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Density Based Problem Space Search for the Capacitated Clustering p-Median Problem

Author

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  • Samad Ahmadi
  • Ibrahim Osman

Abstract

In the Capacitated Clustering Problem (CCP), a given set of n weighted points is to be partitioned into p clusters such that, the total weight of the points in each cluster does not exceed a given cluster capacity. The objective is to find a set of p centers that minimises total scatter of points allocated to them. In this paper a new constructive method, a general framework to improve the performance of greedy constructive heuristics, and a problem space search procedure for the CCP are proposed. The constructive heuristic finds patterns of natural subgrouping in the input data using concept of density of points. Elements of adaptive computation and periodic construction–deconstruction concepts are implemented within the constructive heuristic to develop a general framework for building efficient heuristics. The problem-space search procedure is based on perturbations of input data for which a controlled perturbation strategy, intensification and diversification strategies are developed. The implemented algorithms are compared with existing methods on a standard set of bench-marks and on new sets of large-sized instances. The results illustrate the strengths of our algorithms in terms of solution quality and computational efficiency. Copyright Kluwer Academic Publishers 2004

Suggested Citation

  • Samad Ahmadi & Ibrahim Osman, 2004. "Density Based Problem Space Search for the Capacitated Clustering p-Median Problem," Annals of Operations Research, Springer, vol. 131(1), pages 21-43, October.
    • Handle: RePEc:spr:annopr:v:131:y:2004:i:1:p:21-43:10.1023/b:anor.0000039511.61195.21
    DOI: 10.1023/B:ANOR.0000039511.61195.21
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    Cited by:

    1. 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.
    2. Juan A. Díaz & Dolores E. Luna, 2017. "Primal and dual bounds for the vertex p-median problem with balance constraints," Annals of Operations Research, Springer, vol. 258(2), pages 613-638, November.
    3. Mai, Feng & Fry, Michael J. & Ohlmann, Jeffrey W., 2018. "Model-based capacitated clustering with posterior regularization," European Journal of Operational Research, Elsevier, vol. 271(2), pages 594-605.
    4. I H Osman & S Ahmadi, 2007. "Guided construction search metaheuristics for the capacitated p-median problem with single source constraint," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(1), pages 100-114, January.

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