ILOG CPLEX 11.0 User's Manual

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Ordering-Algorithm Time in the Log FileAfter the number of nonzeros in the lower triangle of AA T , ILOG CPLEX records the timerequired by the ordering algorithm. (The ILOG CPLEX Barrier Optimizer offers you achoice of several ordering algorithms, explained in Choosing an Ordering Algorithm onpage 210.) This section in the log file indicates which ordering algorithm the defaultAutomatic setting chose.Cholesky Factor in the Log FileAfter the time required by the ordering algorithm, ILOG CPLEX records information aboutthe Cholesky factor. ILOG CPLEX computes this matrix on each iteration. The number ofrows in the Cholesky factor represents the number after preprocessing. The next line ofinformation about the Cholesky factor—integer space required—indicates the amount ofmemory needed to store the sparsity pattern of the factored matrix. If this number is low,then the factor can be computed more quickly than when the number is high.Information about the Cholesky factor continues with the number of nonzeros in the factoredmatrix. The difference between this number and the number of nonzeros in AA T indicatesthe fill-level of the Cholesky factor.The final line of information indicates how many floating-point operations are required tocompute the Cholesky factor. This number is the best predictor of the relative time that willbe required to perform each iteration of the barrier optimizer.Iteration Progress in the Log FileAfter the information about the Cholesky factor, the log file records progress at eachiteration. It records both primal and dual objectives (as Primal Obj and Dual Obj) periteration.It also records absolute infeasibilities per iteration. Internally, the ILOG CPLEX BarrierOptimizer treats inequality constraints as equality constraints with added slack and surplusvariables. Consequently, primal constraints in a problem are written as Ax=b and x +s=u,and the dual constraints are written as A T y+z-w=c. As a result, in the log file, theinfeasibilities represent norms, as summarized in Table 10.5.Table 10.5Infeasibilities and Norms in the Log File of a Barrier OptimizationInfeasibility In log file Normprimal Prim Inf |b - Ax|upper Upper Inf |u - (x + s)|dual Dual Inf |c - yA -z+w|204 ILOG CPLEX 11.0 — USER’ S MANUAL
If solution values are large in absolute value, then the infeasibilities may appear inordinatelylarge because they are recorded in the log file in absolute terms. The optimizer uses relativeinfeasibilities as termination criteria.Infeasibility Ratio in the Log FileIf you are using one of the barrier infeasibility algorithms available in the ILOG CPLEXBarrier Optimizer (that is, if you have set BarAlg to either 1 or 2, as discussed later in thischapter), then ILOG CPLEX records an additional column of output titled Inf Ratio, theinfeasibility ratio. This ratio, always positive, is a measure of progress for that particularalgorithm. In a problem with an optimal solution, you will see this ratio increase to a largenumber. In contrast, in a problem that is infeasible or unbounded, this ratio will decrease to avery small number.Understanding Solution Quality from the Barrier LP OptimizerWhen ILOG CPLEX successfully solves a problem with the ILOG CPLEX BarrierOptimizer, it reports the optimal objective value and solution time in a log file, as it does forother LP optimizers.Because barrier solutions (prior to crossover) are not basic solutions, certain solutionstatistics associated with basic solutions are not available for a strictly barrier solution. Forexample, reduced costs and dual values are available for strictly barrier LP solutions, butrange information about them is not.To help you evaluate the quality of a barrier solution more readily, ILOG CPLEX offers aspecial display of information about barrier solution quality. To display this information inthe Interactive Optimizer, use the command display solution quality afteroptimization. When using the Component Libraries, use the method cplex.getQualityor use the routines CPXgetintquality for integer information and CPXgetdblqualityfor double-valued information.Table 10.6Barrier Solution Quality DisplayItemprimal objectivedual objectiveduality gapcomplementarityMeaningprimal objective value c T xdual objective value b T y-u T w+l T zdifference between primal and dual objectivessum of column and row complementarityILOG CPLEX 11.0 — USER’ S MANUAL 205
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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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Page 156 and 157: Types of ILM Runtime LicensesILM ru
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Page 160 and 161: The registerLicense Method for Java
Page 162 and 163: not correct that problem either. In
Page 164 and 165: In the Interactive Optimizer, you c
Page 166 and 167: For models not in the current worki
Page 168 and 169: ◆◆In the .NET API, pass an inst
Page 171 and 172: C H A P T E R9Solving LPs: Simplex
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Page 177 and 178: solution; but examination of soluti
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Page 185 and 186: Numeric DifficultiesILOG CPLEX is d
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Page 189 and 190: automatically perturbs the variable
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Page 193 and 194: smaller in absolute value than the
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Page 197 and 198: C H A P T E R10Solving LPs: Barrier
Page 199 and 200: The ILOG CPLEX Barrier Optimizer is
Page 201 and 202: And then you call the solution rout
Page 203: Here is an example of a log file fo
Page 207 and 208: Normalized errors, for example, rep
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Page 211 and 212: est order. It may require more time
Page 213 and 214: choice of starting-point heuristic
Page 215 and 216: To see the current value of the col
Page 217 and 218: C H A P T E R11Solving Network-Flow
Page 219 and 220: ◆◆l a , the lower bound, sets t
Page 221 and 222: of the objective function calculate
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Page 227 and 228: C H A P T E R12Solving Problems wit
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Page 231 and 232: A similar Java program using Concer
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Page 239 and 240: C H A P T E R13Solving Problems wit
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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
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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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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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