ILOG CPLEX 11.0 User's Manual

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C H A P T E R14Solving Mixed Integer ProgrammingProblems (MIP)The ILOG CPLEX Mixed Integer Optimizer enables you to solve models in which one ormore variables must take integer solution values. This chapter tells you more aboutoptimizing mixed integer programming (MIP) problems with ILOG CPLEX. It includesinformation about:◆ Stating a MIP Problem on page 256◆ Considering Preliminary Issues on page 257◆ Using the Mixed Integer Optimizer on page 261◆ Tuning Performance Features of the Mixed Integer Optimizer on page 264◆ Using the MIP Solution on page 281◆ Progress Reports: Interpreting the Node Log on page 283◆ Troubleshooting MIP Performance Problems on page 288◆ Examples: Optimizing a Simple MIP Problem on page 299◆ Example: Reading a MIP Problem from a File on page 300ILOG CPLEX 11.0 — USER’ S MANUAL 255
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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
Page 203 and 204: Here is an example of a log file fo
Page 205 and 206: If solution values are large in abs
Page 207 and 208: Normalized errors, for example, rep
Page 209 and 210: ◆ workmem in the Interactive Opti
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
Page 223 and 224: then ILOG CPLEX will carry out such
Page 225 and 226: -a 1 + a 2 - a 8 - a 9 + a 14 = 0-
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 257 and 258: Considering Preliminary IssuesWhen
Page 259 and 260: Changing Problem Type in MIPsConcer
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Page 265 and 266: Tuning Tool on page 161 explains mo
Page 267 and 268: Applying HeuristicsPeriodically dur
Page 269 and 270: Selecting VariablesAfter a node has
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Page 277 and 278: ●●CPX_PARAM_TILIM in the Callab
Page 279 and 280: It is possible to apply preprocessi
Page 281 and 282: should be assigned higher priority
Page 283 and 284: variables, however, lose feasibilit
Page 285 and 286: As you can see in that example, ILO
Page 287 and 288: you lines from a node log file wher
Page 289 and 290: Too Much Time at Node 0If you obser
Page 291 and 292: These limits are controlled by the
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Page 297 and 298: Difficulty Solving Subproblems: Ove
Page 299 and 300: Examples: Optimizing a Simple MIP P
Page 301 and 302: C H A P T E R15Solution Pool: Gener
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Filling the Solution PoolThere are
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The amount of preparation in the fi
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immediately invoke populate a secon
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generate solutions of both improvin
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Enumerating All SolutionsWith the s
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improve the solution pool. Changes
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◆◆◆In Concert Technology, the
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◆In the Interactive Optimizer, us
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Parameters of the Solution PoolILOG
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Example: Diverse Solutions through
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existing partial solution. Several
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●●IloCplex.writeFilters in the
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16Using Special Ordered Sets (SOS)I
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Declaring SOS MembersILOG CPLEX off
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C H A P T E R17Using Semi-Continuou
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may be on or off (producing or not
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C H A P T E R18Using Piecewise Line
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functions frequently represent situ
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Figure 18.25f(x)4321x01 2 3 4 5 6 7
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Variable Shipping CostsNow consider
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Developing a ModelAs in other examp
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Solving the ProblemThe following li
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C H A P T E R19Logical Constraints
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◆!= that is, the exclusive-or rel
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Logical Constraints for CountingIn
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20Using Indicator ConstraintsThis c
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What Are Indicator Variables?The bi
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C H A P T E R21Using Logical Constr
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What Is Known?In this particular ex
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●The fact that a limited amount o
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Formulating Logical ConstraintsYou
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C H A P T E R22Early Tardy Scheduli
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Reading the DataThe first part of t
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Consequently, the function can be r
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C H A P T E R23Using Column Generat
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or of other subclasses of IloAlgori
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Developing the Model: Building and
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newPatt[i] for constraint Fill[i];
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The heart of the example is here, i
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Part VInfeasibility and Unboundedne
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24Preprocessing and FeasibilityILOG
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25Managing UnboundednessThis chapte
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Other forms of avoiding under-const
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C H A P T E R26Diagnosing Infeasibi
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How to Invoke the Conflict RefinerT
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This simple model, for example, mig
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In a larger conflict, you can selec
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change bound service lower 2.8and r
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The model is now restored to feasib
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An attempt to display or access a c
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the Conflict Refiner on page 394. Y
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three are combined into a skills co
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C H A P T E R27Repairing Infeasibil
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Specifying PreferencesYou specify t
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The solution values of [40, 30, 80]
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ound; there is no incentive in the
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Part VIAdvanced Programming Techniq
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Figure 28.1ycutting planesobjective
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Adding User Cuts and Lazy Constrain
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Reading and Writing SAV FilesUser c
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426 ILOG CPLEX 11.0 — USER’ S M
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Branch & Cut with GoalsGoals allow
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Special Goals in Branch & CutILOG C
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The following lines in the C++ API
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MyBranchGoal and there is no helper
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When ILOG CPLEX processes one of th
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Although it is now solvable directl
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current node. Thus, if the relaxati
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other node. By default, the candida
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follows the branching performed by
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◆ Return Values for Callbacks on
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Where to Find Examples of Informati
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◆◆◆◆◆●●●●IloCplex
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parallelism, if the application is
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Implementing Callbacks in ILOG CPLE
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Table 30.2Callback MacrosCallback M
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Example: Deriving the Simplex Callb
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The complete program, ilolpex4.cpp,
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◆ Before the program calls CPXlpo
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Notice the comma (,) between the ty
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The Java implementation of the call
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Terminating without CallbacksIf you
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◆◆◆●●With goals, you can
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Introduction to PresolveThis discus
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Restricting Presolve ReductionsAs m
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on. The reasons relate to the fact
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performed on the problem. This func
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Users of the advanced MIP control i
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een called, CPLEX calls the user ca
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are violated. The user can do this
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Solve CallbackThe final callback we
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parameter (Threads, CPX_PARAM_THREA
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optimization requires less synchron
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the parallel MIP optimizer in deter
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Root Relaxation and Parallel MIP Pr
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If a log file is active when the cl
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choosing in LP (C++ API) 53controll
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variable type (C++ API) 62channel e
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MIP preprocessing 278CPX_PARAM_COVE
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CPX_PREREDUCE_NO_PRIMALORDUAL 477CP
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CPXmCPXmemcpy routine 122CPXMIP_ABO
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deterministic searchbarrier optimiz
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feasibility tolerancedefault 192lar
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Iill-conditionedbasis 193factors in
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eturn status (C++ API) 58return sta
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definition 256definition (Java API)
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primal reductions and 385representi
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Network optimizergeneral observatio
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quadraticconstraints 239convex cons
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IloCplex C++ class 56setExpr method
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elative optimality default 291role
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