ILOG CPLEX 11.0 User's Manual

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are violated. The user can do this either by setting CPX_PARAM_MIPCBREDLP to CPX_OFF towork with the original problem in the cut callback, or by using the Advanced PresolveInterface to translate the cuts on the original problem to cuts on the presolved problem, andthen use the presolved cuts in the cut callback.Another, perhaps simpler alternative is to add the cuts or constraints to cut pools beforeoptimization begins. Pools are discussed in User-Cut and Lazy-Constraint Pools onpage 419.Branch Selection CallbackThe next callback to consider is the branch variable selection callback.After CPXsetbranchcallbackfunc is called with a pointer to a user callback routine, theuser routine is called whenever CPLEX makes a branching decision. CPLEX indicateswhich variable has been chosen for branching and allows the user to modify that decision.The user may specify the number of children for the current node (between 0 and 2), and theset of bounds or constraints that are modified for each child through one of the routinesCPXbranchcallbackbranchbds, CPXbranchcallbackbranchconstraints, orCPXbranchcallbackbranchgeneral. The children are explored in the order that they arereturned. The branch callback routine is called for all viable nodes. In particular, it will becalled for nodes that have zero integer infeasibilities; in this case, CPLEX will not havechosen a branch variable, and the default action will be to discard the node. The user canchoose to branch from this node and in this way impose additional restrictions on integersolutions.For example, a user branch routine may call CPXgetcallbacknodeintfeas to identifybranching candidates, call CPXgetcallbackpseudocosts to obtain pseudo-costinformation on these variables, call CPXgetcallbackorder to get priority orderinformation, make a decision based on this and perhaps other information, and then respondthat the current node will have two children, where one has a new lower bound on the branchvariable and the other has a new upper bound on that variable.Alternatively, the branch callback routine can be used to sculpt the search tree by pruningnodes or adjusting variable bounds. Choosing zero children for a node prunes that node,while choosing one node with a set of new variable bounds adjusts bounds on those variablesfor the entire subtree rooted at this node. Note that the user must be careful when using thisroutine for anything other than choosing a different variable to branch on. Pruning a validnode or placing an invalid bound on a variable can prune the optimal solution.We should point out one important detail associated with the use of theCPX_PARAM_MIPCBREDLP parameter in a branch callback. If this parameter is set toCPX_OFF (0), the user can choose branch variables (and add bounds) for the originalproblem. However, not every fractional variable is actually available for branching. Recallthat some variables are replaced by linear combinations of other variables in the presolved488 ILOG CPLEX 11.0 — USER’ S MANUAL
problem. Since branching involves adding new bounds to specific variables in the presolvedproblem, a variable must be present in the presolved problem for it to be branched on. Theuser should use the CPXgetcallbacknodeintfeas routine from the Advanced PresolveInterface to find branching candidates (those for which CPXgetcallbacknodeintfeasreturns CPX_INTEGER_INFEASIBLE). The CPXcopyprotected routine can be used toprevent presolve from removing specific variables from the presolved problem. (In ConcertTechnology, this issue is handled for you automatically.) While restricting branching mayappear to limit your ability to solve a problem, in fact a problem can always be solved tooptimality by branching only on the variables of the presolved problem.Incumbent CallbackThe incumbent callback is used to reject integer feasible solutions that do not meetadditional restrictions the user may wish to impose. The user callback routine will be calledeach time a new incumbent solution has been found, including when solutions are providedby the user’s heuristic callback routine. The user callback routine is called with the newsolution as input. Depending on the API, the callback function changes an argument orinvokes a method to indicate whether or not the new solution should replace the incumbentsolution.For the object-oriented callback classes of the C++, Java, and .NET APIs, all callbackinformation about the model and solution vector pertains to the original, unpresolved model.For the C API, the CPX_PARAM_MIPCBREDLP parameter influences the arguments to theuser callback routine. If this parameter is set to its default value of CPX_ON (1), the solutionvector that is input to the callback is a presolved vector. It contains one value for eachvariable in the presolved problem. The same is true of the various callback support routines(CPXcallbackglobalub, and so forth.). If the parameter is set to CPX_OFF (0), all thesevectors relate to the variables of the original problem. Note that this parameter should not bechanged in the middle of an optimization.Node Selection CallbackThe user can influence the order in which nodes are explored by installing a node selectioncallback (through CPXsetnodecallbackfunc). When CPLEX chooses the node toexplore next, it will call the user callback routine, with CPLEX's choice as an argument. Thecallback has the option of modifying this choice.ILOG CPLEX 11.0 — USER’ S MANUAL 489
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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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◆ qp indicates that you want ILOG
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RootAlg parameter (QPMETHOD in the
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ilolpex1.cpp counterpart. Here the
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C H A P T E R13Solving Problems wit
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Figure 13.2y(0, 1)(-1, 0)d(1, 0)xc(
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Detecting Problem TypeILOG CPLEX de
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COLUMNSMARK0000 'MARKER''INTORG'C15
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C180 R100 159C180 R119 200C180 R120
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QMATRIXC158 C158 1C158 C189 0.5C189
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◆From the Callable Library, use t
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Part IVDiscrete OptimizationThis pa
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Stating a MIP ProblemA mixed intege
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sections does not matter. To enter
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◆milp, miqp, or miqcpindicating t
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1. finding a succession of improvin
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easonable amount of computation tim
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If the solution to the relaxation s
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anches taken so far in this dive. S
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directives about the order in which
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◆ Parameters Affecting Cuts on pa
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◆●●IloCplex.getNcuts in the J
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Relaxation Induced Neighborhood Sea
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Table 14.10Parameters for Controlli
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Library). If this process succeeds,
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After you have solved a MIP, you wi
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Table 14.13Settings of the MIP Disp
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ILOG CPLEX also logs its addition o
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◆ Parent specifies the NodeID of
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parameter settings are also worth c
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When you set a MIP cutoff value, IL
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memory. It also includes several op
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◆◆●●at problem modification
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◆In the Callable Library, use the
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●●Then call CPXprimopt to optim
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◆ The Incumbent and the Solution
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c17: x1 - y11 >= 0c18: x1 - y21 >=
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Populating the Solution PoolILOG CP
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NodesCuts/Node Left Objective IInf
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Note: The parameter to limit the nu
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Example: Using Populate after MIP O
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Limitations Due to Numeric Difficul
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Examining the Solution PoolIn the I
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For a sample of these methods or ro
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◆◆In the Callable Library (C AP
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Then display the objective value of
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◆ If you want to filter solutions
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●●●In the C++ API, use the me
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NAME locationRNGFILTER f2 -inf 0tra
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continuous, a model containing one
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◆The routine setPriorities sets t
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What Are Semi-Continuous Variables?
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With that model, now the applicatio
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Piecewise Linearity in ILOG CPLEXSo
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Reminder: It may help you understan
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overlaps with an endpoint of two ot
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Figure 18.4400003000020000100000Fig
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in demand; in terms of this model,
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348 ILOG CPLEX 11.0 — USER’ S M
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What Are Logical Constraints?For IL
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◆◆Cplex.NotCplex.IfThenAgain, t
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In Concert Technology applications,
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Describing the ProblemThe problem i
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Notice that how much to use and buy
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Then use a for-loop to add the cons
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These lines (the action of the if-s
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Describing the ProblemThe problem i
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Stating Precedence ConstraintsIn ea
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Solving the ProblemAn emphasis on f
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What Is Column Generation?In colloq
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Solving this model with all columns
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Likewise, the application adds an a
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Pattern Generator ModelThe submodel
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Complete ProgramYou can see the ent
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your problem formulation caused thi
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To control the types of reductions
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What Is Unboundedness?Any class of
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Callable Library use the advanced r
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the conflict to arrive at a minimal
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the IIS finder can, and often more.
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Then you will see results like thes
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Now view the entire conflict with t
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The constraints in conflict with th
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If a model contains more than one c
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Immediately after that statement, i
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◆ Groups in the Conflict Refiner
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The infeasibility on which FeasOpt
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Now the following lines invoke Feas
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suggests decreasing the upper bound
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C H A P T E R28User-Cut and Lazy-Co
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However, there is an important dist
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◆◆Through the routine CPXreadco
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Here is an example of an MPS file e
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C H A P T E R29Using GoalsThis chap
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How Goals Are Implemented in Branch
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In the Java API, a Fail goal is ret
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This return statement returns an An
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The Goal StackTo understand how goa
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Page 445 and 446: C H A P T E R30Using Optimization C
Page 447 and 448: Reference Documents about Informati
Page 449 and 450: Query or Diagnostic CallbacksQuery
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Page 469 and 470: C H A P T E R31Goals and Callbacks:
Page 471 and 472: The only functionality that is not
Page 473 and 474: C H A P T E R32Advanced Presolve Ro
Page 475 and 476: once. All of the node relaxation so
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Page 479 and 480: problem, the problem has a presolve
Page 481 and 482: Modifying a ProblemThis section bri
Page 483 and 484: C H A P T E R33Advanced MIP Control
Page 485 and 486: value strictly greater than one. It
Page 487: Cut CallbackThe next example we con
Page 491 and 492: C H A P T E R34Parallel OptimizersT
Page 493 and 494: Threads and Performance Considerati
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Page 497 and 498: optimizer turns out to be the faste
Page 499 and 500: 0 0 3383.7784 16 4505.0000 Cuts: 35
Page 501 and 502: I N D E XIndexAabsolute objective d
Page 503 and 504: ole in converting LP to network flo
Page 505 and 506: emoving from basis (C++ API) 62repr
Page 507 and 508: CPX_PARAM_PCPX_PARAM_POLISHTIMEsolu
Page 509 and 510: CPXcreateprob 467CPXcreateprob rout
Page 511 and 512: CPXwcpxwarning message channel 151C
Page 513 and 514: empty goal 431, 435end methodIloEnv
Page 515 and 516: getDuals method (Java API) 88getMax
Page 517 and 518: emove method (Java API) 94IloModele
Page 519 and 520: ecords singularities 188relocating
Page 521 and 522: from 218head 218sink 219source 219s
Page 523 and 524: control callbacks and 453query call
Page 525 and 526: primal reduction 385primal simplex
Page 527 and 528: eturn statusBounded (Java API) 81Er
Page 529 and 530: solvingdiet problem (Java API) 82mo
Page 531 and 532: arrier 208WorkMem 293WorkMem parame
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