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The planar multiple obnoxious facilities location problem: A Voronoi based heuristic

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  • Drezner, Zvi
  • Kalczynski, Pawel
  • Salhi, Said

Abstract

Consider a situation where a given number of facilities must be located in a convex polygon with the objective of maximizing the minimum distance between facilities and a given set of communities subject to the facilities being farther than a certain distance from one another. This continuous multiple obnoxious facility location problem is very difficult to solve by commercial nonlinear optimizers. We propose a mathematical formulation of two variants of the problem and a heuristic approach based on Voronoi diagrams and a binary linear program. We compare our heuristic with popular state of the art solvers which utilize the multi-start approach: interior point, sparse nonlinear optimizer (SNOPT), GA, IPOPT, and NOMAD running in Matlab. Each problem instance is solved using 100 randomly generated starting solutions, and the best solution is selected. We found that our results are much better and were obtained in a fraction of the time required by other methods. The multiple obnoxious location problem is a perfect example where all-purpose nonlinear non-convex solvers perform poorly and are significantly outperformed by custom designed heuristics.

Suggested Citation

  • Drezner, Zvi & Kalczynski, Pawel & Salhi, Said, 2019. "The planar multiple obnoxious facilities location problem: A Voronoi based heuristic," Omega, Elsevier, vol. 87(C), pages 105-116.
    • Handle: RePEc:eee:jomega:v:87:y:2019:i:c:p:105-116
    DOI: 10.1016/j.omega.2018.08.013
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    References listed on IDEAS

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    1. Colmenar, J. Manuel & Greistorfer, Peter & Martí, Rafael & Duarte, Abraham, 2016. "Advanced Greedy Randomized Adaptive Search Procedure for the Obnoxious p-Median problem," European Journal of Operational Research, Elsevier, vol. 252(2), pages 432-442.
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    Cited by:

    1. Pawel Kalczynski & Atsuo Suzuki & Zvi Drezner, 2023. "Obnoxious facility location in multiple dimensional space," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 331-354, July.
    2. Tammy Drezner & Zvi Drezner & Pawel Kalczynski, 2020. "Gradual cover competitive facility location," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(2), pages 333-354, June.
    3. Marilène Cherkesly & Claudio Contardo, 2021. "The conditional p-dispersion problem," Journal of Global Optimization, Springer, vol. 81(1), pages 23-83, September.
    4. Eliş, Haluk & Tansel, Barbaros & Oğuz, Osman & Güney, Mesut & Kian, Ramez, 2021. "On guarding real terrains: The terrain guarding and the blocking path problems," Omega, Elsevier, vol. 102(C).
    5. Pelegrín, Mercedes & Xu, Liding, 2023. "Continuous covering on networks: Improved mixed integer programming formulations," Omega, Elsevier, vol. 117(C).
    6. Kalczynski, Pawel & Drezner, Zvi, 2022. "The Obnoxious Facilities Planar p-Median Problem with Variable Sizes," Omega, Elsevier, vol. 111(C).
    7. Blanco, Víctor & Gázquez, Ricardo & Saldanha-da-Gama, Francisco, 2023. "Multi-type maximal covering location problems: Hybridizing discrete and continuous problems," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1040-1054.
    8. Kayhan Alamatsaz & S. M. T. Fatemi Ghomi & Mehdi Iranpoor, 2021. "Minimal covering unrestricted location of obnoxious facilities: bi-objective formulation and a case study," OPSEARCH, Springer;Operational Research Society of India, vol. 58(2), pages 351-373, June.
    9. 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.

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