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On heuristic bi-criterion methods for semi-obnoxious facility location

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Abstract

Locating a semi-obnoxious facility, like an airport or correctional center is typically a bi-criterion problem combining a convex objective function representing minimum transportation cost with a multi-extremal objective function representing the non-desirable part of the facility. Generic one or bi-objective heuristic methods can be applied to generate efficient locations for the problem. We consider the location of one facility in the plane and show that a simple random or grid search with filtering already provides a very good picture of the trade-off between the two objectives. Moreover, we argue that instead of using bi-criterion meta-heuristics, one could better exploit the convex–nonconvex structure of the problem applying the constraint method. We show how to evaluate the methods systematically using several heuristics from literature.

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Acknowledgments

This work has been funded by Grants from the Spanish Ministry (TIN2012-37483), Junta de Andalucía (P10-TIC-6002, P11-TIC-7176 and P12-TIC-301), in part financed by the European Regional Development Fund (ERDF) and Fundación Séneca 15254/PI/10, the Agency of Science and Technology of the Region of Murcia. Juana López Redondo is a fellow of the Spanish “Ramón y Cajal” contract program, co-financed by the European Social Fund.

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Authors and Affiliations

  1. Department of Informatics, University of Almería, Almería, Spain

    P. M. Ortigosa & J. L. Redondo

  2. Computer Architecture, Universidad de Málaga and Operations Research and Logistics, Wageningen University, Wageningen, The Netherlands

    E. M. T. Hendrix

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  1. P. M. Ortigosa
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  2. E. M. T. Hendrix
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  3. J. L. Redondo
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Correspondence to E. M. T. Hendrix.

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Ortigosa, P.M., Hendrix, E.M.T. & Redondo, J.L. On heuristic bi-criterion methods for semi-obnoxious facility location. Comput Optim Appl 61, 205–217 (2015). https://doi.org/10.1007/s10589-014-9709-1

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