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Evolutionary, constructive and hybrid procedures for the bi-objective set packing problem

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  • Delorme, Xavier
  • Gandibleux, Xavier
  • Degoutin, Fabien

Abstract

The bi-objective set packing problem is a multi-objective combinatorial optimization problem similar to the well-known set covering/partitioning problems. To our knowledge and surprise, this problem has not yet been studied whereas several applications have been reported. Unfortunately, solving the problem exactly in a reasonable time using a generic solver is only possible for small instances. We designed three alternative procedures for approximating solutions to this problem. The first is derived from the original 'Strength Pareto Evolutionary Algorithm', which is a population-based metaheuristic. The second is an adaptation of the 'Greedy Randomized Adaptative Search Procedure', which is a constructive metaheuristic. As underlined in the overview of the literature summarized here, almost all the recent, effective procedures designed for approximating optimal solutions to multi-objective combinatorial optimization problems are based on a blend of techniques, called hybrid metaheuristics. Thus, the third alternative, which is the primary subject of this paper, is an original hybridization of the previous two metaheuristics. The algorithmic aspects, which differ from the original definition of these metaheuristics, are described, so that our results can be reproduced. The performance of our procedures is reported and the computational results for 120 numerical instances are discussed.

Suggested Citation

  • Delorme, Xavier & Gandibleux, Xavier & Degoutin, Fabien, 2010. "Evolutionary, constructive and hybrid procedures for the bi-objective set packing problem," European Journal of Operational Research, Elsevier, vol. 204(2), pages 206-217, July.
    • Handle: RePEc:eee:ejores:v:204:y:2010:i:2:p:206-217
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    References listed on IDEAS

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    1. Coello Coello, Carlos A. & Aguirre, Arturo Hernandez & Zitzler, Eckart, 2007. "Evolutionary multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1617-1619, September.
    2. Medaglia, Andres L. & Fang, Shu-Cherng, 2003. "A genetic-based framework for solving (multi-criteria) weighted matching problems," European Journal of Operational Research, Elsevier, vol. 149(1), pages 77-101, August.
    3. Delorme, Xavier & Gandibleux, Xavier & Rodriguez, Joaquin, 2004. "GRASP for set packing problems," European Journal of Operational Research, Elsevier, vol. 153(3), pages 564-580, March.
    4. Alidaee, Bahram & Kochenberger, Gary & Lewis, Karen & Lewis, Mark & Wang, Haibo, 2008. "A new approach for modeling and solving set packing problems," European Journal of Operational Research, Elsevier, vol. 186(2), pages 504-512, April.
    5. Matthias Ehrgott & Xavier Gandibleux, 2004. "Approximative solution methods for multiobjective combinatorial optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 1-63, June.
    6. Zhou, Gengui & Gen, Mitsuo, 1999. "Genetic algorithm approach on multi-criteria minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 114(1), pages 141-152, April.
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    Cited by:

    1. Aritra Pal & Hadi Charkhgard, 2019. "A Feasibility Pump and Local Search Based Heuristic for Bi-Objective Pure Integer Linear Programming," INFORMS Journal on Computing, INFORMS, vol. 31(1), pages 115-133, February.
    2. Mavrotas, George & Florios, Kostas, 2013. "An improved version of the augmented epsilon-constraint method (AUGMECON2) for finding the exact Pareto set in Multi-Objective Integer Programming problems," MPRA Paper 105034, University Library of Munich, Germany.
    3. Hela Masri & Saoussen Krichen, 2018. "Exact and approximate approaches for the Pareto front generation of the single path multicommodity flow problem," Annals of Operations Research, Springer, vol. 267(1), pages 353-377, August.
    4. Martí, Rafael & Campos, Vicente & Resende, Mauricio G.C. & Duarte, Abraham, 2015. "Multiobjective GRASP with Path Relinking," European Journal of Operational Research, Elsevier, vol. 240(1), pages 54-71.

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