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Variable Neighborhood Search

In: Handbook of Metaheuristics

Author

Listed:
  • Pierre Hansen

    (École des Hautes Études Commerciales
    GERAD)

  • Nenad Mladenović

    (Mathematical Institute)

  • Jack Brimberg

    (Royal Military College of Canada)

  • José A. Moreno Pérez

    (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 recent developments, i.e., formulation space search and variable formulation search. We then present some families of applications in which VNS has proven to be very successful: (1) exact solution of large scale location problems by primal-dual VNS; (2) generation of solutions to large mixed integer linear programs, by hybridization of VNS and local branching; (3) generation of solutions to very large mixed integer programs using VNS decomposition and exact solvers (4) generation of good feasible solutions to continuous nonlinear programs; (5) adaptation of VNS for solving automatic programming problems from the Artificial Intelligence field and (6) 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, 2019. "Variable Neighborhood Search," International Series in Operations Research & Management Science, in: Michel Gendreau & Jean-Yves Potvin (ed.), Handbook of Metaheuristics, edition 3, chapter 0, pages 57-97, Springer.
    • Handle: RePEc:spr:isochp:978-3-319-91086-4_3
    DOI: 10.1007/978-3-319-91086-4_3
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    Citations

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    Cited by:

    1. Andrei V. Nikolaev & Egor V. Klimov, 2024. "Finding a second Hamiltonian decomposition of a 4-regular multigraph by integer linear programming," Journal of Combinatorial Optimization, Springer, vol. 47(5), pages 1-31, July.
    2. Nevena Čolić & Pavle Milošević & Ivana Dragović & Miljan S. Ćeranić, 2024. "IBA-VNS: A Logic-Based Machine Learning Algorithm and Its Application in Surgery," Mathematics, MDPI, vol. 12(7), pages 1-21, March.
    3. Álvaro D. O. Lopes & Helder R. O. Rocha & Marcos W. J. Servare Junior & Renato E. N. Moraes & Jair A. L. Silva & José L. F. Salles, 2023. "Planning an Integrated Stockyard–Port System for Smart Iron Ore Supply Chains via VND Optimization," Sustainability, MDPI, vol. 15(11), pages 1-20, June.
    4. Dimitrije D. Čvokić & Yury A. Kochetov & Aleksandr V. Plyasunov & Aleksandar Savić, 2022. "A variable neighborhood search algorithm for the $$ (r{\mid }p) $$ ( r ∣ p ) hub–centroid problem under the price war," Journal of Global Optimization, Springer, vol. 83(3), pages 405-444, July.
    5. Gust, Gunther & Schlüter, Alexander & Feuerriegel, Stefan & Úbeda, Ignacio & Lee, Jonathan T. & Neumann, Dirk, 2024. "Designing electricity distribution networks: The impact of demand coincidence," European Journal of Operational Research, Elsevier, vol. 315(1), pages 271-288.

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