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An effective VNS for the capacitated p-median problem

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  • Fleszar, K.
  • Hindi, K.S.
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    Abstract

    In the capacitated p-median problem (CPMP), a set of n customers is to be partitioned into p disjoint clusters, such that the total dissimilarity within each cluster is minimized subject to constraints on maximum cluster capacity. Dissimilarity of a cluster is the sum of the dissimilarities between each customer who belongs to the cluster and the median associated with the cluster. An effective variable neighbourhood search heuristic for this problem is proposed. The heuristic is characterized by the use of easily computed lower bounds to assess whether undertaking computationally expensive calculation of the worth of moves, within the neighbourhood search, is necessary. The small proportion of moves that need to be assessed fully are then evaluated by an exact solution of a relatively small subproblem. Computational results on five standard sets of benchmark problem instances show that the heuristic finds all the best-known solutions. For one instance, the previously best-known solution is improved, if only marginally.

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    File URL: http://www.sciencedirect.com/science/article/B6VCT-4N2D2T8-5/1/3d09649c17a64643bf81be7a8baa0b1f
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    Bibliographic Info

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

    Volume (Year): 191 (2008)
    Issue (Month): 3 (December)
    Pages: 612-622

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    Handle: RePEc:eee:ejores:v:191:y:2008:i:3:p:612-622

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

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    References

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    1. Yagiura, Mutsunori & Ibaraki, Toshihide & Glover, Fred, 2006. "A path relinking approach with ejection chains for the generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 169(2), pages 548-569, March.
    2. Ahmadi, Samad & Osman, Ibrahim H., 2005. "Greedy random adaptive memory programming search for the capacitated clustering problem," European Journal of Operational Research, Elsevier, vol. 162(1), pages 30-44, April.
    3. Mulvey, John M. & Beck, Michael P., 1984. "Solving capacitated clustering problems," European Journal of Operational Research, Elsevier, vol. 18(3), pages 339-348, December.
    4. 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.
    5. Koskosidis, Yiannis A. & Powell, Warren B., 1992. "Clustering algorithms for consolidation of customer orders into vehicle shipments," Transportation Research Part B: Methodological, Elsevier, vol. 26(5), pages 365-379, October.
    6. Scheuerer, Stephan & Wendolsky, Rolf, 2006. "A scatter search heuristic for the capacitated clustering problem," European Journal of Operational Research, Elsevier, vol. 169(2), pages 533-547, March.
    7. Diaz, Juan A. & Fernandez, Elena, 2006. "Hybrid scatter search and path relinking for the capacitated p-median problem," European Journal of Operational Research, Elsevier, vol. 169(2), pages 570-585, March.
    8. Bozkaya, Burcin & Erkut, Erhan & Laporte, Gilbert, 2003. "A tabu search heuristic and adaptive memory procedure for political districting," European Journal of Operational Research, Elsevier, vol. 144(1), pages 12-26, January.
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    Cited by:
    1. Lamb, John D., 2012. "Variable neighbourhood structures for cycle location problems," European Journal of Operational Research, Elsevier, vol. 223(1), pages 15-26.
    2. Alcaraz, Javier & Landete, Mercedes & Monge, Juan F., 2012. "Design and analysis of hybrid metaheuristics for the Reliability p-Median Problem," European Journal of Operational Research, Elsevier, vol. 222(1), pages 54-64.

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