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Variable neighbourhood structures for cycle location problems

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  • Lamb, John D.
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    Abstract

    Variable neighbourhood search is a metaheuristic used mainly to tackle combinatorial optimization problems. Its performance depends on having a good variable neighbourhood structure: that is, a sequence of neighbourhoods that are ideally pairwise disjoint and contain feasible solutions further and further from a given feasible solution. This article defines a variable neighbourhood structure with these properties that is new for cycle location problems. It find bounds for the neighbourhood sizes and shows how to iterate over then when the cycle is a circuit. It tests the structure and iteration method using variable neighbourhood search on a range of median cycle problems and finds a neighbourhood size beyond which there is, on average, no benefit in applying local search. This neighbourhood size is found not to depend on problem size or bound on circuit length.

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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 223 (2012)
    Issue (Month): 1 ()
    Pages: 15-26

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    Handle: RePEc:eee:ejores:v:223:y:2012:i:1:p:15-26

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    Web page: http://www.elsevier.com/locate/eor

    Related research

    Keywords: Heuristics; Variable neighbourhood search; Circuit; Cycle;

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    1. Ilic, Aleksandar & Urosevic, Dragan & Brimberg, Jack & Mladenovic, Nenad, 2010. "A general variable neighborhood search for solving the uncapacitated single allocation p-hub median problem," European Journal of Operational Research, Elsevier, vol. 206(2), pages 289-300, October.
    2. Fleszar, K. & Hindi, K.S., 2008. "An effective VNS for the capacitated p-median problem," European Journal of Operational Research, Elsevier, vol. 191(3), pages 612-622, December.
    3. Fathali, J. & Kakhki, H. Taghizadeh, 2006. "Solving the p-median problem with pos/neg weights by variable neighborhood search and some results for special cases," European Journal of Operational Research, Elsevier, vol. 170(2), pages 440-462, April.
    4. Moreno Perez, Jose A. & Marcos Moreno-Vega, J. & Rodriguez Martin, Inmaculada, 2003. "Variable neighborhood tabu search and its application to the median cycle problem," European Journal of Operational Research, Elsevier, vol. 151(2), pages 365-378, December.
    5. Labbe, Martine & Laporte, Gilbert & Rodriguez Martin, Inmaculada & Gonzalez, Juan Jose Salazar, 2005. "Locating median cycles in networks," European Journal of Operational Research, Elsevier, vol. 160(2), pages 457-470, January.
    6. Mesa, Juan A. & Brian Boffey, T., 1996. "A review of extensive facility location in networks," European Journal of Operational Research, Elsevier, vol. 95(3), pages 592-603, December.
    7. Hansen, Pierre & Mladenovic, Nenad, 2001. "Variable neighborhood search: Principles and applications," European Journal of Operational Research, Elsevier, vol. 130(3), pages 449-467, May.
    8. Hemmelmayr, Vera C. & Doerner, Karl F. & Hartl, Richard F., 2009. "A variable neighborhood search heuristic for periodic routing problems," European Journal of Operational Research, Elsevier, vol. 195(3), pages 791-802, June.
    9. Nagy, Gabor & Salhi, Said, 2005. "Heuristic algorithms for single and multiple depot vehicle routing problems with pickups and deliveries," European Journal of Operational Research, Elsevier, vol. 162(1), pages 126-141, April.
    10. Helsgaun, Keld, 2000. "An effective implementation of the Lin-Kernighan traveling salesman heuristic," European Journal of Operational Research, Elsevier, vol. 126(1), pages 106-130, October.
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