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Variable Neighborhood Search

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Handbook of Metaheuristics

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 146))

Abstract

Variable neighborhood search (VNS) is a metaheuristic for solving combinatorial and global optimization problems whose basic idea is a systematic change of neighborhood both within a descent phase to find a local optimum and in a perturbation phase to get out of the corresponding valley. In this chapter we present the basic schemes of VNS and some of its extensions. We then describe a recent development, i.e., formulation space search. We then present five families of applications in which VNS has proven to be very successful: (i) exact solution of large-scale location problems by primal–dual VNS; (ii) generation of feasible solutions to large mixed integer linear programs by hybridization of VNS and local branching; (iii) generation of good feasible solutions to continuous nonlinear programs; (iv) generation of feasible solutions and/or improved local optima for mixed integer nonlinear programs by hybridization of sequential quadratic programming and branch and bound within a VNS framework, and (v) exploration of graph theory to find conjectures, refutations, and proofs or ideas of proofs.

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Authors and Affiliations

  1. GERAD and Ecole des Hautes Etudes Commerciales, 3000 ch. de la Cote-Sainte-Catherine, Montréal, H3T 2A7, QC, Canada

    Pierre Hansen

  2. School of Mathematics, Brunel University-West London, Uxbridge, UB8 3PH, UK

    Nenad Mladenović

  3. Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, ON, Canada, K7K 7B4

    Jack Brimberg

  4. IUDR and DEIOC, Universidad de La Laguna, 38271, La Laguna, Santa Cruz de Tenerife, Spain

    José A. Moreno Pérez

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  1. Pierre Hansen
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  2. Nenad Mladenović
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  4. José A. Moreno Pérez
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Correspondence to Pierre Hansen , Nenad Mladenović , Jack Brimberg or José A. Moreno Pérez .

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  1. , Département de mathématiques et génie in, École Polytechnique Montréal, Montreal, H3C 3A7, Québec, Canada

    Michel Gendreau

  2. Dépt. Informatique et Recherche, Opérationnelle, Université de Montreal, Pavillon André-Aisenstadt, Montreal, H3C 3J7, Québec, Canada

    Jean-Yves Potvin

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Hansen, P., Mladenović, N., Brimberg, J., Pérez, J.A.M. (2010). Variable Neighborhood Search. In: Gendreau, M., Potvin, JY. (eds) Handbook of Metaheuristics. International Series in Operations Research & Management Science, vol 146. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1665-5_3

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