ILOG CPLEX 11.0 User's Manual

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What Are Logical Constraints?For ILOG CPLEX, a logical constraint combines linear constraints by means of logicaloperators, such as logical-and, logical-or, negation (that is, not), conditional statements (thatis, if ... then ...) to express complex relations between linear constraints. ILOG CPLEX canalso handle certain logical expressions appearing within a linear constraint. One such logicalexpression is the minimum of a set of variables. Another such logical expression is theabsolute value of a variable. There’s more about logical expressions in Which NonlinearExpressions Can Be Extracted? on page 352.What Can Be Extracted from a Model with Logical Constraints?Much the same logical constraints are available in these APIs of ILOG CPLEX.◆ Logical Constraints in the C++ API on page 350◆ Logical Constraints in the Java API on page 351◆ Logical Constraints in the .NET API on page 351For similar facilities in the Callable Library, see Using Indicator Constraints on page 355.Logical Constraints in the C++ APIIn C++ applications, the class IloCplex can extract modeling objects to solve a widevariety of MIPs, as you see in Solving the Model on page 50, summarized in Table 1.1 onpage 51. In fact, the C++ class IloCplex can extract logical constraints as well as somelogical expressions. The logical constraints that IloCplex can extract are these:◆◆◆◆◆IloAndIloOrIloNotIloIfThenIloDiff◆ == that is, the equivalence relationAmong those extractable objects, IloAnd IloOr, IloNot, and IloDiff can also berepresented in your application by means of the overloaded C++ operators:◆◆◆|| (for IloOr)&& (for IloAnd)! (for IloNot)350 ILOG CPLEX 11.0 — USER’ S MANUAL
◆!= that is, the exclusive-or relation (for IloDiff)All those extractable objects accept as their arguments other linear constraints or logicalconstraints, so you can combine linear constraints with logical constraints in complicatedexpressions in your application.For example, to express the idea that two jobs with starting times x1 and x2 and withduration d1 and d2 must not overlap, you can either use overloaded C++ operators, like this:model.add((x1 >= x2 + d2) || (x2 >= x1 + d1));or you can express the same idea, like this:IloOr or(env)or.add(x1 >= x2 + d2);or.add(x2 >= x1 + d1);model.add(or);Since IloCplex can also extract logical constraints embedded in other logical constraints,you can also write logical constraints like this:IloIfThen(env, (x >= y && x >= z), IloNot(x = 700))where x, y, and z are variables in your application.Logical Constraints in the Java APIOf course, because the Java programming language does not support the overloading ofoperators as C++ does, overloaded logical operators are not supported in the Java API ofConcert Technology. However, the Java class IloCplexModeler offers logical modelingfacilities through methods, such as:◆◆◆◆IloCplexModeler.andIloCplexModeler.orIloCplexModeler.notIloCplexModeler.ifThenMoreover, like their C++ counterparts, those extractable Java objects accept as theirarguments other linear constraints or logical constraints, so you can combine linearconstraints with logical constraints in complicated expressions in your Java application.Logical Constraints in the .NET APISimilarly, the .NET API of Concert Technology supports logical constraints, though notoperator overloading. The .NET class Cplex offers these overloaded logical methods:◆◆Cplex.AndCplex.OrILOG CPLEX 11.0 — USER’ S MANUAL 351
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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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Page 306 and 307: Populating the Solution PoolILOG CP
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Page 352 and 353: ◆◆Cplex.NotCplex.IfThenAgain, t
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Page 360 and 361: Describing the ProblemThe problem i
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Page 368 and 369: Describing the ProblemThe problem i
Page 370 and 371: Stating Precedence ConstraintsIn ea
Page 372 and 373: Solving the ProblemAn emphasis on f
Page 374 and 375: What Is Column Generation?In colloq
Page 376 and 377: Solving this model with all columns
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The constraints in conflict with th
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If a model contains more than one c
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Immediately after that statement, i
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◆ Groups in the Conflict Refiner
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408 ILOG CPLEX 11.0 — USER’ S M
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The infeasibility on which FeasOpt
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Now the following lines invoke Feas
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suggests decreasing the upper bound
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416 ILOG CPLEX 11.0 — USER’ S M
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C H A P T E R28User-Cut and Lazy-Co
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However, there is an important dist
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◆◆Through the routine CPXreadco
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Here is an example of an MPS file e
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C H A P T E R29Using GoalsThis chap
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How Goals Are Implemented in Branch
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In the Java API, a Fail goal is ret
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This return statement returns an An
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The Goal StackTo understand how goa
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soon as they are enclosed in a goal
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The global cut goal for lhs[i] ≤
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If a node has multiple evaluators a
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As this example is an extension of
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C H A P T E R30Using Optimization C
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Reference Documents about Informati
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Query or Diagnostic CallbacksQuery
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● Cplex.DisjunctiveCutCallback in
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◆◆●●Cplex.HeuristicCallback
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It is not customary to write such a
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IloCplex::Callback mycallback = cpl
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Here is the previous sample of code
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◆◆cbdata, a pointer to ILOG CPL
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conventions of the Interactive Opti
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een added, it can be deleted by cal
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Interaction Between Callbacks and I
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C H A P T E R31Goals and Callbacks:
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The only functionality that is not
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C H A P T E R32Advanced Presolve Ro
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once. All of the node relaxation so
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- 5x1, + x2 ≤ 0 2y1, + y2, ≥ 1x
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problem, the problem has a presolve
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Modifying a ProblemThis section bri
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C H A P T E R33Advanced MIP Control
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value strictly greater than one. It
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Cut CallbackThe next example we con
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problem. Since branching involves a
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C H A P T E R34Parallel OptimizersT
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Threads and Performance Considerati
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3. Call the parallel optimizer with
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optimizer turns out to be the faste
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0 0 3383.7784 16 4505.0000 Cuts: 35
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I N D E XIndexAabsolute objective d
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ole in converting LP to network flo
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emoving from basis (C++ API) 62repr
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CPX_PARAM_PCPX_PARAM_POLISHTIMEsolu
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CPXcreateprob 467CPXcreateprob rout
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CPXwcpxwarning message channel 151C
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empty goal 431, 435end methodIloEnv
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getDuals method (Java API) 88getMax
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emove method (Java API) 94IloModele
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ecords singularities 188relocating
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from 218head 218sink 219source 219s
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control callbacks and 453query call
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primal reduction 385primal simplex
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eturn statusBounded (Java API) 81Er
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solvingdiet problem (Java API) 82mo
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arrier 208WorkMem 293WorkMem parame
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