IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v62y2015i2p589-607.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-015-9749-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10589-015-9749-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    4. 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.
    5. 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.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. 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.
    4. 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.
    5. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Seizinger, Markus & Brunner, Jens O., 2023. "Optimized planning of nursing curricula in dual vocational schools focusing on the German health care system," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1223-1241.
    2. Johnes, Jill, 2015. "Operational Research in education," European Journal of Operational Research, Elsevier, vol. 243(3), pages 683-696.
    3. Yang, Xiao & Cai, Zonghui & Jin, Ting & Tang, Zheng & Gao, Shangce, 2022. "A three-phase search approach with dynamic population size for solving the maximally diverse grouping problem," European Journal of Operational Research, Elsevier, vol. 302(3), pages 925-953.
    4. Arne Schulz, 2022. "A new mixed-integer programming formulation for the maximally diverse grouping problem with attribute values," Annals of Operations Research, Springer, vol. 318(1), pages 501-530, November.
    5. Ríos-Mercado, Roger Z. & Bard, Jonathan F., 2019. "An exact algorithm for designing optimal districts in the collection of waste electric and electronic equipment through an improved reformulation," European Journal of Operational Research, Elsevier, vol. 276(1), pages 259-271.
    6. Kayse Lee Maass & Vera Mann Hey Lo & Anna Weiss & Mark S. Daskin, 2015. "Maximizing Diversity in the Engineering Global Leadership Cultural Families," Interfaces, INFORMS, vol. 45(4), pages 293-304, August.
    7. Jesús Sánchez-Oro & Manuel Laguna & Rafael Martí & Abraham Duarte, 2016. "Scatter search for the bandpass problem," Journal of Global Optimization, Springer, vol. 66(4), pages 769-790, December.
    8. Fernández, Elena & Kalcsics, Jörg & Nickel, Stefan, 2013. "The maximum dispersion problem," Omega, Elsevier, vol. 41(4), pages 721-730.
    9. Chenchen Wu & Dachuan Xu & Donglei Du & Wenqing Xu, 2016. "An approximation algorithm for the balanced Max-3-Uncut problem using complex semidefinite programming rounding," Journal of Combinatorial Optimization, Springer, vol. 32(4), pages 1017-1035, November.
    10. Marti, Rafael, 2006. "Scatter Search--Wellsprings and Challenges," European Journal of Operational Research, Elsevier, vol. 169(2), pages 351-358, March.
    11. Aringhieri, Roberto & Cordone, Roberto & Grosso, Andrea, 2015. "Construction and improvement algorithms for dispersion problems," European Journal of Operational Research, Elsevier, vol. 242(1), pages 21-33.
    12. García-Martínez, C. & Rodriguez, F.J. & Lozano, M., 2014. "Tabu-enhanced iterated greedy algorithm: A case study in the quadratic multiple knapsack problem," European Journal of Operational Research, Elsevier, vol. 232(3), pages 454-463.
    13. Michele Garraffa & Federico Della Croce & Fabio Salassa, 2017. "An exact semidefinite programming approach for the max-mean dispersion problem," Journal of Combinatorial Optimization, Springer, vol. 34(1), pages 71-93, July.
    14. Felix Prause & Kai Hoppmann-Baum & Boris Defourny & Thorsten Koch, 2021. "The maximum diversity assortment selection problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 521-554, June.
    15. R Aringhieri & R Cordone, 2011. "Comparing local search metaheuristics for the maximum diversity problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(2), pages 266-280, February.
    16. Ronconi, Débora P. & Henriques, Luís R.S., 2009. "Some heuristic algorithms for total tardiness minimization in a flowshop with blocking," Omega, Elsevier, vol. 37(2), pages 272-281, April.
    17. Parreño, Francisco & Álvarez-Valdés, Ramón & Martí, Rafael, 2021. "Measuring diversity. A review and an empirical analysis," European Journal of Operational Research, Elsevier, vol. 289(2), pages 515-532.
    18. 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.
    19. Abilio Lucena, 2005. "Non Delayed Relax-and-Cut Algorithms," Annals of Operations Research, Springer, vol. 140(1), pages 375-410, November.
    20. CASTRO, Marco & SÖRENSEN, Kenneth & GOOS, Peter & VANSTEENWEGEN, Pieter, 2014. "The multiple travelling salesperson problem with hotel selection," Working Papers 2014030, University of Antwerp, Faculty of Business and Economics.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:coopap:v:62:y:2015:i:2:p:589-607. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.