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Extremely non-convex optimization problems: the case of the multiple obnoxious facilities location

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Abstract

The multiple obnoxious facilities location problem is an extremely non-convex optimization problem with millions of local optima. It is a very challenging problem. We improved the best known solution for 33 out of 76 test instances. We believe that the results of many instances reported here are still not optimal and thus better objective function values exist. We challenge the optimization community to design procedures that will further improve some of the results reported here. Optimality can be proven for a small number of new facilities. Proving optimality for a large number of facilities would be an achievement.

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Authors and Affiliations

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

    Pawel Kalczynski & Zvi Drezner

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  1. Pawel Kalczynski
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  2. Zvi Drezner
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Correspondence to Zvi Drezner.

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Kalczynski, P., Drezner, Z. Extremely non-convex optimization problems: the case of the multiple obnoxious facilities location. Optim Lett 16, 1153–1166 (2022). https://doi.org/10.1007/s11590-021-01731-2

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