Only a few theoretical studies of surrogate duality have been carried out since Greenberg and Pierskalla's comprehensive work. Recently, Ram and Karwan examined surrogate duality, and exemplified the existence of ...
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Only a few theoretical studies of surrogate duality have been carried out since Greenberg and Pierskalla's comprehensive work. Recently, Ram and Karwan examined surrogate duality, and exemplified the existence of surrogate duality gaps for a class of mixed integer programming problems. In this paper, we show that the surrogate duality gaps may exist even for integerprogramming problems and present necessary sufficient conditions for surrogate ( or Langrangion) duality gaps to occur. Then, we extend the results for a class of mixed integer programming problems.
We introduce a novel and powerful approach for solving certain classes of mixedinteger programs (MIPs): decomposition branching. Two seminal and widely used techniques for solving MIPs, branch-and-bound and decomposi...
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We introduce a novel and powerful approach for solving certain classes of mixedinteger programs (MIPs): decomposition branching. Two seminal and widely used techniques for solving MIPs, branch-and-bound and decomposition, form its foundation. Computational experiments with instances of a weighted set covering problem and a regionalized p-median facility location problem with assignment range constraints demonstrate its efficacy: it explores far fewer nodes and can be orders of magnitude faster than a commercial solver and an automatic Dantzig-Wolfe approach.
In flat glass manufacturing, glass products of various dimensions are cut from a glass ribbon that runs continuously on a conveyor belt. Placement of glass products on the glass ribbon is restricted by the defects of ...
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In flat glass manufacturing, glass products of various dimensions are cut from a glass ribbon that runs continuously on a conveyor belt. Placement of glass products on the glass ribbon is restricted by the defects of varying severity located on the ribbon as well as the quality grades of the products to be cut. In addition to cutting products, a common practice is to remove defective parts of the glass ribbon as scrap glass. As the glass ribbon moves continuously, cutting decisions need to be made within seconds, which makes this online problem very challenging. A simplifying assumption is to limit scrap cuts to those made immediately behind a defect (a cut-behind-fault or CBF). We propose an online algorithm for the glass cutting problem that solves a series of static cutting problems over a rolling horizon. We solve the static problem using two methods: a dynamic programming algorithm (DP) that utilises the CBF assumption and a mixed integer programming (MIP) formulation with no CBF restriction. While both methods improve the process yield substantially, the results indicate that MIP significantly outperforms DP, which suggests that the computational benefit of the CBF assumption comes at a cost of inferior solution quality.
Primal heuristics play an important role in the solving of mixedinteger programs (MIPs). They often provide good feasible solutions early and help to reduce the time needed to prove optimality. In this paper, we pres...
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Primal heuristics play an important role in the solving of mixedinteger programs (MIPs). They often provide good feasible solutions early and help to reduce the time needed to prove optimality. In this paper, we present a scheme for start heuristics that can be executed without previous knowledge of an LP solution or a previously found integer feasible solution. It uses global structures available within MIP solvers to iteratively fix integer variables and propagate these fixings. Thereby, fixings are determined based on the predicted impact they have on the subsequent domain propagation. If sufficiently many variables can be fixed that way, the resulting problem is solved first as an LP, and then as an auxiliary MIP if the rounded LP solution does not provide a feasible solution already. We present three primal heuristics that use this scheme based on different global structures. Our computational experiments on standard MIP test sets show that the proposed heuristics find solutions for about 60% of the instances and by this, help to improve several performance measures for MIP solvers, including the primal integral and the average solving time.
Adequate response performance is required for the planning of a cooperative logistic network covering multiple enterprises, because this process needs a human expert's evaluation from many aspects. To satisfy this...
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Adequate response performance is required for the planning of a cooperative logistic network covering multiple enterprises, because this process needs a human expert's evaluation from many aspects. To satisfy this requirement, we propose an accurate model based on mixed integer programming for optimizing cooperative logistics networks where "round transportation" exists together with "depot transportation" including lower limit constraints of loading ratio for round transportation vehicles. Furthermore, to achieve interactive response performance, a dummy load is introduced into the model instead of integer variables. The experimental result shows the proposed method obtains an accurate solution within interactive response time. (c) 2008 Wiley Periodicals, Inc.
Algorithms developed to solve linear programming (LP) problems and advances in computer speed have made large-scale LP problems solvable in time for implementation. Solving an LP is relatively easier than solving an M...
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Algorithms developed to solve linear programming (LP) problems and advances in computer speed have made large-scale LP problems solvable in time for implementation. Solving an LP is relatively easier than solving an MIP for modern production planning problems. In this study, we propose a heuristic iterative algorithm between LP solution phases and setup decision computations for solving these difficult MIP production planning problems. By utilizing the shadow price information provided by the LP solution of the previous iteration, the setup decision computation converts an MIP problem into an LP problem, which can be efficiently solved in the current iteration. Extensive experiments show that the proposed heuristic algorithm performs well. (C) 1998 Elsevier Science Ltd. All rights reserved.
Conflict analysis for infeasible subproblems is one of the key ingredients in modern SAT solvers. III contrast, it is common practice for today's mixed integer programming solvers to discard infeasible subproblems...
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Conflict analysis for infeasible subproblems is one of the key ingredients in modern SAT solvers. III contrast, it is common practice for today's mixed integer programming solvers to discard infeasible subproblems and the information they reveal. III this paper, we try to remedy this situation by generalizing SAT infeasibility analysis to mixed integer programming. We present heuristics for branch-and-cut solvers to generate valid inequalities from the Current infeasible subproblem and the associated branching information. SAT techniques can then be used to strengthen the resulting constraints. Extensive Computational experiments show the potential Of Our method. Conflict analysis greatly improves the performance oil particular models, while it does not interfere with the solving process on the other instances. In total, the number of required branching nodes oil general MIP instances was reduced by 18% in the geometric mean, and the solving time was reduced by 11%. On infeasible MIP arising in the context of chip verification and on a model for a particular combinatorial game, the number of nodes was reduced by 80%, thereby reducing the solving time by 50%. (c) 2006 Elsevier B.V. All rights reserved.
作者：
WOLSEY, L1.CORE
Université Catholique de Louvain Voie du Roman Pays 34 1348 Louvain-la-Neuve Belgium
We attempt to motivate and survey recent research on the use of “strong” valid inequalities and reformulation to solve mixed integer programming problems.
We attempt to motivate and survey recent research on the use of “strong” valid inequalities and reformulation to solve mixed integer programming problems.
Many deadlock prevention policies existing in the literature are to add control places (CPs) to cope with deadlocks in practical systems modeled with Petri nets. Since the number of CPs determined by these policies is...
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Many deadlock prevention policies existing in the literature are to add control places (CPs) to cope with deadlocks in practical systems modeled with Petri nets. Since the number of CPs determined by these policies is not minimal under the condition that a controlled systems is live, this usually leads to a liveness-enforcing Petri net supervisor with redundant CPs. Based on mixed integer programming (MIP) and the concept of implicit places (IPs), this paper develops a novel iterative algorithm of simplifying the structural complexity for a live Petri net. Under the condition that liveness is preserved in the iteration, this algorithm computes a feasible solution of an MIP for each CP to confirm whether redundant CPs exist in the live controlled system. Necessary and redundant CPs are then kept in or removed from the simplified live Petri net, respectively. As a result, a live controlled system with simpler structure is obtained, which directly reduces computational cost in further design and verification phases and possibly leads to more permissive behavior. Effectiveness of this algorithm is proved via a theoretic analysis and examples.
A mathematical model based on mixed integer programming is presented in this paper for the passive shimming of magnet in magnetic resonance imaging(MRI) *** this model,the magnetic field inhomogeneity tolerance and th...
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A mathematical model based on mixed integer programming is presented in this paper for the passive shimming of magnet in magnetic resonance imaging(MRI) *** this model,the magnetic field inhomogeneity tolerance and the central value of the magnetic field after shimming are programmed together with the volume of each shim piece as the variables,which increases the degree of freedom and guarantees a better *** magnetic field inhomogeneity tolerance after shimming with a weighting coefficient and the total volume of shim pieces are both contained in the objective function of the *** assigning different values to the weighting coefficient in the objective function,different shimming plans with different emphases can be obtained.A simulation test has been carried out on a small permanent magnet with frame *** solutions are given and compared in this paper,which indicates that a practical shimming plan can be obtained quickly by solving this model.
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