ILOG CPLEX 11.0 User's Manual

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Choosing an Optimizer: Network ConsiderationsAs explained in Using the Callable Library in an Application on page 111, to exploitILOG CPLEX in your own application, you must first create an ILOG CPLEX environment,instantiate a problem object, and populate the problem object with data. As your next step,you call a ILOG CPLEX optimizer.If part of your problem is structured as a network, then you may want to consider calling theILOG CPLEX Network Optimizer. This optimizer may have a positive impact onperformance. There are two alternative ways of calling the network optimizer:◆If your problem is an LP where a large part is a network structure, you may call thenetwork optimizer for the populated LP object.◆ If your entire problem consists of a network flow, you should consider creating a networkobject instead of an LP object. Then populate it, and solve it with the network optimizer.This alternative generally yields the best performance because it does not incur theoverhead of LP data structures. This option is available only for the Callable library.How much performance improvement you observe between using only a simplex optimizerversus using the network optimizer followed by either of the simplex optimizers depends onthe number and nature of the other constraints in your problem. On a pure network problem,performance has been measured as 100 times faster with the network optimizer. However, ifthe network component of your problem is small relative to its other parts, then using thesolution of the network part of the problem as a starting point for the remainder may or maynot improve performance, compared to running the primal or dual simplex optimizer. Onlyexperiments with your own problem can tell.Formulating a Network ProblemA network-flow problem finds the minimal-cost flow through a network, where a networkconsists of a set N of nodes and a set A of arcs connecting the nodes. An arc a in the set A isan ordered pair (i, j) where i and j are nodes in the set N; node i is called the tail or the fromnodeand node j is called the head or the to-node of the arc a. Not all the pairs of nodes in aset N are necessarily connected by arcs in the set A. More than one arc may connect a pair ofnodes; in other words, a 1 =(i,j) and a 2 = (i, j) may be two different arcs in A, bothconnecting the nodes i and j in N.Each arc a may be associated with four values:◆x a is the flow value, that is, the amount passing through the arc a from its tail (or fromnode)to its head (or to-node). The flow values are the modeling variables of a networkflowproblem. Negative values are allowed; a negative flow value indicates that there isflow from the head to the tail.218 ILOG CPLEX 11.0 — USER’ S MANUAL
◆◆l a , the lower bound, sets the minimum flow allowed through the arc a. By default, thelower bound on an arc is 0 (zero).u a , the upper bound, sets the maximum flow allowed through the arc a. By default, theupper bound on an arc is positive infinity.◆ c a , the objective value, specifies the contribution to the objective function of one unit offlow through the arc.Each node n is associated with one value:◆ s n is the supply value at node n.By convention, a node with strictly positive supply value (that is, s n >0) is called a supplynode or a source, and a node with strictly negative supply value (that is, s n
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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
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 181 and 182: Table 9.5 PPriInd Parameter Setting
Page 183 and 184: ILOG CPLEX ignores the coefficients
Page 185 and 186: Numeric DifficultiesILOG CPLEX is d
Page 187 and 188: esult is the same as would be obtai
Page 189 and 190: automatically perturbs the variable
Page 191 and 192: 4. Consider alternate scalings.You
Page 193 and 194: smaller in absolute value than the
Page 195 and 196: exceptions are caught as well, and
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 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
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Page 213 and 214: choice of starting-point heuristic
Page 215 and 216: To see the current value of the col
Page 217: C H A P T E R11Solving Network-Flow
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 260 and 261: ◆milp, miqp, or miqcpindicating t
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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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