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Incorporating inequality constraints in the spectral bundle method 6th

Incorporating inequality constraints in the spectral bundle ...

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6th international integer programming and combinatorial optimization conference, ipco 1998

作者： Helmberg, Christoph Kiwiel, Krzysztof C. Rendl, Franz Konrad-Zuse-Zentrum für Informationstechnik Berlin Takustraβe 7 Berlin14195 Germany Systems Research Institute Polish Academy of Sciences Newelska 6 Warsaw01-447 Poland Technische Universität Graz Institut für Mathematik Steyrergasse 30 GrazA-8010 Austria

ISBN: (纸本)354064590X

Semidefinite relaxations of quadratic 0-1 programming or graph partitioning problems are well known to be of high quality. However, solving them by primal-dual interior point methods can take much time even for problems of moderate size. Recently we proposed a spectral bundle method that allows to compute, within reasonable time, approximate solutions to structured, large equality constrained semidefinite programs if the trace of the primal matrix variable is fixed. the latter property holds for the aforementioned applications. We extend the spectral bundle method so that it can handle inequality constraints without seriously increasing computation time. this makes it possible to apply cutting plane algorithms to semidefinite relaxations of real world sized instances. We illustrate the efficacy of the approach by giving some preliminary computational results. © Springer-Verlag Berlin Heidelberg 1998.

关键词： Constraint theory

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1-sparsity Approximation Bounds for Packing integer Programs 20th

1-sparsity Approximation Bounds for Packing Integer Programs

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20th international conference on integer programming and combinatorial optimization, ipco 2019

作者： Chekuri, Chandra Quanrud, Kent Torres, Manuel R. University of Illinois at Urbana-Champaign UrbanaIL United States

ISBN: (纸本)9783030179526

We consider approximation algorithms for packing integer programs (PIPs) of the form where c, A, and b are nonnegative. We let denote the width of A which is at least 1. Previous work by Bansal et al. [1] obtained an -approximation ratio where is the maximum number of nonzeroes in any column of A (in other words the -column sparsity of A). they raised the question of obtaining approximation ratios based on the -column sparsity of A (denoted by) which can be much smaller than Motivated by recent work on covering integer programs (CIPs) [4, 7] we show that simple algorithms based on randomized rounding followed by alteration, similar to those of Bansal et al. [1] (but with a twist), yield approximation ratios for PIPs based on First, following an integrality gap example from [1], we observe that the case of is as hard as maximum independent set even when In sharp contrast to this negative result, as soon as width is strictly larger than one, we obtain positive results via the natural LP relaxation. For PIPs with width where we obtain an -approximation. In the large width regime, when we obtain an -approximation. We also obtain a -approximation when. © 2019, Springer Nature Switzerland AG.

关键词： Approximation algorithms

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7th international conference on Principles and Practice of Constraint programming, CP 2001

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7th international conference on Principles and Practice of Constraint programming, CP 2001

ISBN: (纸本)3540428631

the proceedings contain 84 papers. the special focus in this conference is on Principles and Practice of Constraint programming. the topics include: Hybrid benders decomposition algorithms in constraint logic programming;a hybrid framework integrating mixed integer programming and constraint logic programming;towards stochastic constraint programming;global cut framework for removing symmetries;capturing structure with satisfiability;phase transitions and backbones of 3-sat and maximum 3-sat;solving non-binary CSPS using the hidden variable encoding;a filtering algorithm for the stretch constraint;network flow problems in constraint programming;pruning for the minimum constraint family and for the number of distinct values constraint family;components for state restoration in tree search;constraint-based verification of client-server protocols;lower bounds for non-binary constraint optimization problems;a general scheme for multiple lower bound computation in constraint optimization;solving disjunctive constraints for interactive graphical applications;non-overlapping constraints between convex polytopes;formal models of heavy-tailed behavior in combinatorial search;in search of a phase transition in the ac-matching problem;a CLP approach to the protein side-chain placement problem;solving constraints over floating-point numbers;optimal pruning in parametric differential equations;an efficient filtering technique combining domain partition and arc consistency;the expressive power of binary linear programming;the traveling tournament problem description and benchmarks;structural constraint-based modeling and reasoning with basic configuration cells;solving Boolean satisfiability using local search guided by unit clause elimination and fast optimal instruction scheduling for single-issue processors with arbitrary latencies.

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the semidefinite relaxation of the κ-partition polytope is strong

The semidefinite relaxation of the κ-partition polytope is ...

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9th international conference on integer programming and combinatorial optimization, ipco 2002

作者： Eisenblätter, Andreas Takustr. 7 D-14195 Berlin Germany

ISBN: (纸本)9783540478676

Radio frequency bandwidth has become a very scarce resource. this holds true in particular for the popular mobile communication system GSM. Carefully planning the use of the available frequencies is thus of great importance to GSM network operators. Heuristic optimization methods for this task are known, which produce frequency plans causing only moderate amounts of disturbing interference in many typical situations. In order to thoroughly assess the quality of the plans, however, lower bounds on the unavoidable interference are in demand. the results obtained so far using linear programming and graph theoretic arguments do not suffice. By far the best lower bounds are currently obtained from semidefinite programming. the link between semidefinite programming and the bound on unavoidable interference in frequency planning is the semidefinite relaxation of the graph minimum κ-partition problem. Here, we take first steps to explain the surprising strength of the semidefinite relaxation. this bases on a study of the solution set of the semidefinite relaxation in relation to the circumscribed κ-partition polytope. Our focus is on the huge class of hypermetric inequalities, which are valid and in many cases facet-defining for the κ-partition polytope. We show that a "slightly shifted version" of the hypermetric inequalities is implicit to the semidefinite relaxation. In particular, no feasible point for the semidefinite relaxation violates any of the facet-defining triangle inequalities for the κ-partition polytope by more than √2 - 1 or any of the (exponentially many) facet-defining clique constraints by 1/2 or more. © 2002 Springer-Verlag Berlin Heidelberg.

关键词： Linear programming

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A multi-exchange local search algorithm for the capacitated facility location problem - (Extended abstract)

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10th international integer programming and combinatorial optimization conference

作者： Zhang, JW Chen, B Ye, YY Stanford Univ Dept Management Sci & Engn Sch Engn Stanford CA 94305 USA Univ Warwick Warwick Business Sch Coventry CV4 7AL W Midlands England

ISBN: (纸本)3540221131

We present a multi-exchange local search algorithm for approximating the capacitated facility location problem (CFLP), where a new local improvement operation is introduced that possibly exchanges multiple facilities simultaneously. We give a tight analysis for our algorithm and show that the performance guarantee of the algorithm is between 3 + 2root2 - epsilon and 3 + 2 root2 + epsilon for any given constant epsilon > 0. Previously known best approximation ratio for the CFLP is 7.88, due to Mahdian and Pal (2003), based on the operations proposed by Pal, Tardos and Wexler (2001). Our upper bound 3 + 2root2 + epsilon also matches the best known ratio, obtained by Chudak and Williamson (1999), for the CFLP with uniform capacities. In order to obtain the tight bound of our new algorithm, we make interesting use of the notion of exchange graph of Pal et al. and techniques from the area of parallel machine scheduling.

关键词： capacitated facility location approximation algorithm local search algorithm

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Exact solution of one production scheduling problem 7th

Exact solution of one production scheduling problem

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7th international conference on optimization Problems and their Applications, OPTA 2018

作者： Borisovsky, Pavel Sobolev Institute of Mathematics Omsk Russia

ISBN: (纸本)9783319937991

In this study, one variant of multi-product scheduling problem is considered. the problem asks to find the optimal selection of a set of tasks to produce a given number of products in required amounts, to allocate the task on units, and to find the order of execution of tasks for each unit. the production rates for each task, the task-unit suitability matrix, and the sequence dependent changeover times for task pairs are given. For the one-unit problem, two combinatorial algorithms are proposed: a branch-and-bound algorithm and a parallel dynamic programming algorithm. the last one is implemented using the CUDA library for running on a Graphical Processing Unit (GPU). For the multiple-units problem, both approaches are combined in a branch-and-bound algorithm with bounds provided by the dynamic programming procedure. the algorithms are compared with CPLEX solver applied to the considered problem formulated as a mixed integer linear program. Although, the main limitation of using the proposed algorithms is a requirement of large amount of memory, the experiments showed their superior performance over CPLEX in terms of running time for rather large sized instances. the advantage of parallelization and using the GPU is also demonstrated. © Springer international Publishing AG, part of Springer Nature 2018.

关键词： Dynamic programming

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A mickey-mouse decomposition theorem 4th

A mickey-mouse decomposition theorem

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4th international conference on integer programming and combinatorial optimization, ipco 1995

作者： Conforti, Michele Cornuéjols, Gérard Kapoor, Ajai Vuškovic, Kristina Dipartimento di Matematica Para eci Applicata Università di Padova Via Belzoni 7 Padova35131 Italy Carnegie Mellon University Schenley Park PittsburghPA15213 United States Department of Combinatorics and Optimization University of Waterloo WaterlooONN2L 3G1 Canada

A graph is signable to be without, odd holes if we can assign labels "even" or "odd" to its edges in such a way that the number of edges labelled "odd" in every triangle is odd and the nu... 详细信息

ISBN: (纸本)9783540594086

A graph is signable to be without, odd holes if we can assign labels "even" or "odd" to its edges in such a way that the number of edges labelled "odd" in every triangle is odd and the number of edges labelled "odd" in every chordless cycle of length greater than three is even. Note that a graph has no odd holes if it is signed to be without odd holes with every edge having an "odd5’ label. We derive a co-NP characterization of such graphs. A mickey-mouse M is a cycle C = Xi,..,, Xn,Xi with two chords x,Xj and Xi+Xj (indices taken modulo n). the chordless cycles Cj = Xj,..., Xi,, Xj and C2 = Xi+1,…,Xj, Xi+1 are the ears of the mickey-mouse. A mickey-mouse has big ears if both Ci and C2 have length greater than three. In this paper we show that if a graph G is signable to be without odd holes and contains a mickey-mouse with big ears, with chords Xi,Xj and Xi+Xj, then the removal of the nodes adjacent to Xj, together with the nodes adjacent to both Xi, and Xi+i disconnects G. © Springer-Verlag Berlin Heidelberg 1995.

关键词： Graph theory

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the semidefinite relaxation of the k-partition polytope is strong

The semidefinite relaxation of the k-partition polytope is s...

引用

9th international integer programming and combinatorial optimization conference, ipco 2002

作者： Eisenblätter, Andreas Takustr. 7 BerlinD-14195 Germany

ISBN: (纸本)9783540478676

Radio frequency bandwidth has become a very scarce resource. this holds true in particular for the popular mobile communication system GSM. Carefully planning the use of the available frequencies is thus of great importance to GSM network operators. Heuristic optimization methods for this task are known, which produce frequency plans causing only moderate amounts of disturbing interference in many typical situations. In order to thoroughly assess the quality of the plans, however, lower bounds on the unavoidable interference are in demand. the results obtained so far using linear programming and graph theoretic arguments do not suffice. By far the best lower bounds are currently obtained from semidefinite programming. the link between semidefinite programming and the bound on unavoidable interference in frequency planning is the semidefinite relaxation of the graph minimum k-partition problem. Here, we take first steps to explain the surprising strength of the semidefinite relaxation. this bases on a study of the solution set of the semidefinite relaxation in relation to the circumscribed k-partition polytope. Our focus is on the huge class of hypermetric inequalities, which are valid and in many cases facet-defining for the k-partition polytope. We show that a "slightly shifted version" of the hypermetric inequalities is implicit to the semidefinite relaxation. In particular, no feasible point for the semidefinite relaxation violates any of the facet-defining triangle inequalities for the k-partition polytope by more than √2 - 1 or any of the (exponentially many) facet-defining clique constraints by 1/2 or more. © Springer-Verlag Berlin Heidelberg 2002.

关键词： Linear programming

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A genetic algorithm approach for the multidimensional two-way number partitioning problem 1

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7th international conference on Learning and Intelligent optimization, LION 7

作者： Pop, P.C. Matei, O. Department of Mathematics and Informatics Technical University of Cluj-Napoca Cluj-Napoca Romania Department of Electrical Engineering Technical University of Cluj-Napoca Cluj-Napoca Romania

ISBN: (数字)9783642449734

ISBN: (纸本)9783642449727

this paper addresses the problem of partitioning a set of vectors into two subsets such that the sums per every coordinate should be exactly or approximately equal. this problem, introduced by Kojic [8], is called the multidimensional two-way number partitioning problem (MDTWNPP) and generalizes the classical two-way number partitioning problem. We propose an efficient genetic algorithm based heuristic for solving the multidimensional two-way number partitioning problem. the performances of our genetic algorithm have been compared with the existing numerical results obtained by CPLEX based on an integer linear programming formulation of the problem. the obtained preliminary results, in the case of medium and large instances, reveal that our proposed methodology performs very well in terms of both quality of the solutions and the computational times compared with the previous method of solving the MDTWNPP. © 2013 Springer-Verlag.

关键词： combinatorial optimization

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Robust optimization for the hazardous materials transportation network design problem

Robust optimization for the hazardous materials transportati...

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7th international conference on combinatorial optimization and Applications, COCOA 2013

作者： Xin, Chunlin Letu, Qingge Bai, Yin School of Economics and Management Beijing University of Chemical Technology 100029 China Research Center for Operations Management and Strategy Decision China Data Mining Group NEC Laboratories 100084 China

ISBN: (纸本)9783319037790

We consider the problem of designing a transportation network for hazardous materials (HTNDP). For HTNDP, it was shown that deciding whether there exists an optimal path of risk 0 is NP-hard. A natural way to handle NP-hard problems is approximation solutions or FPT algorithms. We prove that HTNDP does not admit any approximation, neither any FPT algorithm, unless P=NP. the hazmat network design problem faces significant uncertainty in conflicting numbers of edge risk reported by different researchers and many factors affecting edge risk could induce different results since the edge risk is often difficult to characterize. In this paper, we use maximum regret criterion robust optimization to model the problem as a bi-level integer programming problem under edge risk uncertainty where an interval of possible risk values is associated with each arc. We present a heuristic approach that always finds a robust and stable hazmat network. At the end, we test our method on a random instance on a network of Guangdong province in China to illustrate the efficiency of our model and algorithm. Our experimental tests illustrate that the robust interval risk scenario network performs very well, and can handle the risk change better compared with the deterministic scenario network. Overall, the numerical analysis reveals that the maximum regret criterion robust optimization used in HTNDP is more conservative but has the merit of robustness. © Springer international Publishing Switzerland 2013.

关键词： Heuristic methods

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