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New local searches for solving the multi-source Weber problem

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Abstract

This paper presents three new heuristic approaches for the solution of the multi-source Weber problem in the plane: a constructive heuristic that finds a good starting solution, a decomposition approach which uses Delaunay triangulation, and a new efficient neighborhood structure based on the single facility limited distance median problem. A new heuristic incorporating all these approaches provided high quality solutions in reasonable computing time. We conclude that these heuristics successfully compete with the metaheuristic based methods found in the literature improving ten best known solutions. The ideas here may be extended to a variety of other continuous location as well as data mining problems.

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Notes

  1. The constructive algorithm idea was presented in Brimberg et al. (2012a) and appeared in the proceedings of that conference (Brimberg et al. 2012b).

  2. We thank Pawel Kalczynski, California State University at Fullerton, for solving the problems on Mathematica.

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Acknowledgments

We would like to thank the referees for their time and constructive comments that helped to improve the presentation as well as the content of the paper. This research had been supported in part by a Natural Sciences and Engineering Research Council of Canada Discovery Grant (NSERC #20541-2008). Work of Nenad Mladenovic was conducted at National Research University Higher School of Economics, Russia and supported by RSF Grant 14-41-00039.

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Authors and Affiliations

  1. Steven G. Mihaylo College of Business and Economics, California State University-Fullerton, Fullerton, CA, 92834, USA

    Zvi Drezner

  2. Department of Mathematics and Computer Science, The Royal Military College of Canada, Kingston, ON, Canada

    Jack Brimberg

  3. Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, Serbia

    Nenad Mladenović

  4. Centre for Logistics and Heuristic Optimization, Kent Business School, University of Kent, Canterbury, CT2 7PE, UK

    Said Salhi

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  1. Zvi Drezner
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  4. Said Salhi
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Correspondence to Said Salhi.

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Drezner, Z., Brimberg, J., Mladenović, N. et al. New local searches for solving the multi-source Weber problem. Ann Oper Res 246, 181–203 (2016). https://doi.org/10.1007/s10479-015-1797-5

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