ILOG CPLEX 11.0 User's Manual

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If the solution to the relaxation still has one or more fractional-valued integer variables afterILOG CPLEX tries to add cuts, then ILOG CPLEX branches on a fractional variable togenerate two new subproblems, each with more restrictive bounds on the branching variable.For example, with binary variables, one node will fix the variable at 0 (zero), the other,at 1 (one).The subproblems may result in an all-integer solution, in an infeasible solution, or anotherfractional solution. If the solution is fractional, ILOG CPLEX repeats the process.◆ Applying Cutoff Values on page 266◆ Applying Tolerance Parameters on page 266◆ Applying Heuristics on page 267◆ When an Integer Solution Is Found: the Incumbent on page 267◆ Controlling Strategies: Diving and Backtracking on page 267◆ Selecting Nodes on page 268◆ Selecting Variables on page 269◆ Changing Branching Direction on page 269◆ Solving Subproblems on page 270◆ Using Node Files on page 270Applying Cutoff ValuesILOG CPLEX cuts off nodes when the value of the objective function associated with thesubproblem at that node is worse than the cutoff value.You set the cutoff value by means of the CutUp parameter (for a minimization problem) orthe CutLo parameter (for a maximization problem), to indicate to ILOG CPLEX that integerfeasible solutions worse than this cutoff value should be discarded. The default value of thelower cutoff is -1e+75; the default value of the upper cutoff is 1e+75. The defaults, ineffect, mean that no cutoff is to be supplied. You can supply any number that you findappropriate for your problem. It is never required that you supply a cutoff, and in fact formost applications is it not done.Applying Tolerance ParametersILOG CPLEX will use the value of the best integer solution found so far, as modified by thetolerance parameters ObjDif (absolute objective function difference) or RelObjDif(relative objective function difference) as the cutoff. Again, it is not typical that users setthese parameters, but they are available if you find them useful. Use care in changing thesetolerances: if either of them is nonzero, you may miss the optimal solution by as much asthat amount. For example, in a model where the true minimum is 100 and the absolute cutoffis set to 5, if a feasible solution of say, 103 is found at some point, the cutoff will discard allnodes with a solution worse than 98, and thus the solution of 100 would be overlooked.266 ILOG CPLEX 11.0 — USER’ S MANUAL
Applying HeuristicsPeriodically during the branch & cut algorithm, ILOG CPLEX may apply a heuristicprocess that attempts to compute an integer solution from available information, such as thesolution to the relaxation at the current node. This activity does not replace the branchingsteps, but sometimes is able to inexpensively locate a new feasible solution sooner than bybranching, and a solution found in this way is treated in the same way as any other feasiblesolution. At intervals in the tree, new cuts beyond those computed at the root node may alsobe added to the problem.When an Integer Solution Is Found: the IncumbentAfter ILOG CPLEX finds an integer solution, it does the following:◆◆◆It makes that integer solution the incumbent solution and that node the incumbent node.It makes the value of the objective function at that node (modified by the objectivedifference parameter) the new cutoff value.It prunes from the tree all subproblems for which the value of the objective function is nobetter than the incumbent.Controlling Strategies: Diving and BacktrackingYou control the path that CPLEX traverses in the tree through several parameters, assummarized in Table 14.5.Table 14.5 Parameters for Controlling Branch & Cut StrategyInteractive OptimizerCommandConcert TechnologyIloCPLEX MethodCallable Library Routineset mip strategybacktrackset mip strategynodeselectset mip strategyvariableselectset mip strategybbintervalset mip strategybranchsetParam(BtTol, n) CPXsetdblparam(env, CPX_PARAM_BTTOL, n)setParam(NodeSel, i) CPXsetintparam(env, CPX_PARAM_NODESEL, i)setParam(VarSel, i) CPXsetintparam(env, CPX_PARAM_VARSEL, i)setParam(BBInterval, i) CPXsetintparam(env, CPX_PARAM_BBINTERVAL, i)setParam(BrDir, i) CPXsetintparam(env, CPX_PARAM_BRDIR, i)During the branch & cut algorithm, ILOG CPLEX may choose to continue from the presentnode and dive deeper into the tree, or it may backtrack (that is, begin a new dive fromelsewhere in the tree). The value of the backtrack parameter, BtTol, influences thisdecision, in terms of the relative degradation of the objective function caused by theILOG CPLEX 11.0 — USER’ S MANUAL 267
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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
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
Page 241 and 242: Figure 13.2y(0, 1)(-1, 0)d(1, 0)xc(
Page 243 and 244: Detecting Problem TypeILOG CPLEX de
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Page 247 and 248: C180 R100 159C180 R119 200C180 R120
Page 249 and 250: QMATRIXC158 C158 1C158 C189 0.5C189
Page 251 and 252: ◆From the Callable Library, use t
Page 253: Part IVDiscrete OptimizationThis pa
Page 256 and 257: Stating a MIP ProblemA mixed intege
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Page 284 and 285: Table 14.13Settings of the MIP Disp
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Page 290 and 291: parameter settings are also worth c
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Page 296 and 297: ◆◆●●at problem modification
Page 298 and 299: ◆In the Callable Library, use the
Page 300 and 301: ●●Then call CPXprimopt to optim
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Page 306 and 307: Populating the Solution PoolILOG CP
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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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