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A parallel branch and bound algorithm for solving large scale integer multiobjective problems

A parallel branch and bound algorithm for solving large scal...

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2010 7th international conference on Informatics and Systems, INFOS2010

作者： Ismail, Mahmoud M. Abd El-Wahed, Waiel F. Abd El-raoof, Osama Operations Research Department Faculty of Computers and Information Systems Zagazig EL-Sharkia Egypt Department of Operations Research Faculty of Computers and Information Menofia Univ. Egypt Decision Support Faculty of Computers and Information Menofia Univ. Egypt

ISBN: (纸本)9789774033964

the multi-objective integer programming problems in large scale are considered time consuming. In the past, mathematical structures were used that can get benefits of high processing powers and parallel processing. the Branch and Bound (B&B) algorithm is one of the most used methods to solve combinatorial optimization problems. A general approach to generate all non-dominated solutions of the multi-objective integer programming (MOIP) Problem is developed. In this paper, a supervisor-master-sub-master-worker algorithm to solve large scale integer multi-objective problems that can get the benefits of mathematical structures and high processing powers has been proposed. this approach addresses several issues related to the characteristics of the algorithm itself and the properties of parallel computing systems. From the solved benchmark example this algorithm proved to provide a considerable high performance. Results show that a consistently better efficiency can be achieved in solving integer equations, providing reduction of time.

关键词： integer programming

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Generating multiple solutions for mixed integer programming problems

Generating multiple solutions for mixed integer programming ...

引用

12th international conference on integer programming and combinatorial optimization, ipco XII

作者： Danna, Emilie Fenelon, Mary Zonghao, Gu Wunderling, Roland ILOG Inc. 889 Aider Avenue Incline Village NV 89451 United States

ISBN: (纸本)9783540727910

As mixed integer programming (MIP) problems become easier to solve in pratice, they are used in a growing number of applications where producing a unique optimal solution is often not enough to answer the underlying business problem. Examples include problems where some optimization criteria or some constraints are difficult to model, or where multiple solutions are wanted for quick solution repair in case of data changes. In this paper, we address the problem of effectively generating multiple solutions for the same model, concentrating on optimal and near-optimal solutions. We first define the problem formally, study its complexity, and present three different algorithms to solve it. the main algorithm we introduce, the one-tree algorithm, is a modification of the standard branch-and-bound algorithm. Our second algorithm is based on MIP heuristics. the third algorithm generalizes a previous approach that generates solutions sequentially. We then show with extensive computational experiments that the one-tree algorithm significantly outperforms previously known algorithms in terms of the speed to generate multiple solutions, while providing an acceptable level of diversity in the solutions produced. © Springer-Verlag Berlin Heidelberg 2007.

关键词： integer programming

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Approximating disjoint-path problems using greedy algorithms and packing integer programs 6th

Approximating disjoint-path problems using greedy algorithms...

引用

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

作者： Kolliopoulos, Stavros G. Stein, Clifford Dartmouth College Department of Computer Science HanoverNH03755-3510 United States

ISBN: (纸本)354064590X

the edge and vertex-disjoint path problems together with their unsplittable flow generalization are NP-hard problems with a multitude of applications in areas such as routing, scheduling and bin packing. Given the hardness of the problems, we study polynomial-time approximation algorithms with bounded performance guarantees. We introduce techniques which yield new algorithms for a wide range of disjoint-path problems. We use two basic techniques. First, we propose simple greedy algorithms for edge- and vertex-disjoint paths and second, we propose the use of a framework based on packing integer programs for more general problems such as unsplittable flow. As part of our tools we develop improved approximation algorithms for a class of packing integer programs, a result that we believe is of independent interest. © Springer-Verlag Berlin Heidelberg 1998.

关键词： Approximation algorithms

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On the unique-lifting property

引用

17th international conference on integer programming and combinatorial optimization, ipco 2014

作者： Averkov, Gennadiy Basu, Amitabh Institute of Mathematical Optimization Faculty of Mathematics University of Magdeburg Germany Department of Applied Mathematics and Statistics Johns Hopkins University United States

ISBN: (纸本)9783319075563

We study the uniqueness of minimal liftings of cut generating functions obtained from maximal lattice-free polytopes. We prove a basic invariance property of unique minimal liftings for general maximal lattice-free polytopes. this generalizes a previous result by Basu, Cornuéjols and Köppe [3] for simplicial maximal lattice-free polytopes, thus completely settling this fundamental question about lifting. We also extend results from [3] for minimal liftings in maximal lattice-free simplices to more general polytopes. these nontrivial generalizations require the use of deep theorems from discrete geometry and geometry of numbers, such as the Venkov-Alexandrov-McMullen theorem on translative tilings, and McMullen's characterization of zonotopes. © 2014 Springer international Publishing Switzerland.

关键词： Topology

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On the relationship between combinatorial and LP-based approaches to NP-hard scheduling problems 6th

On the relationship between combinatorial and LP-based appro...

引用

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

作者： Uma, R.N. Wein, Joel Department of Computer Science Polytechnic University BrooklynNY11201 United States

ISBN: (纸本)354064590X

Enumerative approaches, such as branch-and-bound, to solv- ing optimization problems require a subroutine that produces a lower bound on the value of the optimal solution. In the domain of scheduling problems the requisite lower bound has typically been derived from either the solution to a linear-programming relaxation of the problem or the solution of a combinatorial relaxation. In this paper we investigate, from both a theoretical and practical perspective, the relationship between several linear-programming based lower bounds and combinatorial lower bounds for two scheduling problems in which the goal is to minimize the average weighted completion time of the jobs scheduled. We establish a number of facts about the relationship between these dif- ferent sorts of lower bounds, including the equivalence of certain linear- programming-based lower bounds for both of these problems to combi- natorial lower bounds used in successful branch-and-bound algorithms. As a result we obtain the first worst-case analysis of the quality of the lower bound delivered by these combinatorial relaxations. We then give an empirical evaluation of the strength of the various lower bounds and heuristics. this extends and puts in a broader context a recent experimental evaluation by Savelsbergh and the authors of the empirical strength of both heuristics and lower bounds based on different LP-relaxations of a single-machine scheduling problem. We observe that on most kinds of synthetic data used in experimental studies a simple heuristic, used in successful combinatorial branch-and-bound algorithms for the problem, outperforms on average all of the LP-based heuristics. However, we identify other classes of problems on which the LP-based heuristics are superior, and report on experiments that give a qualitative sense of the range of dominance of each. Finally, we consider the impact of local improvement on the solutions. © Springer-Verlag Berlin Heidelberg 1998.

关键词： Linear programming

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Optimal Selective Maintenance for Systems Operating Under Random Environments 7

Optimal Selective Maintenance for Systems Operating Under Ra...

引用

7th international conference on Control, Decision and Information Technologies (CoDIT)

作者： Khatab, A. Diallo, C. Venkatadri, U. Aghezzaf, E-H Univ Lorraine LGIPM F-57000 Metz France Dalhousie Univ Dept Ind Engn Halifax NS Canada Univ Ghent Dept Ind Syst Engn & Prod Design Ghent Belgium Flanders Make Ind Syst Engn ISyE Lommel Belgium

ISBN: (纸本)9781728159539

this paper proposes a new variant of the joint selective maintenance and repairperson assignment problem (SM&RAP) in multicomponent systems. the system carry out missions under random operating environments (OE). Between consecutive missions there are scheduled breaks of finite length within which maintenance actions are performed. Current selective maintenance (SM) models assume that the OE is static and does not change over the course of a mission. However, many mission critical systems are subjected to harsh and varying OE which impacts the mission success probability. this paper develops a new SM optimization model in systems under a random OE. the OE randomness is modeled as a random shock process, and the occurrence of a shock directly impacts the failure process of the components. A nonlinear SM optimization model along with its binary integer programming version are developed and solved to optimality. Numerical experiments are provided where the results obtained demonstrate the added value and the benefit of including the impact of the OE when dealing with SM&RAP.

关键词： combinatorial optimization

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the traveling tournament problem description and benchmarks 7

引用

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

作者： Easton, Kelly Nemhauser, George Trick, Michael School of Industrial and Systems Engineering Georgia Institute of Technology AtlantaGA30332 United States Graduate School of Industrial Administration Carnegie Mellon PittsburghPA15213 United States

ISBN: (纸本)3540428631

the Traveling Tournament Problem is a sports timetabling problem that abstracts two issues in creating timetables: home/away pattern feasibility and team travel. Instances of this problem seem to be very difficult even for a very small number of teams, making it an interesting challenge for combinatorial optimization techniques such as integer programming and constraint programming. We introduce the problem, describe one way of modeling it, and give some interesting classes of instances with base computational results. © Springer-Verlag Berlin Heidelberg 2001.

关键词： integer programming

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On ideal clutters, metrics and multiflows 5th

On ideal clutters, metrics and multiflows

引用

5th international conference integer programming and combinatorial optimization, ipco 1996

作者： Novick, Beth Sebő, András Clemson University ClemsonSC29634-1907 United States CNRS Laboratoire Leibniz Grenoble France

ISBN: (纸本)3540613102

"Binary clutters" contain various objects studied in combinatorial optimization, such as paths, Chinese Postman Tours, multiflows and one-sided circuits on surfaces. Minimax theorems about these can be generalized in terms of ideal binary clutters. Seymour has conjectured a characterization of these, and the goal of the present work is to study this conjecture in terms of multiflows in matroids. Seymour's conjecture is equivalent to the following: Let F be a binary clutter. then the Cut Condition is sufficient in the underlying matroid, for all F Ε F as demand-set, to have a multiflow, if and only if it implies the so called K5, F7 and R10-conditions. these three conditions are applications of the general "Metric Condition" to particular 0–1 bipartite weightings. In this paper we prove the following weakening of this conjecture: the Cut Condition is sufficient for all F Ε F as demand-set, to have a multiflow, if and only if it implies the Metric Condition for every bipartite 0–1 weighting. A special case of this result has been stated as a conjecture in Robertson and Seymour's "Graph Minors" volume, (1991, "Open Problem 11 (A. Sebő)"). Using Lehman's theorem on minimal non-ideal clutters, we sharpen the properties of minimally non-ideal clutters for the binary and graphic special cases. © Springer-Verlag Berlin Heidelberg 1996.

关键词： combinatorial optimization

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High performance integer optimization for crew scheduling 7th

High performance integer optimization for crew scheduling

引用

7th international conference and Exhibition on High-Performance Computing and Networking (HPCN EUROPE 99)

作者： Sanders, P Takkula, T Wedelin, D Max Planck Inst Comp Sci Saarbrucken Germany Chalmers Univ Technol S-41296 Gothenburg Sweden

ISBN: (纸本)3540658211

Performance aspects of a Lagrangian relaxation based heuristic for solving large 0-1 integer linear programs are discussed. In particular, we look at its application to airline and railway crew scheduling problems. We present a scalable parallelization of the original algorithm used in production at Carmen Systems AB, Goteborg, Sweden, based on distributing the variables and a new sequential active set strategy which requires less work and is better adapted to the memory hierachy properties of modern RISC processors. the active set strategy can even be parallelized on networks of workstations.

关键词： integer programming

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An implementation of a combinatorial approximation algorithm for minimum-cost multicommodity flow 6th

An implementation of a combinatorial approximation algorithm...

引用

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

作者： Goldberg, Andrew V. Oldham, Jeffrey D. Plotkin, Serge Stein, Cliff NEC Research Institute Inc PrincetonNJ08540 United States Department of Computer Science Stanford University StanfordCA94305-9045 United States Department of Computer Science Dartmouth College HanoverNH03755 United States

ISBN: (纸本)354064590X

the minimum-cost multicommodity flow problem involves simultaneously shipping multiple commodities through a single network so that the total flow obeys arc capacity constraints and has minimum cost. Multicommodity flow problems can be expressed as linear programs, and most theoretical and practical algorithms use linear-programming algorithms specialized for the problems' structures. combinatorial approximation algorithms in [GK96, KP95b, PST95] yield flows with costs slightly larger than the minimum cost and use capacities slightly larger than the given capacities. theoretically, the running times of these algorithms are much less than that of linear-programming-based algorithms. We combine and modify the theoretical ideas in these approximation algorithms to yield a fast, practical implementation solving the minimumcost multicommodity flow problem. Experimentally, the algorithm solved our problem instances (to 1% accuracy) two to three orders of magnitude faster than the linear-programming package CPLEX [CPL95] and the linear-programming based multicommodity flow program PPRN [CN96]. © Springer-Verlag Berlin Heidelberg 1998.

关键词： Approximation algorithms

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