ILOG CPLEX 11.0 User's Manual

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easonable amount of computation time, a user might choose a larger relative MIP Gap toallow early termination; for example, a relative MIP Gap of 0.05 (corresponding to 5%).Conversely, in a model where the objective function amounts to billions of dollars and thedata are accurate to a degree that further processing is worthwhile, a tighter relative MIPGap (even 0.0) may be advantageous to avoid any chance of missing the best possiblesolution.ILOG CPLEX also terminates optimization when it reaches a limit that you have set. Youcan set limits on time, number of nodes, size of tree memory, and number of integersolutions. Table 14.4 summarizes those parameters and their purpose.Table 14.4Parameters to Limit MIP OptimizationTo set a limit onUse this parameterConcert Technology Callable LibraryInteractive Optimizerelapsed time TiLim CPX_PARAM_TILIM timelimitnumber of nodes NodeLim CPX_PARAM_NODELIM mip limits nodessize of tree TreLim CPX_PARAM_TRELIM mip limits treememorynumber of integer solutions IntSolLim CPX_PARAM_INTSOLLIM mip limits solutionsrelative MIP gap tolerance EpGap CPX_PARAM_EPGAP mip tolerances mipgapabsolute MIP gap tolerance EpAGap CPX_PARAM_EPAGAP mip tolerances absmipgapILOG CPLEX also terminates when an error occurs, such as when ILOG CPLEX runs outof memory or when a subproblem cannot be solved. If an error is due to failure to solve asubproblem, an additional line appears in the node log file to indicate the reason for thatfailure. For suggestions about overcoming such errors, see Troubleshooting MIPPerformance Problems on page 288.Tuning Performance Features of the Mixed Integer OptimizerThe ILOG CPLEX Mixed Integer Optimizer contains a wealth of features intended to aid inthe solution of challenging MIP models. While default strategies are provided that solve themajority of models without user involvement, there exist difficult models that benefit fromattention to performance tuning.To help you decide whether default settings of parameters are best for your model, orwhether other parameter settings may improve performance, the tuning tool is available.264 ILOG CPLEX 11.0 — USER’ S MANUAL
Tuning Tool on page 161 explains more about this utility and directs you to examples of itsuse.This section discusses the ILOG CPLEX features and parameters that are the most likely tooffer help with difficult models.◆ Branch & Cut or Dynamic Search on page 265◆ Probing on page 270◆ Cuts on page 271◆ Heuristics on page 275◆ Preprocessing: Presolver and Aggregator on page 277◆ Starting from a Solution on page 279◆ Issuing Priority Orders on page 280Branch & Cut or Dynamic SearchIn addition to a robust branch & cut algorithm, ILOG CPLEX also offers a dynamic searchalgorithm. The dynamic search algorithm consists of the same building blocks asbranch & cut: LP relaxation, branching, cuts, and heuristics. The following sections of themanual describe performance and tuning in relation to branch & cut. The parametersmentioned in this context have a similar effect in the dynamic search algorithm as inconventional branch & cut. In fact, the generic description in relation to branch & cutsuffices for both branch & cut and dynamic search.ILOG CPLEX offers the MIP search parameter (MIPSearch, CPX_PARAM_MIPSEARCH) foryou to control whether it pursues dynamic search or conventional branch & cut in solvingyour problem. At its default setting, this parameter specifies that ILOG CPLEX shouldchoose which algorithm to apply on the basis of characteristics it finds in your model. Othersettings allow you to specify which search to pursue.Because many parameter settings directly affect the branch & cut and dynamic searchalgorithms, here is a general description of how branch & cut is implemented withinILOG CPLEX.In the branch & cut algorithm, ILOG CPLEX solves a series of continuous subproblems. Tomanage those subproblems efficiently, ILOG CPLEX builds a tree in which eachsubproblem is a node. The root of the tree is the continuous relaxation of the original MIPproblem.If the solution to the relaxation has one or more fractional variables, ILOG CPLEX will tryto find cuts. Cuts are constraints that cut away areas of the feasible region of the relaxationthat contain fractional solutions. ILOG CPLEX can generate several types of cuts. (Cuts onpage 271 tells you more about that topic.)ILOG CPLEX 11.0 — USER’ S MANUAL 265
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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
Page 213 and 214: choice of starting-point heuristic
Page 215 and 216: To see the current value of the col
Page 217 and 218: C H A P T E R11Solving Network-Flow
Page 219 and 220: ◆◆l a , the lower bound, sets t
Page 221 and 222: of the objective function calculate
Page 223 and 224: then ILOG CPLEX will carry out such
Page 225 and 226: -a 1 + a 2 - a 8 - a 9 + a 14 = 0-
Page 227 and 228: C H A P T E R12Solving Problems wit
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Page 231 and 232: A similar Java program using Concer
Page 233 and 234: ◆ qp indicates that you want ILOG
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Page 239 and 240: C H A P T E R13Solving Problems wit
Page 241 and 242: Figure 13.2y(0, 1)(-1, 0)d(1, 0)xc(
Page 243 and 244: Detecting Problem TypeILOG CPLEX de
Page 245 and 246: COLUMNSMARK0000 'MARKER''INTORG'C15
Page 247 and 248: C180 R100 159C180 R119 200C180 R120
Page 249 and 250: QMATRIXC158 C158 1C158 C189 0.5C189
Page 251 and 252: ◆From the Callable Library, use t
Page 253: Part IVDiscrete OptimizationThis pa
Page 256 and 257: Stating a MIP ProblemA mixed intege
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Page 262 and 263: 1. finding a succession of improvin
Page 266 and 267: If the solution to the relaxation s
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Page 270 and 271: directives about the order in which
Page 272 and 273: ◆ Parameters Affecting Cuts on pa
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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
Page 290 and 291: parameter settings are also worth c
Page 292 and 293: When you set a MIP cutoff value, IL
Page 294 and 295: memory. It also includes several op
Page 296 and 297: ◆◆●●at problem modification
Page 298 and 299: ◆In the Callable Library, use the
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 310 and 311: Note: The parameter to limit the nu
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Limitations Due to Numeric Difficul
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Examining the Solution PoolIn the I
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For a sample of these methods or ro
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◆◆In the Callable Library (C AP
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Then display the objective value of
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◆ If you want to filter solutions
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●●●In the C++ API, use the me
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NAME locationRNGFILTER f2 -inf 0tra
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continuous, a model containing one
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◆The routine setPriorities sets t
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What Are Semi-Continuous Variables?
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With that model, now the applicatio
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Piecewise Linearity in ILOG CPLEXSo
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Reminder: It may help you understan
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overlaps with an endpoint of two ot
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Figure 18.4400003000020000100000Fig
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in demand; in terms of this model,
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348 ILOG CPLEX 11.0 — USER’ S M
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What Are Logical Constraints?For IL
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◆◆Cplex.NotCplex.IfThenAgain, t
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In Concert Technology applications,
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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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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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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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