ILOG CPLEX 11.0 User's Manual

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◆ Parent specifies the NodeID of the parent.◆ Depth indicates the depth of this node in the branch & cut tree.Those additional items are not applicable in dynamic search.Troubleshooting MIP Performance ProblemsEven the most sophisticated methods currently available to solve pure integer and mixedinteger programming problems require noticeably more computation than the methods forsimilarly sized continuous problems. Many relatively small integer programming modelsstill take enormous amounts of computing time to solve. Indeed, some such models havenever yet been solved. In the face of these practical obstacles to a solution, properformulation of the model is crucial to successful solution of pure integer or mixed integerprograms.For help in formulating a model of your own integer or mixed integer problem, you maywant to consult H.P. Williams’s textbook about practical model building (referenced inFurther Reading on page 39 in the preface of this manual).Also you may want to develop a better understanding of the branch & cut algorithm. For thatpurpose, Williams’s book offers a good introduction, and Nemhauser and Wolsey’s book(also referenced in Further Reading on page 39 in the preface of this manual) goes intogreater depth about branch & cut as well as other techniques implemented in theILOG CPLEX MIP Optimizer.Tuning Performance Features of the Mixed Integer Optimizer on page 264 in this chapter hasalready discussed several specific features that are important for performance tuning ofdifficult models. Here are more specific performance symptoms and the remedies that can betried.◆ Too Much Time at Node 0 on page 289◆ Trouble Finding More than One Feasible Solution on page 289◆ Large Number of Unhelpful Cuts on page 290◆ Lack of Movement in the Best Node on page 290◆ Time Wasted on Overly Tight Optimality Criteria on page 291◆ Slightly Infeasible Integer Variables on page 292◆ Running out of Memory on page 292◆ Difficulty Solving Subproblems: Overcoming Degeneracy on page 297◆ Unsatisfactory Optimization of Subproblems on page 297288 ILOG CPLEX 11.0 — USER’ S MANUAL
Too Much Time at Node 0If you observe that a very long time passes before the search begins processing nodes, it maybe that the root relaxation problem itself is taking a long time. The standard screen displaywill print a line telling "Root relaxation solution time =" once this root solve iscomplete, and a large solution time would be an indicator of an opportunity for tuning. Ifyou set the MIPDisplay parameter to 4, you may get a further indication of the difficultiesthis root solve has run into. Tuning techniques found in Solving LPs: Simplex Optimizers onpage 171, Solving Problems with a Quadratic Objective (QP) on page 227, and SolvingProblems with Quadratic Constraints (QCP) on page 239 are applicable to tuning the rootsolve of a MIP model, too. In particular, it is worth considering setting the RootAlgparameter to a nondefault setting, such as the barrier optimizer, to see if a simple change inalgorithm will speed up this step sufficiently.For some problems, ILOG CPLEX will spend a significant amount of time performingcomputation at node 0, apart from solving the continuous LP, QP, or QCP root relaxation.While this investment of time normally saves in the overall branch & cut, it does not alwaysdo so. Time spent at node 0 can be reduced by two parameters.First, you can try turning off the node heuristic by setting the parameter HeurFreq to -1.Second, try a less expensive variable selection strategy by setting the parameter VarSel to4, pseudo reduced costs.It is worth noting that setting the MIPEmphasis parameter to 1, resulting in an emphasis onfeasibility instead of optimality, often also speeds up the processing of the root node. If yourpurposes are compatible with this emphasis, consider using it.Trouble Finding More than One Feasible SolutionFor some models, ILOG CPLEX finds an integer feasible solution early in the process andthen does not find a better one for quite a while. One possibility, of course, is that the firstfeasible solution is optimal and will eventually be proven optimal. In that case, there are nobetter solutions.One possible approach to finding more feasible solutions is to increase the frequency of thenode heuristic, by setting the heuristic frequency parameter (HeurFreq,CPX_PARAM_HEURFREQ) to a value such as 10 or 5 or even 1. This heuristic can beexpensive, so exercise caution when setting this parameter to values less than 10.Another approach to finding more feasible solutions is to try a node selection strategyalternative. Setting the node selection parameter (NodeSel , CPX_PARAM_NODESEL) to 2invokes a best-estimate search, which sometimes does a better job of locating good qualityfeasible solutions than the default node selection strategy.The settings 1 (one) and 4 of the MIP emphasis parameter (MIPEmphasis,CPX_PARAM_MIPEMPHASIS) both address the issue of finding feasible solutions. TheseILOG CPLEX 11.0 — USER’ S MANUAL 289
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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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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
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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
Page 274 and 275: ◆●●IloCplex.getNcuts in the J
Page 276 and 277: Relaxation Induced Neighborhood Sea
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 290 and 291: parameter settings are also worth c
Page 292 and 293: When you set a MIP cutoff value, IL
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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
Page 302 and 303: ◆ The Incumbent and the Solution
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Page 306 and 307: Populating the Solution PoolILOG CP
Page 308 and 309: NodesCuts/Node Left Objective IInf
Page 310 and 311: Note: The parameter to limit the nu
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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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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