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Tabu search and GRASP for the capacitated clustering problem

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Abstract

The capacitated clustering problem (CCP) consists of forming a specified number of clusters or groups from a set of elements in such a way that the sum of the weights of the elements in each cluster is within some capacity limits, and the sum of the benefits between the pairs of elements in the same cluster is maximized. This problem—which has been recently tackled with a GRASP/VNS approach—arises in the context of facility planners at mail processing and distribution. We propose a tabu search and several GRASP variants to find high quality solutions to this NP-hard problem. These variants are based on several neighborhoods, including a new one, in which we implement a one-for-two swapping strategy. We also hybridize both methodologies to achieve improved outcomes. The maximally diverse grouping problem (MDGP) is a special case of the CCP in which all the elements have a weight of 1 U. This problem has been recently studied in the academic context when forming student groups, and we adapt the best method reported in the literature, a tabu search with strategic oscillation (TS_SO), to the CCP. On the other hand, the handover minimization in mobility networks is a problem equivalent to the CCP in which we minimize the sum of the benefits (costs) of the edges between different clusters. GRASP with Path Relinking has been recently applied to it. Our empirical study with 133 instances shows the superiority of the new GRASP with tabu search for the CCP with respect to these three previous approaches: the GRASP/VNS, the adapted TS_SO, and the GRASP with Path Relinking.

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Acknowledgments

This research has been partially supported by the University of Valencia (UV-INV-PRECOMP13-115334), Ministerio de Educación Cultura y Deporte of Spain (Grant Ref. PRX12/00016), the Ministerio de Economía y Competitividad of Spain (Grant Ref. TIN2012-35632) and the Generalitat Valenciana (Prometeo 2013/049). The authors would like to thank Profs. Morán-Mirabal, González-Velarde, Resende, and Silva for sharing their GRASP with PR code with them.

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Authors and Affiliations

  1. Departamento de Estadística e Investigación Operativa, Universidad de Valencia, Valencia, Spain

    Anna Martínez-Gavara, Vicente Campos & Rafael Martí

  2. Departamento de Ciencias de la Computación, Universidad Rey Juan Carlos, Móstoles, Spain

    Micael Gallego

  3. Leeds School of Business, University of Colorado at Boulder, Boulder, USA

    Manuel Laguna

Authors
  1. Anna Martínez-Gavara
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  2. Vicente Campos
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  3. Micael Gallego
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  4. Manuel Laguna
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  5. Rafael Martí
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Correspondence to Rafael Martí.

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Martínez-Gavara, A., Campos, V., Gallego, M. et al. Tabu search and GRASP for the capacitated clustering problem. Comput Optim Appl 62, 589–607 (2015). https://doi.org/10.1007/s10589-015-9749-1

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