ILOG CPLEX 11.0 User's Manual

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Root Relaxation and Parallel MIP ProcessingIn some models, the continuous root relaxation takes significant solution time before parallelbranching begins. These models have potential for additional speed increases by running theroot relaxation step in parallel. If the root problem is an LP or QP and the Threadsparameter is set to a value greater than 1 (one), the concurrent optimizer is invoked bydefault. This provides a form of parallelism that assigns the available threads to multipleoptimizers. If the root problem is a QCP, the barrier optimizer alone is used.You can try a different form of parallelism at the root by selecting the barrier optimizerspecifically with the starting algorithm parameter:◆◆RootAlg in Concert Technology;CPX_PARAM_STARTALG in the Callable Library;◆ set mip strategy startalgorithm in the Interactive Optimizer.In such a case, the parallel threads will all be applied to the barrier algorithm.Memory Considerations and the Parallel MIP OptimizerBefore the parallel MIP optimizer invokes parallel processing, it makes separate, internalcopies of the initial problem. The individual processors use these copies during computation,so each of them requires an amount of memory roughly equal to the size of the presolvedmodel.Output from the Parallel MIP OptimizerThe parallel MIP optimizer generates slightly different output in the node log (see ProgressReports: Interpreting the Node Log on page 283) from the sequential MIP optimizer. Thefollowing paragraphs explain those differences.ILOG CPLEX prints a summary of timing statistics specific to the parallel MIP optimizer atthe end of optimization. You can see typical timing statistics in the following sample run.Problem 'fixnet6.mps.gz' read.Read time = 0.02 sec.CPLEX> oTried aggregator 1 time.MIP Presolve modified 308 coefficients.Aggregator did 1 substitutions.Reduced MIP has 477 rows, 877 columns, and 1754 nonzeros.Presolve time = 0.00 sec.Clique table members: 2.MIP emphasis: balance optimality and feasibility.Root relaxation solution time = 0.00 sec.NodesCuts/Node Left Objective IInf Best Integer Best Node ItCnt Gap* 0+ 0 97863.0000 3192.0420 60 96.74%* 0+ 0 4505.0000 3192.0420 60 29.14%498 ILOG CPLEX 11.0 — USER’ S MANUAL
0 0 3383.7784 16 4505.0000 Cuts: 35 114 24.89%0 0 3489.7887 13 4505.0000 Cuts: 17 134 22.54%0 0 3531.4512 16 4505.0000 Cuts: 11 149 21.61%* 0+ 0 4501.0000 3531.4512 149 21.54%0 0 3552.4474 19 4501.0000 Cuts: 9 159 21.07%0 0 3588.7513 19 4501.0000 Cuts: 8 178 20.27%0 0 3597.3630 20 4501.0000 Cuts: 5 185 20.08%0 0 3598.6200 21 4501.0000 Cuts: 6 190 20.05%0 0 3601.2921 22 4501.0000 Cuts: 3 194 19.99%* 0+ 0 4457.0000 3601.2921 194 19.20%0 0 3602.5189 23 4457.0000 Cuts: 3 197 19.17%0 0 3633.5846 20 4457.0000 Cuts: 2 204 18.47%0 0 3638.8299 22 4457.0000 Covers: 1 206 18.36%0 0 3649.9331 22 4457.0000 Cuts: 3 212 18.11%0 0 3652.9758 28 4457.0000 Cuts: 5 218 18.04%0 0 3656.7563 24 4457.0000 Cuts: 3 227 17.95%0 0 3659.1865 29 4457.0000 Cuts: 4 232 17.90%0 0 3664.7373 26 4457.0000 Covers: 1 236 17.78%0 0 3676.2923 33 4457.0000 Covers: 5 244 17.52%0 0 3676.7448 31 4457.0000 Flowcuts: 2 250 17.51%0 0 3676.9154 33 4457.0000 Flowcuts: 2 254 17.50%* 0+ 0 3994.0000 3676.9154 254 7.94%* 0+ 0 3990.0000 3676.9154 254 7.85%* 0+ 0 3985.0000 3676.9154 254 7.73%0 2 3680.6918 22 3985.0000 3676.9154 254 7.73%* 22 5 integral 0 3983.0000 3770.3216 358 5.34%Root node processing (before b&c):Real time = 1.39Parallel b&c, 2 threads:Real time = 0.24Sync time (average) = 0.08Wait time (average) = 0.03-------Total (root+branch&cut) = 1.63 sec.Cover cuts applied: 13Flow cuts applied: 40Gomory fractional cuts applied: 6Solution pool: 8 solutions savedMIP - Integer optimal solution: Objective = 3.9830000000e+03Solution time = 1.63 sec. Iterations = 426 Nodes = 40The sample reports that the processors spent an average of 0.03 of a second of real timewaiting for other processors to provide nodes to be processed. The Sync time is the averagetime a processor spends trying to synchronize by accessing globally shared data. Becauseonly one processor at a time can access such data, the amount of time spent insynchronization is really crucial: any other processor that tries to access this region mustwait, thus sitting idle, and this idle time is counted separately from the Wait time.There is another difference in the way logging occurs in the parallel MIP optimizer. Whenthis optimizer is called, it makes a number of copies of the problem. These copies are knownas clones. The parallel MIP optimizer creates as many clones as there are threads available toit. When the optimizer exits, these clones and the memory they used are discarded.ILOG CPLEX 11.0 — USER’ S MANUAL 499
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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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◆milp, miqp, or miqcpindicating t
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1. finding a succession of improvin
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easonable amount of computation tim
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If the solution to the relaxation s
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anches taken so far in this dive. S
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directives about the order in which
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◆ Parameters Affecting Cuts on pa
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◆●●IloCplex.getNcuts in the J
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Relaxation Induced Neighborhood Sea
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Table 14.10Parameters for Controlli
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Library). If this process succeeds,
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After you have solved a MIP, you wi
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Table 14.13Settings of the MIP Disp
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ILOG CPLEX also logs its addition o
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◆ Parent specifies the NodeID of
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parameter settings are also worth c
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When you set a MIP cutoff value, IL
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memory. It also includes several op
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◆◆●●at problem modification
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◆In the Callable Library, use the
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●●Then call CPXprimopt to optim
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◆ The Incumbent and the Solution
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c17: x1 - y11 >= 0c18: x1 - y21 >=
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Populating the Solution PoolILOG CP
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NodesCuts/Node Left Objective IInf
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Note: The parameter to limit the nu
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Example: Using Populate after MIP O
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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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Page 451 and 452: ● Cplex.DisjunctiveCutCallback in
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Page 457 and 458: IloCplex::Callback mycallback = cpl
Page 459 and 460: Here is the previous sample of code
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Page 469 and 470: C H A P T E R31Goals and Callbacks:
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Page 473 and 474: C H A P T E R32Advanced Presolve Ro
Page 475 and 476: once. All of the node relaxation so
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Page 479 and 480: problem, the problem has a presolve
Page 481 and 482: Modifying a ProblemThis section bri
Page 483 and 484: C H A P T E R33Advanced MIP Control
Page 485 and 486: value strictly greater than one. It
Page 487 and 488: Cut CallbackThe next example we con
Page 489 and 490: problem. Since branching involves a
Page 491 and 492: C H A P T E R34Parallel OptimizersT
Page 493 and 494: Threads and Performance Considerati
Page 495 and 496: 3. Call the parallel optimizer with
Page 497: optimizer turns out to be the faste
Page 501 and 502: I N D E XIndexAabsolute objective d
Page 503 and 504: ole in converting LP to network flo
Page 505 and 506: emoving from basis (C++ API) 62repr
Page 507 and 508: CPX_PARAM_PCPX_PARAM_POLISHTIMEsolu
Page 509 and 510: CPXcreateprob 467CPXcreateprob rout
Page 511 and 512: CPXwcpxwarning message channel 151C
Page 513 and 514: empty goal 431, 435end methodIloEnv
Page 515 and 516: getDuals method (Java API) 88getMax
Page 517 and 518: emove method (Java API) 94IloModele
Page 519 and 520: ecords singularities 188relocating
Page 521 and 522: from 218head 218sink 219source 219s
Page 523 and 524: control callbacks and 453query call
Page 525 and 526: primal reduction 385primal simplex
Page 527 and 528: eturn statusBounded (Java API) 81Er
Page 529 and 530: solvingdiet problem (Java API) 82mo
Page 531 and 532: arrier 208WorkMem 293WorkMem parame
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