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Variable Neighborhood Search

In: Handbook of Metaheuristics

Author

Listed:
  • Pierre Hansen

    (GERAD and Ecole des Hautes Etudes Commerciales)

  • Nenad Mladenović

    (Brunel University-West London)

  • Jack Brimberg

    (Royal Military College of Canada)

  • José A. Moreno Pérez

    (IUDR and DEIOC, Universidad de La Laguna)

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.

Suggested Citation

  • Pierre Hansen & Nenad Mladenović & Jack Brimberg & José A. Moreno Pérez, 2010. "Variable Neighborhood Search," International Series in Operations Research & Management Science, in: Michel Gendreau & Jean-Yves Potvin (ed.), Handbook of Metaheuristics, chapter 0, pages 61-86, Springer.
    • Handle: RePEc:spr:isochp:978-1-4419-1665-5_3
    DOI: 10.1007/978-1-4419-1665-5_3
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    Citations

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    Cited by:

    1. J. Fabian Meier & Uwe Clausen, 2018. "Solving Single Allocation Hub Location Problems on Euclidean Data," Transportation Science, INFORMS, vol. 52(5), pages 1141-1155, October.
    2. James F. Campbell & Morton E. O'Kelly, 2012. "Twenty-Five Years of Hub Location Research," Transportation Science, INFORMS, vol. 46(2), pages 153-169, May.
    3. Ann Campbell & Michel Gendreau & Barrett Thomas, 2011. "The orienteering problem with stochastic travel and service times," Annals of Operations Research, Springer, vol. 186(1), pages 61-81, June.
    4. Kuhn, Heinrich & Schubert, Daniel & Holzapfel, Andreas, 2021. "Integrated order batching and vehicle routing operations in grocery retail – A General Adaptive Large Neighborhood Search algorithm," European Journal of Operational Research, Elsevier, vol. 294(3), pages 1003-1021.
    5. Vesna Radonjić Ɖogatović & Marko Ɖogatović & Milorad Stanojević & Nenad Mladenović, 2020. "Revenue maximization of Internet of things provider using variable neighbourhood search," Journal of Global Optimization, Springer, vol. 78(2), pages 375-396, October.
    6. Andrew Lim & Zhenzhen Zhang & Hu Qin, 2017. "Pickup and Delivery Service with Manpower Planning in Hong Kong Public Hospitals," Transportation Science, INFORMS, vol. 51(2), pages 688-705, May.
    7. Angel Juan & Javier Faulin & Albert Ferrer & Helena Lourenço & Barry Barrios, 2013. "MIRHA: multi-start biased randomization of heuristics with adaptive local search for solving non-smooth routing problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 109-132, April.
    8. Sebastian Henn, 2012. "Variable Neighborhood Search for the Order Batching and Sequencing Problem with Multiple Pickers," FEMM Working Papers 120004, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    9. Juanjo Peiró & Ángel Corberán & Rafael Martí & Francisco Saldanha-da-Gama, 2019. "Heuristic Solutions for a Class of Stochastic Uncapacitated p-Hub Median Problems," Transportation Science, INFORMS, vol. 53(4), pages 1126-1149, July.
    10. Dolinskaya, Irina & Shi, Zhenyu (Edwin) & Smilowitz, Karen, 2018. "Adaptive orienteering problem with stochastic travel times," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 109(C), pages 1-19.
    11. Trung Hieu Tran & Jesse R. O’Hanley & M. Paola Scaparra, 2017. "Reliable Hub Network Design: Formulation and Solution Techniques," Transportation Science, INFORMS, vol. 51(1), pages 358-375, February.

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