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Multiobjective scatter search for a commercial territory design problem

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Abstract

In this paper, a multiobjective scatter search procedure for a bi-objective territory design problem is proposed. A territory design problem consists of partitioning a set of basic units into larger groups that are suitable with respect to some specific planning criteria. These groups must be compact, connected, and balanced with respect to the number of customers and sales volume. The bi-objective commercial territory design problem belongs to the class of NP-hard problems. Previous work showed that large instances of the problem addressed in this work are practically intractable even for the single-objective version. Therefore, the use of heuristic methods is the best alternative for obtaining approximate efficient solutions for relatively large instances. The proposed scatter search-based framework contains a diversification generation module based on a greedy randomized adaptive search procedure, an improvement module based on a relinked local search strategy, and a combination module based on a solution to an assignment problem.

The proposed metaheuristic is evaluated over a variety of instances taken from literature. This includes a comparison with two of the most successful multiobjective heuristics from literature such as the Scatter Tabu Search Procedure for Multiobjective Optimization (SSPMO) by Molina et al. (INFORMS J. Comput. 19(1):91–100, 2007), and the Non-dominated Sorting Genetic Algorithm (NSGA-II) by Deb et al. (Parallel problem solving from nature – PPSN VI, Lecture notes in computer science, vol. 1917, Springer, Berlin, pp. 849–858, 2000). Experimental work reveals that the proposed procedure consistently outperforms both heuristics, SSPMO and NSGA-II, on all instances tested.

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Acknowledgements

We are very grateful to the reviewers whose comments helped improve the presentation of this work. This work was supported by the Mexican National Council for Science and Technology under grants SEP-CONACYT 48499–Y and SEP-CONACYT 61903, Universidad Autónoma de Nuevo León under its Scientific and Technological Research Support, grant UANL-PAICYT CE012–09, by Tecnológico de Monterrey under research grant CAT128, and by the Spanish Ministerio de Ciencia e Innovación under project TIN2009-07869. The first author gently acknowledges a doctoral fellowship from Universidad Autónoma de Nuevo León, grant NL–2006–C09–32652.

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Authors and Affiliations

  1. CIRRELT, HEC Montréal, Université de Montréal, Montreal, Canada

    M. Angélica Salazar-Aguilar

  2. Graduate Program in Systems Engineering, Universidad Autónoma de Nuevo León, San Nicolás de los Garza, Mexico

    Roger Z. Ríos-Mercado

  3. Center for Quality and Manufacturing, Tecnológico de Monterrey, Monterrey, Mexico

    José L. González-Velarde

  4. Department of Applied Economics, Universidad de Málaga, Malaga, Spain

    Julián Molina

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  1. M. Angélica Salazar-Aguilar
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  2. Roger Z. Ríos-Mercado
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  3. José L. González-Velarde
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  4. Julián Molina
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Correspondence to M. Angélica Salazar-Aguilar.

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Salazar-Aguilar, M.A., Ríos-Mercado, R.Z., González-Velarde, J.L. et al. Multiobjective scatter search for a commercial territory design problem. Ann Oper Res 199, 343–360 (2012). https://doi.org/10.1007/s10479-011-1045-6

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