ILOG CPLEX 11.0 User's Manual

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Branch & Cut with GoalsGoals allow you to take control of the branch & cut search procedure used by ILOG CPLEXto solve MIP problems. To help you understand how to use goals with ILOG CPLEX, thesesections review how this procedure works.◆ Overview of Goals in Branch & Cut on page 428◆ How Goals Are Implemented in Branch & Cut on page 429◆ About the Method execute in Branch & Cut on page 429Overview of Goals in Branch & CutThe branch & cut search procedure manages a search tree consisting of nodes. Every noderepresents a subproblem to be solved, and the root node of the tree represents the entireproblem. Nodes are called active if they have not yet been processed.The tree is first initialized to contain the root node as the only active node. ILOG CPLEXprocesses active nodes from the tree until either no more active nodes are available or somelimit has been reached. Once a node has been processed, it is no longer active.When processing a node, ILOG CPLEX starts by solving the continuous relaxation of itssubproblem (that is, the subproblem without integrality constraints). If the solution violatesany cuts, ILOG CPLEX adds them to the node problem and re-solves. This procedure isiterated until no more violated cuts are found by ILOG CPLEX. If at any point the relaxationbecomes infeasible, the node is pruned, that is, it is removed from the tree.To solve the node problem, ILOG CPLEX checks whether the solution satisfies theintegrality constraints. If so, and if its objective value is better than that of the currentincumbent, the solution of the node problem is used as the new incumbent. Otherwise,ILOG CPLEX splits the node problem into one or two smaller subproblems, typically bybranching on a variable that violates its integrality constraint. These subproblems are addedto the tree as active nodes and the current node is deactivated.The primary use of goals is to take control of these last steps, namely the integer-feasibilitytest and the creation of subproblems. However, as discussed later, goals also allow you toadd local and global cuts.428 ILOG CPLEX 11.0 — USER’ S MANUAL
How Goals Are Implemented in Branch & CutNote: The discussion of the details of using goals will be presented mainly in terms of theC++ API. The Java and .NET APIs follow the same design and are thus equivalent at thislevel of discussion. In cases where a difference between these APIs needs to be observed,the point will be raised. Where the difference is only in syntax, the other syntax will bementioned in parentheses following the C++ syntax.In C++, goals are implemented in objects of type IloCplex::GoalI (having handle classIloCplex::Goal). In Java, goals are implemented in objects of type IloCplex.Goal(and there are no handle classes). In .NET, goals are implemented by the class Cplex.Goal.The method IloCplex::GoalI::execute (IloCplex.Goal.execute) is where thecontrol is implemented. This method is called by IloCplex after a node relaxation has beensolved and all cuts have been added. Invoking the method execute of a goal is oftenreferred to as executing a goal. When the method execute is executed, other methods of theclass IloCplex::GoalI (IloCplex.Goal or Cplex.Goal) can be called to queryinformation about the current node problem and the solution of its relaxation.About the Method execute in Branch & CutTypically, the implementation of the method execute will perform the following steps:1. Check feasibility. An interesting possibility here is that the feasibility check may includemore than verifying integrality of the solution. This allows you to enforce constraints thatcould not reasonably be expressed using linear constraints through cuts or branching. Inother words, this allows you to use goals in a way that makes them part of the model tobe solved. Such a use is common in Constraint Programming, but it is less frequentlyused in Mathematical Programming. Note, however, that this CP-style application ofgoals prevents you from making use of MP-style advanced starting information, eitherfrom a MIP Start file or by restarting a previous optimization with one that uses goals.2. Optionally find local or global cuts to be added. Local cuts will be respected only for thesubtree below the current node, whereas global cuts will be enforced for all nodes fromthen on.3. Optionally construct a solution and pass it to ILOG CPLEX.4. Instruct ILOG CPLEX how to proceed. Instruct ILOG CPLEX how to proceed throughthe return value of the method execute; the return value is execute is another goal.ILOG CPLEX simply continues by executing this goal.ILOG CPLEX 11.0 — USER’ S MANUAL 429
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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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Page 410 and 411: The infeasibility on which FeasOpt
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Page 419 and 420: C H A P T E R28User-Cut and Lazy-Co
Page 421 and 422: However, there is an important dist
Page 423 and 424: ◆◆Through the routine CPXreadco
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Page 427: C H A P T E R29Using GoalsThis chap
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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
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Page 469 and 470: C H A P T E R31Goals and Callbacks:
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Page 473 and 474: C H A P T E R32Advanced Presolve Ro
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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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