ILOG CPLEX 11.0 User's Manual

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◆ The Incumbent and the Solution Pool on page 320◆ Parameters of the Solution Pool on page 321◆ Filtering the Solution Pool on page 323What Is the Solution Pool?The solution pool stores multiple solutions to a mixed integer programming (MIP) model.With this feature, you can direct the algorithm to generate multiple solutions in addition tothe optimal solution. For example, some constraints may be difficult to formulate efficientlyas linear expressions, or the objective may be difficult to quantify exactly. In such cases,obtaining multiple solutions will help you choose one which best fits all your criteria,including the criteria that could not be expressed easily in a conventional MIP model.Furthermore, you can use the solution pool and tools associated with it to explore andevaluate alternative solutions in a variety of ways:◆◆◆◆You can collect solutions within a given percentage of the optimal solution. To do so,apply the solution pool gap parameters (relative or absolute), as explained in Parametersof the Solution Pool on page 321.You can collect a set of diverse solutions. To do so, use the solution pool replacementparameter (SolnPoolReplace, CPX_PARAM_SOLNPOOLREPLACE) to set the solutionpool replacement strategy to CPX_SOLNPOOL_DIV, as explained in the documentation ofthat parameter in the ILOG CPLEX Parameter Reference Manual. In order to control thediversity of solutions even more finely, apply a diversity filter, as explained in DiversityFilters on page 324.In an advanced application of this feature, you can collect solutions with specificproperties. To do so, see Filtering the Solution Pool on page 323You can collect all solutions or all optimal solutions to a MIP model. To do so, set thesolution pool intensity parameter to its highest value, as explained in the documentationof SolnPoolIntensity, CPX_PARAM_SOLNPOOLINTENSITY in the ILOG CPLEXParameter Reference Manual.Example: Simple Facility Location ProblemA simple version of a facility location problem appears throughout this chapter to show howthe solution pool and the tools associated with it work. A company is considering opening asmany as four warehouses in order to serve nine different regions. The goal is to minimize thesum of fixed costs associated with opening warehouses (constraint c2) as well as the various302 ILOG CPLEX 11.0 — USER’ S MANUAL
transportation costs incurred to ship goods from the warehouses to the regions (constraintc3).Whether or not to open a warehouse is represented by binary variable xi, for i=1 to 4.Whether or not to ship goods from warehouse i to region j is represented by binary variableyji, for j=1 to 9 and i=1 to 4.Each region needs a specified amount of goods, and each warehouse can store only a limitedquantity of goods (constraints c4 to c7). In addition, each region must be served by exactlyone warehouse (constraints c8 to c16). Constraints c17 to c52 complete the model bystating that warehouse i must be open in order for goods to be shipped from warehouse i toany region j.The model for this simple facility location problem is available online in the formatted LPfile yourCPLEXdir/examples/data/location.lp. In standard form, a model for thesimple facility location problem looks like this:Minimizeobj: costSubject Toc1: - cost + fixed + transport = 0c2: - fixed + 130 x1 + 150 x2 + 170 x3 + 180 x4 = 0c3: - transport+ 10 y11 + 30 y12 + 25 y13 + 55 y14+ 10 y21 + 25 y22 + 25 y23 + 45 y24+ 20 y31 + 23 y32 + 30 y33 + 40 y34+ 25 y41 + 10 y42 + 26 y43 + 40 y44+ 28 y51 + 12 y52 + 20 y53 + 29 y54+ 36 y61 + 19 y62 + 16 y63 + 22 y64+ 40 y71 + 39 y72 + 22 y73 + 27 y74+ 75 y81 + 65 y82 + 55 y83 + 35 y84+ 34 y91 + 43 y92 + 41 y93 + 62 y94 = 0c4: 10 y11 + 10 y21 + 12 y31 + 15 y41 + 15 y51 + 15 y61 + 20 y71 + 25 y81 +30 y91 - 90 x1
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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
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 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
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
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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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◆◆Cplex.NotCplex.IfThenAgain, t
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354 ILOG CPLEX 11.0 — USER’ S M
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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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