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Variable neighbourhood structures for cycle location problems

Listed author(s):
  • Lamb, John D.
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    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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    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
    DOI: 10.1016/j.ejor.2012.05.038
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    1. 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.
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    4. Hansen, Pierre & Mladenovic, Nenad, 2001. "Variable neighborhood search: Principles and applications," European Journal of Operational Research, Elsevier, vol. 130(3), pages 449-467, May.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
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