no value None of these emphasis settings changes the fundamental nature of the CPLEX
95. ristic RINS heuristic Setting the value to 1 turns off the RINS heuristic Setting the value to 0 the default applies the RINS heuristic at an interval chosen automatically by CPLEX Setting the value to a positive integer applies the RINS heuristic at the requested node interval For example setting RINSHeur to 20 dictates that the RINS heuristic be called at node 0 20 40 60 etc IBM ILOG AMPL V12 2 USER S GUIDE 67 round default 1 This directive specifies whether to round integer variables to integral values before returning the solution and whether to report that CPLEX returned noninteger values for integer values Table 7 4 Settings for the round Directive value meaning round nonintegral integer variables do not modify solve_result A N do not modify solve_message 8 modify even if maxerr lt le 9 Modifications take place only if CPLEX assigned nonintegral values to one or more integer variables and for round lt 8 only if the maximum deviation from integrality maxerr exceeded the minimum integrality tolerance 1e 9 startalgorithm i default 0 This directive specifies the algorithm that CPLEX will apply to solve the initial LP relaxation The recognized values of i are Table 7 5 Settings for the startalgorithm Directive 0 Automatic Primal simplex Dual simplex Network simplex Barrier Sifting Concurrent oak woah strongcand i1 default 10 strongit i2 default 0 Thes
96. rms of dtoa routine of the gdtoa package C N T E N T S Table of Contents Chapter 1 Welcome to AMPL 026 erare A A AA 9 USING IS QUITE a ai 9 Installing AMPL 0 0000000 a a a a dee 10 Usage Notes coi A A A ae ee 10 InstallediFiles ii a A A ee A ee eee 11 Chapter 2 Using AMPL lt a la ee a e alti A Ae tie dt 13 Running AMPL is eioi toaa go eet ete teen tates neat 13 Using a Text Editor 0 0 cece cee eee eee eens 13 Running AMPL in Batch Mode 00 e eee eee eee eee eee 14 Chapter 3 AMPL Solver Interaction 20000 c eee ees 17 Choosing a Solver a 0isc00 cet Oe hie oie eee EE Bee Vere E ES 17 Specifying Solver OptionS 0 0 ccc eee eee 18 Initial Variable Values and Solvers 0 cece eee eee eee nee eee eee 19 Problem and Solution Files 5 oca te cca Pickle e ta wie tan eine dia 19 Saving temporary files 0 0 0 cette tenes 20 Creating Auxiliary Files 2 2 0 0 ccc eee eee 21 Running Solvers Outside AMPL 0 cece eee eee eee eee 22 Using MPS File Format cone i ee eee eee eee eee ees 22 Temporary Files Directory 0 00 c eee eee eee 23 IBM ILOG AMPL V12 2 USER S GUIDE 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Customizing AMPE aeii a ah hes ee Neat ee ek at tee eA 25 Command Line Switches 60 c eee 25 Persistent Option Settings oleo a ia eink 26 Using CPLEX with AMPL 000 e cece e eee eee 29 Problems Handled by
97. roduce the tree structure shown above Tf there are more than a few integer variables the branching process has the potential to create more nodes than any computer can hold There are two key circumstances however in which branching from a particular node can be discontinued The node s subproblem has no fractional valued integer variables It thus provides a feasible solution to the original integer program If this solution yields a better objective value than any other feasible solution found so far it becomes the incumbent and is saved for future comparison The node s subproblem has no feasible solution or has an optimum that is worse than a certain cutoff value Since any subproblems under this node would be more restricted they would also either be infeasible or have an optimum value worse than the cutoff Thus none of these subproblems need be considered In these cases the node is said to be fathomed Because subproblems become more restricted with each branching the likelihood of fathoming a node becomes greater as the algorithm gets deeper into the tree So long as nodes are not created by branching much faster than they are inactivated by fathoming the tree can be kept to a reasonable size When no active nodes are left CPLEX is finished and it reports the final incumbent solution back to AMPL If the cutoff value has been set throughout the algorithm to the objective value of the current incumbent CPLEX s default stra
98. rticular number of passes cutsfactor r default 4 0 The cutsfactor directive controls the number of additional cuts generated by CPLEX While the constraints generated by CPLEX improve performance in most cases in some problems the additional memory to store them and time required to solve the larger LP subproblems may outweigh the performance gains from the tighter problem formulation In such cases use this directive to limit the number of cuts that CPLEX generates CPLEX will generate no more than r times the number of rows in the problem eachcutlim i default 2100000000 This directive limits the number of cuts of each type that may be generated This directive may be useful on models where such a large number of one type of cut are generated that the overall limit on cuts is reached before generating all types of cuts By default there is no limit on cuts of each type only an overall limit on cuts as specified with the cutsfactor directive fraccand i default 200 This directive limits the number of candidate variables CPLEX will examine when generating fractional cuts on a MIP model For most purposes the default of 200 will be satisfactory fracpass i default 0 This directive controls the number of passes CPLEX performs when generating fractional cuts on a MIP model The default of 0 instructs CPLEX to automatically determine the number of passes and should suffice for most problems Set it to a positive integer to specify a part
99. s and automatic differentiation of nonlinear functions To take advantage of these features solvers must be written to utilize AMPL s interface IBM provides no support for the usage of AMPL with solvers not distributed by IBM You choose a solver for a particular problem by giving its executable filename in the AMPL option solver command For example to use the AMPL compatible CPLEX solver type ampl option solver cplexamp Most solvers have algorithmic options such as CPLEX with its Mixed Integer and Barrier options In these cases you give the solver executable name to AMPL for example with option solver cplexamp the solver will determine from the problem characteristics as passed by AMPL for example a quadratic objective or integer variables as well as solver options you specify which algorithmic options will be used IBM ILOG AMPL V12 2 USER S GUIDE 17 Specifying Solver Options You can specify option settings for a particular solver through the AMPL option command CPLEX specific directives are described later in this document Since all solvers provide default settings for their options this is necessary only when your problem requires certain nondefault settings in order to solve or when certain settings yield improved performance or solution accuracy To specify solver options enter option solver options settings where solver is replaced by the name of the solver you are using This approach allows
100. s ordinary constraints The idea of lazy constraints is to keep the node subproblems small and easy as much as possible by leaving out constraints which are probably not going to be violated User cuts are constraints that are not necessary to define the feasible region of the integer program but tighten the model User cuts are checked periodically during the CPLEX branch and cut process If CPLEX finds a user cut which is violated by the solution to the node subproblem the user cut will be added to the problem as an ordinary constraint A user could add all the user cuts as ordinary constraints but as with lazy constraints the idea is to keep the node subproblems small and easy and only add the user cuts as they are found to be needed The way in which a constraint is handled depends on the value of the lazy setting and the value of the lazy directive Table 8 1 Settings for the lazy Directive 0 Treat constraints with lazy of 1 or 2 as ordinary constraints 1 Treat constraints with lazy of 1 as lazy constraints 2 Treat constraints with lazy of 2 as user cuts 3 Treat constraints with lazy of 1 as lazy constraints and treat constraints with lazy of 2 as user cuts Another form of algorithmic control is provided by the suffix bestnode of your model s objective function which returns the best node value at the present state of optimization after control is returned to AMPL from the solve command If the optimization termi
101. s therein before it reads any other files mentioned on the command line or prompts for any interactive commands IBM ILOG AMPL V12 2 USER S GUIDE If you want AMPL to preserve all of your option settings from one session to the next you can cause AMPL to write the options into a text file named by setting the AMPL option OPTIONS_INOUT ampl option OPTIONS INOUT c amplopt txt Before exiting AMPL writes a series of option commands to the file named by OPTIONS INOUT which when read will set all of the options to the values they had at the end of the session To use this text file set the corresponding environment variable to the same filename C gt set OPTIONS INOUT c amplopt txt After you do this AMPL will read and execute the commands in amplopt txt when it starts up When you end a session AMPL will write the current option settings including any changes you have made during the session into this file so that they will be preserved for use in your next session If both the OPTIONS _IN and OPTIONS _INOUT environment variables are defined the file referred to by OPTIONS_IN will be processed first then the file referred to by OPTIONS _INOUT IBM ILOG AMPL V12 2 USER S GUIDE 27 28 IBM ILOG AMPL V12 2 USER S GUIDE Using CPLEX with AMPL Problems Handled by CPLEX CPLEX is designed to solve linear programs as described in Chapters 1 8 and 15 16 of AMPL A Modeling Language for Mathematical Pro
102. sil IBM ILOG AMPL Version 12 2 User s Guide Standard Command line Version Including CPLEX Directives May 2010 Copyright International Business Machines Corporation 1987 2010 US Government Users Restricted Rights Use duplication or disclosure restricted by GSA ADP Schedule Contract with IBM Corp Copyright notice O Copyright International Business Machines Corporation 1987 2010 US Government Users Restricted Rights Use duplication or disclosure restricted by GSA ADP Schedule Contract with IBM Corp IBM the IBM logo ibm com Websphere ILOG the ILOG design and CPLEX are trademarks or registered trademarks of International Business Machines Corp registered in many jurisdictions worldwide Other product and service names might be trademarks of IBM or other companies A current list of IBM trademarks is available on the Web at Copyright and trademark information at http www ibm com legal copytrade shtml Adobe the Adobe logo PostScript and the PostScript logo are either registered trademarks or trademarks of Adobe Systems Incorporated in the United States and or other countries Linux is a registered trademark of Linus Torvalds in the United States other countries or both Microsoft Windows Windows NT and the Windows logo are trademarks of Microsoft Corporation in the United States other countries or both Java and all Java based trademarks and logos are trademarks of Sun Microsystems Inc i
103. sis statuses can be set either within AMPL or by a previous optimization Information on interpreting and setting variable statuses is provided in CPLEX Status Codes in AMPL on page 85 Problem and Solution Files When you type solve AMPL processes your model and data to create a temporary problem file such as steel n1 which will be read by the solver It then loads and executes the solver program which is responsible for creating a solution file such as steel sol AMPL reads the solution file and makes the solution values available through the variable constraint and objective names you have declared in your AMPL model Unless you specify otherwise AMPL then deletes the temporary problem and solution files IBM ILOG AMPL V12 2 USER S GUIDE 19 20 You can display the solution information for example the values of the decision variables and constraints in your AMPL session with commands such as display For example if you have just solved a problem created from steel mod and steel dat you could type ampl display Make Time To save this output in a file you can use redirection ampl display Make Time gt mysol txt Note that when you simply mention the name of a constraint in a display statement AMPL will display the dual value shadow price of that constraint not its left hand side value You can use the AMPL suffix notation to display the left hand side value as described in the book AMPL A Modeling Language for
104. slate a model into MPS file format as outlined below With this feature you may be able to solve AMPL models with a solver that reads its problem input in MPS file format If you choose to use this feature you will find AMPL s ability to produce auxiliary files very useful since these files can be used to relate the MPS file format information to the sets variables constraints and objectives defined in the AMPL model However you will not be able to bring the solution variable values dual values and so on back into AMPL further work with the solution must be performed outside of AMPL To translate your model into MPS file format use the write command as outlined above with mas the first letter of the filename To illustrate the command shown below creates a file named steel mps ampl write msteel In most cases you will need to run your solver separately to obtain the solution Note that the MPS format does not provide a way to distinguish between objective maximization and minimization However CPLEX assumes that the objective is to be minimized There is no standardization on this issue other solvers may assume maximization Thus it is incumbent upon the user of the MPS format to ensure that the objective sense in the AMPL model corresponds to the solver s interpretation Temporary Files Directory If the TMPDIR option is not set AMPL writes the problem and solution files and other temporary files to the current direc
105. te at the current node with the values at parent nodes in the tree If the value of the current node has degraded increased for a minimization decreased for a maximization by at least a certain amount IBM ILOG AMPL V12 2 USER S GUIDE relative to the values at parent nodes then a backtrack is performed The cutoff for degradation is determined by an internal heuristic that is regulated by the value of r Lower values of r which can range from 0 to 1 favor backtracking resulting in a strategy that is more nearly breadth first The search jumps around fairly high in the tree solving somewhat dissimilar subproblems Good solutions are likely to be found sooner through this strategy but the processing time per node is also greater Higher values of r discourage backtracking yielding a strategy that is more nearly depth first Successive subproblems are more similar nodes are processed faster and integer solutions are often quickly found deep in the search tree Considerable time may be wasted in searching the descendants of one node however before backtracking to a better part of the tree The default value of 9999 gives a moderately breadth first search and represents a good compromise Lower values often pay off when the LP subproblems are expensive to solve Setting i2 to 0 chooses a pure depth first strategy regardless of r CPLEX automatically uses this strategy to search for an initial feasible integer solution at the ou
106. tegy then the reported solution is declared optimal Other cutoff options described below cannot provide a provably optimal solution but may allow the algorithm to finish much faster CPLEX s memory requirement for solving linear subproblems is about the same as its requirement for linear programs discussed in the previous section In the branch amp cut algorithm however each active node of the tree requires additional memory The total memory that CPLEX needs to prove optimality for an integer program can thus be much larger and less predictable than for a linear program of comparable size IBM ILOG AMPL V12 2 USER S GUIDE Because a single integer program generates many LP subproblems even small instances can be very computation intensive and require significant amounts of memory In contrast to solving linear programming problems where little user intervention is required to obtain optimal results you may have to set some of the following directives to get satisfactory results on integer programs You can either change the way that the branch amp cut algorithms work or relax the conditions for optimality as explained in the two corresponding subsections below The first directive to consider for changing the behavior is the mipemphasis directive which directs the branch amp cut algorithm to focus on different balances of optimality and feasibility If memory consumption is an issue set the memoryemphasis directive it is descr
107. tempt to tighten the bounds on primal and dual variables possibly causing additional variables to be fixed and additional constraints to be dropped AMPL s presolve phase as described in Section 14 1 of the AMPL book also performs many but not all of these transformations To see how many variables and constraints are eliminated by AMPL s presolve set option show_stats to 1 To suppress AMPL s presolver so that all presolving is done in CPLEX set option presolve to 0 CPLEX s presolve can be suppressed by changing i to 0 from its default of 1 In rare cases the presolved linear program although smaller is actually harder to solve Thus if CPLEX reports that many variables and constraints have been eliminated by presolve you may want to compare runs with and without presolve On the other hand if CPLEX consistently reports that presolve eliminates no variables or constraints you can save a little processing time by turning presolve off To request a report of the number of eliminations performed by presolve see the prestats directive below prestats i default 0 When this directive is changed to 1 from its default of 0 CPLEX reports on the activity of the aggregation and presolve routines Presolve eliminated 1645 rows and 2715 columns in 3 passes Aggregator did 22 substitutions Presolve Time 1 70 sec During the development of a large or complex model it is a good idea to monitor this report and to turn on its AMPL coun
108. termine the choice of branching variable based on specific problem features Use ordertype to specify the type of priority order The default value i 0 bypasses order generation Setting i 1 generates a priority order where variables with larger costs receive higher priority Setting i 2 generates a priority order where variables with smaller bound ranges receive higher priority This setting tends to be useful for models with binary variables that represent a logical decision and associated general integer variables that represent resource levels enabled by the outcome of the decision Setting i 3 tends to help set covering problems In such problems setting a binary variable to 1 covers a group of rows but incurs a cost Binary variables with smaller costs per row covered are good choices to set to 1 An i value of 3 gives higher priority to variables with smaller cost per coefficient count This tends to identify such binary variables quickly IBM ILOG AMPL V12 2 USER S GUIDE polishafter absmipgap r1 default 0 0 polishafter intsol il default 2100000000 polishafter mipgap r2 default 0 polishafter nodes i2 default 2100000000 polishafter time r3 default le 75 This group of directives controls the solution polishing phase of CPLEX which can follow the usual branch amp cut phase to improve on the existing integer solution Solution polishing will start once CPLEX has finished some necessary setup work has a solution available t
109. terpart by setting option show_stats to 1 An unexpectedly large number of eliminated variables or constraints may indicate that the formulation is in error or can be substantially simplified scale i default 0 This directive governs the scaling of the coefficient matrix The default value of i 0 implements an equilibration scaling method which is generally very effective You can turn off the default scaling by setting i 1 A value of 1 invokes a modified more aggressive scaling method that can produce improvements on some problems Since CPLEX has internal logic that determines when it need not scale a problem setting the scale directive to 1 rarely improves performance IBM ILOG AMPL V12 2 USER S GUIDE 43 Directives for Controlling the Simplex Algorithm Several key strategies of the primal and dual simplex algorithms can be changed through CPLEX directives If you are repeatedly solving a class of linear programs that requires substantial computer time experimentation with alternative strategies can be worthwhile advance i default 0 By default i1 0 the advanced basis indicator is off You can set it according to Table 6 2 Table 6 2 Settings for the advance Directive Setting Effect 0 This is the default value The advanced basis indicator is off 1 The advanced indicator is on CPLEX uses an advanced basis supplied by the user Preprocessing is skipped The advanced indicator is o
110. the primal and the dual algorithms In general the barrier method tends to work well when the product of the constraint matrix and its transpose remains sparse The siftopt directive instructs CPLEX to use a sifting method that solves a sequence of LP subproblems eventually converging to an optimal solution for the full original model Sifting is especially applicable to models with many more columns than rows when the eventual solution is likely to have a majority of variables placed at their lower bounds The concurrentopt directive instructs CPLEX to make use of multiple processors on your computer by launching concurrent threads to solve your model in parallel The concurrentopt algorithm has two modes depending on the setting of the parallelmode directive In the opportunistic mode the first thread uses dual simplex a second thread uses barrier a third thread if your computer has that many processors uses primal simplex and any additional processors are added to making barrier parallel On a machine with enough memory this strategy will result in a solution being returned by the fastest of the available IBM ILOG AMPL V12 2 USER S GUIDE 39 algorithms on each problem eliminating the need to choose a single optimizer for all purposes In the deterministic mode one thread will be used for dual simplex and if available a second thread will be used for barrier with crossover memoryemphasis i default 0 workfilelim r default 128
111. tion 38 mixed integer 55 algorithmic control directives 60 AMPL notation for options 19 batch mode 14 command line switches 25 end session 13 execute solver outside AMPL 22 installing 10 launching AMPL 13 learning the AMPL language 9 let command 90 solver interface 17 ampl prompt 13 append directives 33 IBM ILOG AMPL ASCII format problem and solution files 21 autoopt directive 39 auxiliary files creating 21 auxrootthreads directive 62 backtrack directive 62 baralg directive 47 barcorr directive 48 bardisplay directive 53 bargrowth directive 47 bariterlim directive 51 barobj range directive 48 baropt directive 39 barrier algorithm directives 47 barstart directive 48 basic solution simplex algorithm 38 basis simplex algorithm 38 V12 2 USER S GUIDE Index 93 batch mode 14 bbinterval directive 62 bestnode suffix 79 binary format problem and solution files 21 boundstr directive 57 branch directive 63 C cliquecuts directive 65 clocktype directive 51 71 coeffreduce directive 57 command display 20 let 90 option 18 25 option solver 17 predefined commands 26 solution 20 write 20 21 command line switches 25 comptol directive 48 concurrentopt directive 39 conflictdisplay directive 33 covercuts directive 65 CPLEX append directives 33 barrier algorithm 29 barrier algorithm QP extension 31 choice of algorithm 37 cplex_options option 32 linear programs 37 mem
112. tomatically stored and used between CPLEX invocations The readbasis and writebasis directives are included for backward compatibility with previous versions of CPLEX for AMPL which did not use variable status information If the readbasis directive is specified then the initial basis is instead read from the file 1 which must also be in the standard MPS basis format This basis determines the initial solution If the writebasis directive is specified CPLEX writes a record of the final simplex basis to the file named 2 in the standard MPS basis format Normally this is an optimal basis but it may be otherwise if an optimum does not exist or could not be found by the chosen algorithm or 1f the iterations were terminated prematurely by one of the directives described below readvector f1 writevector f2 These directives are used to take a barrier algorithm solution and write it to or read it from a CPLEX vec file Because AMPL always instructs CPLEX to take its barrier method solution and apply a hybrid method to obtain a basic solution this feature can only be used if a barrier iteration limit is exceeded If the readvector directive is specified CPLEX will read in a vec file named 1 and use it to initiate the hybrid crossover method that results in an optimal basic solution Note that CPLEX will not perform additional barrier iterations after reading in the vec file Similarly if the writevector directive is specified CPLEX will
113. tory You can give a specific location for the temporary files by setting option TMPDIR to a valid path On a PC you might use ampl option TMPDIR D temp On a UNIX platform a typical choice would be ampl option TMPDIR tmp IBM ILOG AMPL V12 2 USER S GUIDE 23 24 IBM ILOG AMPL V12 2 USER S GUIDE Command Line Switches Customizing AMPL Certain AMPL options normally set with the option command during an AMPL session can also be set when AMPL is first invoked This is done using a command line switch consisting of a hyphen and a single letter followed in some cases by a numeric or string value You will find these switches most useful when you have one or more model data or run file that you want AMPL to process using different option settings at different times without actually editing the files themselves The table below summarizes the command line switches and their equivalent names when set with the AMPL option command Table 4 1 AMPL Option Names for Command Line Switches Switch AMPL Option Description Cn Cautions n n 0 suppress caution messages n 1 report caution messages default n 2 treat cautions as errors en eexit n n gt 0 abandon command after n errors n lt 0 abort AMPL after Inl errors n 0 report any number of errors IBM ILOG AMPL V12 2 USER S GUIDE 25 Switch AMPL Option Description f funcwar
114. ts a solution to be found to the remaining ones Clearly knowing the composition of an IIS can help localize the source of the infeasibility When iisfind is used CPLEX uses the iis suffix to specify which variables and constraints are in the IIS as explained in Diagnosing Infeasibilities on page 81 IBM ILOG AMPL V12 2 USER S GUIDE 33 Directive for Tuning 34 CPLEX can try various values for algorithmic directives to find a set of values that will reduce solution time The directives below are used to control the tuning algorithm The algorithm progresses by trying different sets of values in trial runs tunefile f1 tunefileprm f2 These directives tell CPLEX to do tuning and to write the results to file 1 using AMPL directive names or to file 2 in CPLEX PRM format The tuning algorithm can take up to six to ten times longer than a regular solve invocation but the results may save time in future runs pretunefile f1 pretunefileprm f2 These directives tell CPLEX to write out the current non default directive settings before starting tuning The files may be used to return to the pre tuning settings since CPLEX will change all settings to the tuned values as part of the tuning algorithm The file 1 uses AMPL directive names and the file 2 is written in CPLEX PRM format The pretunefileprm 2 file may contain some CPLEX display settings which are not included in the pretunefile 1 form of the file paramfile f1
115. ts the maximum absolute value of the objective function CPLEX s barrier algorithm looks at this value to detect unbounded problems Any positive value is acceptable input However care should be taken to avoid choosing a value so small that CPLEX will conclude a problem is unbounded when it is not barstart i default 1 This directive controls the starting point CPLEX uses to initiate the barrier method The default setting of 1 will suffice for most problems Consider other values 2 3 and 4 if the barrier method appears to converge slowly or when the predual directive is specified comptol r default le 8 This directive specifies the complementarity tolerance used by the barrier algorithm to test convergence The barrier algorithm will terminate with an optimal solution if the relative complementarity is smaller than this value Any positive number larger than 1e 10 is acceptable input crossover i default 1 On a linear problem by default i 1 CPLEX initiates the crossover algorithm to convert the barrier solution to a basic or vertex solution using a primal simplex like method If i 2 a dual simplex like method is used for the crossover The crossover algorithm can be turned off by setting i 0 densecol i default 0 CPLEX uses this directive to distinguish dense columns in the constraint matrix Because barrier algorithm performance can improve dramatically if dense columns are treated separately changing this value may impro
116. tset of the branch amp cut procedure branch il default 0 The branch directive determines the direction in which CPLEX branches on the selected fractional variable When branching on a variable x that has fractional value r CPLEX creates one subproblem that has the constraint x gt ceil r and one that has the constraint x lt floor r these are the up branch and down branch respectively By default 11 0 CPLEX uses an internal heuristic to decide whether it should first process the subproblem on the up branch or on the down branch You may instead specify consistent selection of the up branch 11 1 or down branch i1 1 Sometimes one of these settings leads the algorithm to examine and discard the poorer branches high in the tree reducing the tree size and overall solution time Branching control can also be exercised using the direction suffix described in Algorithmic Control on page 77 fpheur i3 default 0 This directive tells CPLEX whether or not to apply the feasibility pump heuristic and to what effect The default strategy is specified with 0 and allows CPLEX to decide whether or not to apply the heuristic The value of 1 specifies that the feasibility pump heuristic should not be applied The value of 1 directs CPLEX to seek any solution while the value of 2 directs CPLEX to seek a solution with a good objective value The feasibility pump heuristic can be quite expensive but it is sometimes able to find solutions on pro
117. ty criterion for CPLEX s branch and bound algorithm absmipgap r1 default 0 0 mipgap r2 default 1 0e 4 The optimal value of your integer program is bounded on one side by the best integer objective value found so far and on the other side by a value deduced from all the node subproblems solved so far The search is terminated when either best node best integer lt r1 IBM ILOG AMPL V12 2 USER S GUIDE 69 or best node best integer le 10 best integer lt r2 Thus the returned objective value will be no more than rl from the optimum and will also be within about 100 r2 percent of the optimum if the optimal value is significantly greater than 1 in magnitude Increasing r1 or r2 allows a solution further from optimum to be accepted The search may be significantly shortened as a result Valid values for r2 lie between 1e 9 and 1 0 integrality r default 1 0e 5 In the optimal solution to a subproblem a variable is considered to have an integral value if it lies within r of an integer For some problems increasing r may give an acceptable solution faster This parameter may be set to 0 to improve the robustness of MIP solutions most commonly with little if any impact on the performance of the optimizer lowercutoff rl default 1 0e75 uppercutoff r2 default 1 0e75 These directives specify alternative cutoff values a node is fathomed if its subproblem has an objective less than rl for maximization pro
118. u can list several strings which AMPL will automatically concatenate ampl option cplex options crash 0 dual ampl feasibility 1 0e 8 scale 1 ampl lpiterlim 100 In this form you must take care to supply the space that goes between the directives here we have put it before feasibility and iterations If you have specified the directives above and then want to try setting say optimality to 1 0e 8 and changing crash to 1 you could use ampl option cplex options ampl optimality 1 0e 8 crash 1 However this will replace the previous cplex_options string The other previously specified directives such as feasibility and iterations will revert to their default values IBM ILOG AMPL V12 2 USER S GUIDE CPLEX supplies a default value for every directive not explicitly specified defaults are indicated in the discussion below To append new directives to cplex_options use this form ampl option cplex options cplex options ampl optimality 1 0e 8 crash 1 A in front of an option name denotes the current value of that option so this statement just appends more directives to the current directive string As a result the string contains two directives for crash but the new one overrides the earlier one Directives for Handling Infeasible Problems The following directives are useful when CPLEX finds that your problem is infeasible Setting these options directs CPLEX to take additional steps when solve is
119. uadratic program is given as T 7 minimize ix Ox cx subject to Ax b I lt x lt u where represents lt gt or operators In the above formula Q represents a matrix of quadratic objective function coefficients Its diagonal elements Q are the coefficients of the quadratic terms xf The nondiagonal elements Q and Q are added together to be the coefficient of the term x x IBM ILOG AMPL V12 2 USER S GUIDE The CPLEX linear programming algorithms incorporate an extension for quadratic programming For a problem to be solvable using this option the following conditions must hold 1 All constraints must be linear 2 The objective must be a sum of terms each of which is either a linear expression or a product of two linear expressions 3 For any values of the variables whether or not they satisfy the constraints the quadratic part of the objective must have a nonnegative value if a minimization or a nonpositive value if a maximization The last condition is known as positive semi definiteness for minimization or negative semi definiteness for maximization CPLEX automatically recognizes nonlinear problems that satisfy these conditions and invokes the barrier algorithm to solve them Nonlinear problems of any other kind are rejected with an appropriate message Most CPLEX features applying to continuous LP models apply also to continuous QP models likewise most features applying to linear MIP models
120. using the suffix sstatus_num in place of sstatus The entries in the third column are comments The output of the display command shows that variable Incr MID_C is in the basis and InCr W_TEX at its lower bound at optimality You can change a variable s basis status using AMPL s 1et command This may be useful in instances where you want to provide an initial basis to jump start CPLEX IBM ILOG AMPL V12 2 USER S GUIDE CPLEX Synonyms The following list contains alternative names for certain CPLEX directives The use of primary names is recommended Table A 1 CPLEX Synonyms Synonym agglim dense display doperturb endbasis endvector growth heuristic iterations mipsolutions Primary Directive aggfill densecol Ipdisplay perturb writebasis writevector bargrowth rootheuristic Ipiterlim solutionlim IBM ILOG AMPL V12 2 USER S GUIDE 91 92 Synonym nodes nodesel presolvedual startalg startalgorithm startbasis startvector subalgorithm time treememory varsel writeprob Primary Directive nodelim nodeselect predual mipstartalg mipstartalg readbasis readvector mipalgorithm timelimit treememlim varselect file IBM ILOG AMPL V12 2 USER S GUIDE symbol notation for options 19 syntax set initial values 19 A absmipgap directive 69 advance directive 44 aggcutlim directive 57 aggfill directive 41 aggregate directive 41 algorithm directives for selec
121. ve optimization time Columns with more nonzeros than this setting are considered to be dense If left at the default value CPLEX will automatically determine a value considering factors such as the size of the problem Any nonnegative integer is acceptable input ordering i default 0 This directive selects the method used to permute the rows of the constraint matrix in order to reduce fill in the Cholesky factor There is a trade off between ordering speed and sparsity of the Cholesky factor The automatic default setting usually chooses the best ordering for the problem The approximate minimum degree AMD algorithm i 1 balances speed and fill The approximate minimum fill AMF algorithm i 2 usually generates slightly better orderings than AMD at the cost of more ordering run time The nested dissection ND algorithm triggered by using i 3 sometimes reduces Barrier run time dramatically ten IBM ILOG AMPL V12 2 USER S GUIDE fold reductions have been observed for some problems This option sometimes produces worse orderings though and it requires much more ordering run time gcpconvergetol default le 7 This directive sets the tolerance on complementarity for convergence in quadratically constrained problems QCP The barrier algorithm terminates with an optimal solution if the relative complementarity is smaller than this value Changing this tolerance to a smaller value may result in greater numerical precision of the
122. verride these conventions so that you can start from a saved basis and can stop when a certain criterion is satisfied Command line versions of CPLEX for AMPL can also be stopped by using break typically by pressing the Control and C keys simultaneously The best solution found so far is returned IBM ILOG AMPL V12 2 USER S GUIDE bariterlim i default 2100000000 CPLEX stops after i barrier method iterations and returns its current solution whether or not it has determined that the solution is optimal clocktype i default 2 The default setting of clocktype 2 means that CPLEX will measure time in terms of elapsed wall clock seconds A setting of 1 means that CPLEX will measure time in terms of CPU seconds lpiterlim i default 2 1e 9 or larger CPLEX stops after i simplex method iterations and returns its current solution whether or not it has determined that the solution is optimal lowerobj r1 default 1 0e 75 upperobj r2 default 1 0e 75 CPLEX stops at the first iteration where the solution is feasible in the constraints and the objective value is below r1 or above r2 At their default values these directives have no practical effect Setting r1 for a minimization or r2 for a maximization to a good value for the objective will cause CPLEX to stop as soon as it achieves this value readbasis f1 writebasis f2 Current versions do not require you to explicitly save the basis to hot start CPLEX variable status is au

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