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Multi-objective variable neighborhood search: an application to combinatorial optimization problems

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  • Abraham Duarte
  • Juan Pantrigo
  • Eduardo Pardo
  • Nenad Mladenovic

Abstract

Solutions to real-life optimization problems usually have to be evaluated considering multiple conflicting objectives. These kind of problems, known as multi-objective optimization problems, have been mainly solved in the past by using evolutionary algorithms. In this paper, we explore the adaptation of the Variable Neighborhood Search (VNS) metaheuristic to solve multi-objective combinatorial optimization problems. In particular, we describe how to design the shake procedure, the improvement method and the acceptance criterion within different VNS schemas (Reduced VNS, Variable Neighborhood Descent and General VNS), when two or more objectives are considered. We validate these proposals over two multi-objective combinatorial optimization problems. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Abraham Duarte & Juan Pantrigo & Eduardo Pardo & Nenad Mladenovic, 2015. "Multi-objective variable neighborhood search: an application to combinatorial optimization problems," Journal of Global Optimization, Springer, vol. 63(3), pages 515-536, November.
    • Handle: RePEc:spr:jglopt:v:63:y:2015:i:3:p:515-536
    DOI: 10.1007/s10898-014-0213-z
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    References listed on IDEAS

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    1. Mladenovic, Nenad & Urosevic, Dragan & Pérez-Brito, Dionisio & García-González, Carlos G., 2010. "Variable neighbourhood search for bandwidth reduction," European Journal of Operational Research, Elsevier, vol. 200(1), pages 14-27, January.
    2. Gomes da Silva, Carlos & Climaco, Joao & Figueira, Jose, 2006. "A scatter search method for bi-criteria {0, 1}-knapsack problems," European Journal of Operational Research, Elsevier, vol. 169(2), pages 373-391, March.
    3. Juan Pantrigo & Rafael Martí & Abraham Duarte & Eduardo Pardo, 2012. "Scatter search for the cutwidth minimization problem," Annals of Operations Research, Springer, vol. 199(1), pages 285-304, October.
    4. Gomes da Silva, Carlos & Figueira, Jose & Climaco, Joao, 2007. "Integrating partial optimization with scatter search for solving bi-criteria {0, 1}-knapsack problems," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1656-1677, March.
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    4. Eduardo G. Pardo & Antonio García-Sánchez & Marc Sevaux & Abraham Duarte, 2020. "Basic variable neighborhood search for the minimum sitting arrangement problem," Journal of Heuristics, Springer, vol. 26(2), pages 249-268, April.
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    11. Angelo Sifaleras, 2023. "In memory of Professor Nenad Mladenović (1951–2022)," SN Operations Research Forum, Springer, vol. 4(1), pages 1-18, March.
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