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Tabu search and GRASP for the capacitated clustering problem

Author

Listed:
  • Anna Martínez-Gavara
  • Vicente Campos
  • Micael Gallego
  • Manuel Laguna
  • Rafael Martí

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. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Anna Martínez-Gavara & Vicente Campos & Micael Gallego & Manuel Laguna & Rafael Martí, 2015. "Tabu search and GRASP for the capacitated clustering problem," Computational Optimization and Applications, Springer, vol. 62(2), pages 589-607, November.
    • Handle: RePEc:spr:coopap:v:62:y:2015:i:2:p:589-607
    DOI: 10.1007/s10589-015-9749-1
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    References listed on IDEAS

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    1. Micael Gallego & Abraham Duarte & Manuel Laguna & Rafael Martí, 2009. "Hybrid heuristics for the maximum diversity problem," Computational Optimization and Applications, Springer, vol. 44(3), pages 411-426, December.
    2. Z P Fan & Y Chen & J Ma & S Zeng, 2011. "A hybrid genetic algorithmic approach to the maximally diverse grouping problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(1), pages 92-99, January.
    3. Thomas Feo & Olivier Goldschmidt & Mallek Khellaf, 1992. "One-Half Approximation Algorithms for the k-Partition Problem," Operations Research, INFORMS, vol. 40(1-supplem), pages 170-173, February.
    4. Celso C. Ribeiro & Eduardo Uchoa & Renato F. Werneck, 2002. "A Hybrid GRASP with Perturbations for the Steiner Problem in Graphs," INFORMS Journal on Computing, INFORMS, vol. 14(3), pages 228-246, August.
    5. Z P Fan & Y Chen & J Ma & S Zeng, 2011. "Erratum: A hybrid genetic algorithmic approach to the maximally diverse grouping problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(7), pages 1423-1430, July.
    6. M Gallego & M Laguna & R Martí & A Duarte, 2013. "Tabu search with strategic oscillation for the maximally diverse grouping problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 64(5), pages 724-734, May.
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    Cited by:

    1. Zheng Wang & Wei Xu & Xiangpei Hu & Yong Wang, 2022. "Inventory allocation to robotic mobile-rack and picker-to-part warehouses at minimum order-splitting and replenishment costs," Annals of Operations Research, Springer, vol. 316(1), pages 467-491, September.
    2. Zhou, Qing & Benlic, Una & Wu, Qinghua & Hao, Jin-Kao, 2019. "Heuristic search to the capacitated clustering problem," European Journal of Operational Research, Elsevier, vol. 273(2), pages 464-487.
    3. Napoletano, Antonio & Martínez-Gavara, Anna & Festa, Paola & Pastore, Tommaso & Martí, Rafael, 2019. "Heuristics for the Constrained Incremental Graph Drawing Problem," European Journal of Operational Research, Elsevier, vol. 274(2), pages 710-729.
    4. Jack Brimberg & Nenad Mladenović & Raca Todosijević & Dragan Urošević, 2019. "Solving the capacitated clustering problem with variable neighborhood search," Annals of Operations Research, Springer, vol. 272(1), pages 289-321, January.
    5. Marcos J. Negreiros & Nelson Maculan & Pablor L. Batista & João A. Rodrigues & Augusto W. C. Palhano, 2022. "Capacitated clustering problems applied to the layout of IT-teams in software factories," Annals of Operations Research, Springer, vol. 316(2), pages 1157-1185, September.

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