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

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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.

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Acknowledgments

This research has been partially supported by the Spanish Ministry of “Economía y Competitividad”, Grants Ref. TIN2011-28151, and TIN2012-35632-C02, and the Government of the Community of Madrid, Grant Ref. S2009/TIC-1542.

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Authors and Affiliations

  1. Dept. Ciencias de la Computación, Universidad Rey Juan Carlos, c/ Tulipán s/n, 28933 , Móstoles, Madrid, Spain

    Abraham Duarte, Juan J. Pantrigo & Eduardo G. Pardo

  2. Laboratory of Industrial and Human Automation control, Mechanical Engineering and Computer Science (LAMIH), Université de Valenciennes, Mont Houy, 59313 , Valenciennes, France

    Nenad Mladenovic

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  1. Abraham Duarte
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  2. Juan J. Pantrigo
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  3. Eduardo G. Pardo
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  4. Nenad Mladenovic
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Correspondence to Abraham Duarte.

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Duarte, A., Pantrigo, J.J., Pardo, E.G. et al. Multi-objective variable neighborhood search: an application to combinatorial optimization problems. J Glob Optim 63, 515–536 (2015). https://doi.org/10.1007/s10898-014-0213-z

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  • DOI: https://doi.org/10.1007/s10898-014-0213-z

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