ILOG CPLEX 11.0 User's Manual

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Note: The parameter to limit the number of integer solutions in a MIP (IntSolLim inConcert Technology or CPX_PARAM_INTSOLLIM in the Callable Library or mip limitssolutions in the Interactive Optimizer) does not apply to the populate procedure; if youwant to limit the populate procedure, apply the populate limit parameter (PopulateLim,CPX_PARAM_POPULATELIM) instead.◆◆◆Time limit, as in a standard MIP optimization.●●●TiLim in Concert TechnologyCPX_PARAM_TILIM in the Callable Library (C API)timelimit in the Interactive OptimizerNode limit, as in a standard MIP optimization.●●●NodeLim in Concert TechnologyCPX_PARAM_NODELIM in the Callable Library (C API)mip limit nodes in the Interactive OptimizerIn the absence of other stopping criteria, the populate procedure stops when it cannotenumerate any more solutions.In particular, if you specify an objective tolerance with the relative or absolute solutionpool gap parameters, populate stops if it cannot enumerate any more solutions within thespecified objective tolerance.However, there may exist additional solutions that are feasible, and if you have specifiedan objective tolerance, those feasible solutions may also satisfy this additional criterion.(For example, there may be a great many solutions to a given problem with the sameinteger values but different values for continuous variables.) Depending on the solutionpool intensity parameter, populate may or may not enumerate all possible solutions.Consequently, populate may stop when it has enumerated only a subset of the solutionssatisfying your criteria.Choosing Whether to Accumulate or PopulateBoth MIP optimization and populate generate a series of solutions, but the two proceduresdiffer in their aims. The aim of MIP optimization is optimality: after a solution has beenfound, MIP optimization will generate only solutions of improving objective value, and theprocedure will stop when optimality has been proven. In contrast, the aim of populate is togenerate as many solutions as possible: after a solution has been found, populate may310 ILOG CPLEX 11.0 — USER’ S MANUAL
generate solutions of both improving and degrading objective value, and it will stop onlywhen it cannot generate any additional solutions or because other stopping criteria intervene.In order to decide which procedure is better for your application, you should first try theMIP optimizer. If the solutions produced are sufficient for your application, then the MIPoptimizer is the appropriate choice. If not, then you should try populate to generate moresolutions and to have more control over the properties of the generated solutions.Advanced Use: Interaction of MIP Optimization and PopulateShould you call MIP optimization and then populate, or should you call populate alone?You can call populate after you call the MIP optimizer, or you can call populate on its ownafter you read or create a model. In order to decide which to do, you need to know moreabout the two procedures.Recall that the algorithm underlying populate works in two phases. If you call the MIPoptimizer after the model is read, it will gather and store information about the search as itsolves the model. In practice, its activity constitutes the first phase of the populate algorithm.In the general case, if you then call populate, populate will re-use the information stored bythe MIP optimizer and carry out only the second phase.In contrast, if you call populate immediately after the model is read, populate will performboth the first phase and the second phase.If you specify a nondefault setting of the pool intensity parameter, then calling the MIPoptimizer and afterwards calling populate will give the same results in terms of performanceand solutions generated as calling populate alone. (The exception to this generalizationoccurs when the pool intensity parameter is set at its default value, 0 (zero) that is,automatic. For details about that case, see the documentation of the solution pool intensityparameter.)Calling populate alone is simpler than calling populate after MIP optimization. However, ifyou want more control over the details of the two phases (for example, if you want to specifydifferent stopping criteria for each phase), then you need to call MIP optimization followedby populate, instead of calling populate alone. The risk associated with this approach is thatpopulate might not be able to reuse the information about the tree from the previous MIPoptimization; in that case, populate will start from scratch; that is, it again performs the firstphase, followed by the second phase. In particular, this repetition of the first phase willhappen if you increase the pool intensity parameter between the call to MIP optimizationand the call to populate.More information about this topic can be found the documentation about the parameterSolnPoolIntensity (CPX_PARAM_SOLNPOOLINTENSITY) in the ILOG CPLEXParameter Reference Manual.In short, if you want the simplicity of a black box, call populate alone; if you need morecontrol, call MIP optimization, then populate.ILOG CPLEX 11.0 — USER’ S MANUAL 311
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ILOG CPLEX 11.0User’s ManualSepte
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C O N T E N T STable of ContentsILO
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Building the Model by Column . . .
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Program Description . . . . . . . .
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Cholesky Factor in the Log File . .
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Examples: QCP . . . . . . . . . . .
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Chapter 18 Using Piecewise Linear F
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Representing the Data. . . . . . .
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Reading and Writing MPS Files . . .
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Protected Variables in Presolve Red
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P R E F A C EMeet ILOG CPLEXILOG CP
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When a linear optimization problem
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◆◆◆◆implemented in ILOG CPL
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Solution Pool: Generating and Keepi
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Table 1ExamplesExample Source File
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◆◆◆◆◆◆Overview of the A
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Wolsey, Laurence A., Integer Progra
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C H A P T E R1ILOG Concert Technolo
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Compiling and LinkingCompilation an
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The class IloNumVar provides method
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IloModel object itself and added to
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Table 1.1 Concert Technology Modeli
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Choosing an OptimizerSolving the ex
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Table 1.4 on page 55 summarizes the
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Dynamic control of the solution pro
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However, querying solution values v
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parameter for the getQuality method
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model2.add(model1);model2.add(IloCo
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Example: Optimizing the Diet Proble
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Concert Technology, as demonstrated
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method IloModel::add returns the mo
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Licenses in a Java ApplicationILOG
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Models that consist only of such co
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The special case of linear expressi
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IloObjective obj = cplex.add(cplex.
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Solving the ModelOnce you have crea
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IloCplex cplex = new IloCplex();Ilo
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IloCplex.setParam(IloCplex.IntParam
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Thus, the suggested method for sett
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Basis InformationWhen solving an LP
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where A is a sparse matrix. A spars
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The example starts by evaluating th
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IloMPModeler.setLinearCoefs, and Il
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◆What is the purpose (the objecti
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Step 3Create the modelGo to the com
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Step 9Add nutritional constraintsGo
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Step 14Display the solutionGo to th
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Step 18Enclose the application in t
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C H A P T E R4ILOG CPLEX Callable L
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◆◆file reading and writing rout
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◆◆If data already exist in MPS,
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For example, let’s look at the sy
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As you modify a problem object thro
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However, ILOG CPLEX updates the nam
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whether an optimization should be a
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Callable Library have names greater
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◆CPXsetstrparam accepts arguments
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Here’s another way to visualize a
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program—can discover the length o
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Part IIProgramming ConsiderationsTh
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◆ Test Data on page 135◆ Choose
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◆ Use the MIP optimizer if the pr
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Choose Clarity First, Efficiency La
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1. If you can reproduce the behavio
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indices, errors will occur. Therefo
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Understanding File FormatsThe refer
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definitions that it finds. The firs
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◆◆IloXmlReader creates a reader
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Controlling Message ChannelsIn both
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more calls to the message handling
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Concert Technology Message Channels
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Types of ILM Runtime LicensesILM ru
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char *inststr = NULL;char *envstr =
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The registerLicense Method for Java
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not correct that problem either. In
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In the Interactive Optimizer, you c
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For models not in the current worki
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◆◆In the .NET API, pass an inst
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C H A P T E R9Solving LPs: Simplex
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The symbolic names for these settin
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When no candidates are present, the
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solution; but examination of soluti
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Then to later read an advanced basi
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Table 9.5 PPriInd Parameter Setting
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ILOG CPLEX ignores the coefficients
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Numeric DifficultiesILOG CPLEX is d
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esult is the same as would be obtai
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automatically perturbs the variable
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4. Consider alternate scalings.You
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smaller in absolute value than the
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exceptions are caught as well, and
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C H A P T E R10Solving LPs: Barrier
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The ILOG CPLEX Barrier Optimizer is
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And then you call the solution rout
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Here is an example of a log file fo
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If solution values are large in abs
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Normalized errors, for example, rep
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◆ workmem in the Interactive Opti
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est order. It may require more time
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choice of starting-point heuristic
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To see the current value of the col
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C H A P T E R11Solving Network-Flow
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◆◆l a , the lower bound, sets t
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of the objective function calculate
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then ILOG CPLEX will carry out such
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-a 1 + a 2 - a 8 - a 9 + a 14 = 0-
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C H A P T E R12Solving Problems wit
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convex QPs, Q must be positive semi
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A similar Java program using Concer
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◆ qp indicates that you want ILOG
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RootAlg parameter (QPMETHOD in the
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ilolpex1.cpp counterpart. Here the
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C H A P T E R13Solving Problems wit
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Figure 13.2y(0, 1)(-1, 0)d(1, 0)xc(
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Detecting Problem TypeILOG CPLEX de
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COLUMNSMARK0000 'MARKER''INTORG'C15
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C180 R100 159C180 R119 200C180 R120
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QMATRIXC158 C158 1C158 C189 0.5C189
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◆From the Callable Library, use t
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Part IVDiscrete OptimizationThis pa
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Stating a MIP ProblemA mixed intege
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sections does not matter. To enter
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Page 262 and 263: 1. finding a succession of improvin
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Page 278 and 279: Table 14.10Parameters for Controlli
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Page 282 and 283: After you have solved a MIP, you wi
Page 284 and 285: Table 14.13Settings of the MIP Disp
Page 286 and 287: ILOG CPLEX also logs its addition o
Page 288 and 289: ◆ Parent specifies the NodeID of
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Page 292 and 293: When you set a MIP cutoff value, IL
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Page 296 and 297: ◆◆●●at problem modification
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Page 300 and 301: ●●Then call CPXprimopt to optim
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Page 306 and 307: Populating the Solution PoolILOG CP
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Page 312 and 313: Example: Using Populate after MIP O
Page 314 and 315: Limitations Due to Numeric Difficul
Page 316 and 317: Examining the Solution PoolIn the I
Page 318 and 319: For a sample of these methods or ro
Page 320 and 321: ◆◆In the Callable Library (C AP
Page 322 and 323: Then display the objective value of
Page 324 and 325: ◆ If you want to filter solutions
Page 326 and 327: ●●●In the C++ API, use the me
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Page 330 and 331: continuous, a model containing one
Page 332 and 333: ◆The routine setPriorities sets t
Page 334 and 335: What Are Semi-Continuous Variables?
Page 336 and 337: With that model, now the applicatio
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Page 340 and 341: Reminder: It may help you understan
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Page 350 and 351: What Are Logical Constraints?For IL
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Describing the ProblemThe problem i
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Notice that how much to use and buy
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Then use a for-loop to add the cons
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These lines (the action of the if-s
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Describing the ProblemThe problem i
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Stating Precedence ConstraintsIn ea
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Solving the ProblemAn emphasis on f
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What Is Column Generation?In colloq
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Solving this model with all columns
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Likewise, the application adds an a
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Pattern Generator ModelThe submodel
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Complete ProgramYou can see the ent
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your problem formulation caused thi
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To control the types of reductions
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What Is Unboundedness?Any class of
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Callable Library use the advanced r
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the conflict to arrive at a minimal
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the IIS finder can, and often more.
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Then you will see results like thes
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Now view the entire conflict with t
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The constraints in conflict with th
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If a model contains more than one c
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Immediately after that statement, i
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◆ Groups in the Conflict Refiner
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408 ILOG CPLEX 11.0 — USER’ S M
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The infeasibility on which FeasOpt
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Now the following lines invoke Feas
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suggests decreasing the upper bound
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416 ILOG CPLEX 11.0 — USER’ S M
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C H A P T E R28User-Cut and Lazy-Co
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However, there is an important dist
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◆◆Through the routine CPXreadco
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Here is an example of an MPS file e
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C H A P T E R29Using GoalsThis chap
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How Goals Are Implemented in Branch
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In the Java API, a Fail goal is ret
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This return statement returns an An
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The Goal StackTo understand how goa
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soon as they are enclosed in a goal
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The global cut goal for lhs[i] ≤
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If a node has multiple evaluators a
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As this example is an extension of
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C H A P T E R30Using Optimization C
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Reference Documents about Informati
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Query or Diagnostic CallbacksQuery
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● Cplex.DisjunctiveCutCallback in
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◆◆●●Cplex.HeuristicCallback
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It is not customary to write such a
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IloCplex::Callback mycallback = cpl
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Here is the previous sample of code
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◆◆cbdata, a pointer to ILOG CPL
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conventions of the Interactive Opti
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een added, it can be deleted by cal
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Interaction Between Callbacks and I
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C H A P T E R31Goals and Callbacks:
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The only functionality that is not
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C H A P T E R32Advanced Presolve Ro
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once. All of the node relaxation so
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- 5x1, + x2 ≤ 0 2y1, + y2, ≥ 1x
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problem, the problem has a presolve
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Modifying a ProblemThis section bri
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C H A P T E R33Advanced MIP Control
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value strictly greater than one. It
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Cut CallbackThe next example we con
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problem. Since branching involves a
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C H A P T E R34Parallel OptimizersT
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Threads and Performance Considerati
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3. Call the parallel optimizer with
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optimizer turns out to be the faste
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0 0 3383.7784 16 4505.0000 Cuts: 35
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I N D E XIndexAabsolute objective d
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ole in converting LP to network flo
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emoving from basis (C++ API) 62repr
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CPX_PARAM_PCPX_PARAM_POLISHTIMEsolu
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CPXcreateprob 467CPXcreateprob rout
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CPXwcpxwarning message channel 151C
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empty goal 431, 435end methodIloEnv
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getDuals method (Java API) 88getMax
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emove method (Java API) 94IloModele
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ecords singularities 188relocating
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from 218head 218sink 219source 219s
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control callbacks and 453query call
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primal reduction 385primal simplex
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eturn statusBounded (Java API) 81Er
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solvingdiet problem (Java API) 82mo
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arrier 208WorkMem 293WorkMem parame
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