ILOG CPLEX 11.0 User's Manual

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Table 14.13Settings of the MIP Display ParameterSetting Effect0 no display1 display integer feasible solutions2 display nodes under mip interval control3 same as 2, but add information on node cuts4 same as 3, but add LP display for root node5 same as 3, but add LP display for all nodesThe MIPInterval parameter controls how frequently node log lines are printed. Its defaultis 100 and can be set to any positive integer value. A line is recorded in the node log forevery node with an integer solution if the MIPDisplay parameter is set to 1 (one) or higher,and also for any node whose number is a multiple of the MIPInterval value if theMIPDisplay is set to 2 or higher.Here is an example of a log file from the Interactive Optimizer, where the MIPIntervalparameter has been set to 10:Tried aggregator 1 time.No MIP presolve or aggregator reductions.Presolve time = 0.00 sec.Root relaxation solution time = 0.00 secObjective is integral.NodesNode Left Objective IInf Best IntegerCuts/Best Node ItCnt Gap0 0 4.0000 6 4.0000 12* 4 2 0 5.0000 4.0000 17 20.00%10 1 cutoff 5.0000 4.0000 31 20.00%Solution pool: 1 solution savedMIP-Integer optimal solution: Objective = 5.0000000000e+000Solution time = 0.02 sec. Iterations = 41 Nodes = 13In that example, ILOG CPLEX found the optimal objective function value of 5.0 afterexploring 13 nodes and performing 41 (dual simplex) iterations, and ILOG CPLEX found anoptimal integer solution at node 4. The MIP interval parameter was set at 10, so every tenthnode was logged, in addition to the node where an integer solution was found.284 ILOG CPLEX 11.0 — USER’ S MANUAL
As you can see in that example, ILOG CPLEX logs an asterisk (*) in the left-most columnfor any node where it finds an integer-feasible solution or new incumbent. In the nextcolumn, it logs the node number. It next logs the number of nodes left to explore.In the next column, Objective, ILOG CPLEX either records the objective value at thenode or a reason to fathom the node. (A node is fathomed if the solution of a subproblem atthe node is infeasible; or if the value of objective function at the node is worse than thecutoff value for branch & cut; or if the node supplies an integer solution.) This column is leftblank for lines where the first column contains an asterisk (*) indicating a node whereILOG CPLEX found an integer-feasible solution or new incumbent.In the column labeled IInf, ILOG CPLEX records the number of integer-infeasiblevariables and special ordered sets. If no solution has been found, the column titled BestInteger is blank; otherwise, it records the best integer solution found so far.The column labeled Cuts/Best Node records the best objective function value achievable.If the word Cuts appears in this column, it means various cuts were generated; if a particularname of a cut appears, then only that kind of cut was generated.The column labeled ItCnt records the cumulative iteration count of the algorithm solvingthe subproblems. Until a solution has been found, the column labeled Gap is blank. If asolution has been found, the relative gap value is printed: when it is less than 999.99, thevalue is printed; otherwise, hyphens are printed. The gap is computed as:(best integer - best node ) * objsen / (abs (best integer) + 1e-10)Consequently, the printed gap value may not always move smoothly. In particular, there maybe sharp improvements whenever a new best integer solution is found. Moreover, if thepopulate procedure is invoked, the printed gap value may become negative after the optimalsolution has been found and proven optimal.ILOG CPLEX 11.0 — USER’ S MANUAL 285
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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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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
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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 260 and 261: ◆milp, miqp, or miqcpindicating t
Page 262 and 263: 1. finding a succession of improvin
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Page 266 and 267: If the solution to the relaxation s
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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 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
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Page 310 and 311: Note: The parameter to limit the nu
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Page 316 and 317: Examining the Solution PoolIn the I
Page 318 and 319: For a sample of these methods or ro
Page 320 and 321: ◆◆In the Callable Library (C AP
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
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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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