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A multi-objective parallel variable neighborhood search for the bi-objective obnoxious p-median problem

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Abstract

Researchers and practitioners have addressed many variants of facility locations problems. Each location problem can be substantially different from each other depending on the objectives and/or constraints considered. In this paper, the bi-objective obnoxious p-median problem (Bi-OpM) is addressed given the huge interest to locate facilities such as waste or hazardous disposal facilities, nuclear power or chemical plants and noisy or polluting services, among others. The Bi-OpM aims to locate p facilities maximizing two different objectives: the distance between each customer and their nearest facility center and the dispersion among facilities. To address the Bi-OpM problem a Multi-objective Parallel Variable Neighborhood Search approach (Mo-PVNS) is implemented. Computational results indicate the superiority of the Mo-PVNS compared to the state-of-art algorithms.

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Acknowledgements

Ana D. López-Sánchez acknowledges support from the Spanish Ministerio de Economía, Industria y Competitividad through Grant Number ECO2016-76567-C4-1-R. Jesús Sánchez-Oro and J. Manuel Colmenar acknowledge support from the Spanish Ministerio de Ciencia, Innovación y Universidades (MCIU / AEI / FEDER, UE) under Grant Ref. PGC2018-095322-B-C22, and Comunidad de Madrid y Fondos Estructurales de la Unión Europea with Grant Ref. P2018/TCS-4566.

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Authors and Affiliations

  1. Rey Juan Carlos University, C/ Tulipán s/n. 28933 Móstoles, Madrid, Spain

    Jesús Sánchez-Oro & J. Manuel Colmenar

  2. Pablo de Olavide University, Ctra. Utrera Km 1. 41013, Seville, Spain

    Ana D. López-Sánchez

Authors
  1. Jesús Sánchez-Oro
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  2. Ana D. López-Sánchez
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  3. J. Manuel Colmenar
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Correspondence to J. Manuel Colmenar.

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Appendix

Appendix

In this section we provide a breakdown of results for each algorithm and instance on all the metrics we have shown in the paper (See Tables 9, 10, 11, 12, 13, 14, 15).

Table 9 Number of efficient solutions obtained for each algorithm on each instance
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Table 10 Hypervolume value of the final set of non-dominated solutions for each algorithm on each instance
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Table 11 Coverage measure of the final set of non-dominated solutions for each algorithm on each instance
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Table 12 \(\epsilon \) indicator of the final set of non-dominated solutions for each algorithm on each instance
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Table 13 Generational Distance of the final set of non-dominated solutions for each algorithm on each instance
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Table 14 \(\varDelta \) Generalized Spread of the final set of non-dominated solutions for each algorithm on each instance
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Table 15 Execution time (in sec) of the final set of non-dominated solutions for each algorithm on each instance
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Sánchez-Oro, J., López-Sánchez, A.D. & Colmenar, J.M. A multi-objective parallel variable neighborhood search for the bi-objective obnoxious p-median problem. Optim Lett 16, 301–331 (2022). https://doi.org/10.1007/s11590-020-01690-0

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