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Incorporating neighborhood reduction for the solution of the planar p-median problem

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  • Zvi Drezner

    (California State University-Fullerton)

  • Said Salhi

    (University of Kent)

Abstract

Two efficient neighborhood reduction schemes are proposed for the solution of the p-median problem on the plane. Their integration into a local search significantly reduces the run time with an insignificant deterioration in the quality of the solution. For completeness this fast local search is also embedded into one of the most powerful metaheuristic algorithms, which is a combination of a genetic algorithm and a new improvement algorithm, recently developed for this continuous location problem. Excellent results for instances with up to 1060 demand points with various values of p are reported. Eight new best known solutions for ten instances of a large problem with 3038 demand points and up to 500 facilities are also found.

Suggested Citation

  • Zvi Drezner & Said Salhi, 2017. "Incorporating neighborhood reduction for the solution of the planar p-median problem," Annals of Operations Research, Springer, vol. 258(2), pages 639-654, November.
    • Handle: RePEc:spr:annopr:v:258:y:2017:i:2:d:10.1007_s10479-015-1961-y
    DOI: 10.1007/s10479-015-1961-y
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    References listed on IDEAS

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    Cited by:

    1. Pawel Kalczynski & Jack Brimberg & Zvi Drezner, 2022. "Less is more: discrete starting solutions in the planar p-median problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 34-59, April.
    2. Kalczynski, Pawel & Drezner, Zvi, 2022. "The Obnoxious Facilities Planar p-Median Problem with Variable Sizes," Omega, Elsevier, vol. 111(C).
    3. Zvi Drezner & Taly Dawn Drezner, 2020. "Biologically Inspired Parent Selection in Genetic Algorithms," Annals of Operations Research, Springer, vol. 287(1), pages 161-183, April.
    4. Richard L. Church & Zvi Drezner & Pawel Kalczynski, 2023. "Extensions to the planar p-median problem," Annals of Operations Research, Springer, vol. 326(1), pages 115-135, July.
    5. Sven Jäger & Anita Schöbel, 2020. "The blockwise coordinate descent method for integer programs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(2), pages 357-381, April.

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