IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v254y2016i3p780-800.html
   My bibliography  Save this article

Iterated maxima search for the maximally diverse grouping problem

Author

Listed:
  • Lai, Xiangjing
  • Hao, Jin-Kao

Abstract

The maximally diverse grouping problem (MDGP) is to partition the vertices of an edge-weighted and undirected complete graph into m groups such that the total weight of the groups is maximized subject to some group size constraints. MDGP is a NP-hard combinatorial problem with a number of relevant applications. In this paper, we present an innovative heuristic algorithm called iterated maxima search (IMS) algorithm for solving MDGP. The proposed approach employs a maxima search procedure that integrates organically an efficient local optimization method and a weak perturbation operator to reinforce the intensification of the search and a strong perturbation operator to diversify the search. Extensive experiments on five sets of 500 MDGP benchmark instances of the literature show that IMS competes favorably with the state-of-the-art algorithms. We provide additional experiments to shed light on the rationality of the proposed algorithm and investigate the role of the key ingredients.

Suggested Citation

  • Lai, Xiangjing & Hao, Jin-Kao, 2016. "Iterated maxima search for the maximally diverse grouping problem," European Journal of Operational Research, Elsevier, vol. 254(3), pages 780-800.
    • Handle: RePEc:eee:ejores:v:254:y:2016:i:3:p:780-800
    DOI: 10.1016/j.ejor.2016.05.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221716303381
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2016.05.018?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. Johnes, Jill, 2015. "Operational Research in education," European Journal of Operational Research, Elsevier, vol. 243(3), pages 683-696.
    2. Duarte, Abraham & Marti, Rafael, 2007. "Tabu search and GRASP for the maximum diversity problem," European Journal of Operational Research, Elsevier, vol. 178(1), pages 71-84, April.
    3. Gintaras Palubeckis & Armantas Ostreika & Dalius Rubliauskas, 2015. "Maximally diverse grouping: an iterated tabu search approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(4), pages 579-592, April.
    4. Krass, Dmitry & Ovchinnikov, Anton, 2010. "Constrained group balancing: Why does it work," European Journal of Operational Research, Elsevier, vol. 206(1), pages 144-154, October.
    5. Weitz, R. R. & Lakshminarayanan, S., 1997. "An empirical comparison of heuristic and graph theoretic methods for creating maximally diverse groups, VLSI design, and exam scheduling," Omega, Elsevier, vol. 25(4), pages 473-482, August.
    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.
    7. Bhadury, Joyendu & Mighty, E. Joy & Damar, Hario, 2000. "Maximizing workforce diversity in project teams: a network flow approach," Omega, Elsevier, vol. 28(2), pages 143-153, April.
    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. Arne Schulz, 2023. "The balanced maximally diverse grouping problem with integer attribute values," Journal of Combinatorial Optimization, Springer, vol. 45(5), pages 1-27, July.
    2. Lai, Xiangjing & Hao, Jin-Kao & Fu, Zhang-Hua & Yue, Dong, 2021. "Neighborhood decomposition based variable neighborhood search and tabu search for maximally diverse grouping," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1067-1086.
    3. Arne Schulz, 2024. "Efficient neighborhood evaluation for the maximally diverse grouping problem," Annals of Operations Research, Springer, vol. 341(2), pages 1247-1265, October.
    4. 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.
    5. Schulz, Arne, 2021. "The balanced maximally diverse grouping problem with block constraints," European Journal of Operational Research, Elsevier, vol. 294(1), pages 42-53.
    6. 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.
    7. Huerta-Muñoz, Diana L. & Ríos-Mercado, Roger Z. & Ruiz, Rubén, 2017. "An iterated greedy heuristic for a market segmentation problem with multiple attributes," European Journal of Operational Research, Elsevier, vol. 261(1), pages 75-87.
    8. 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.
    9. Alfonsas Misevičius & Aleksandras Andrejevas & Armantas Ostreika & Dovilė Verenė & Gintarė Žekienė, 2024. "An Improved Hybrid Genetic-Hierarchical Algorithm for the Quadratic Assignment Problem," Mathematics, MDPI, vol. 12(23), pages 1-25, November.
    10. Gliesch, Alex & Ritt, Marcus, 2021. "A hybrid heuristic for the maximum dispersion problem," European Journal of Operational Research, Elsevier, vol. 288(3), pages 721-735.

    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. 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.
    2. 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.
    3. Lai, Xiangjing & Hao, Jin-Kao & Fu, Zhang-Hua & Yue, Dong, 2021. "Neighborhood decomposition based variable neighborhood search and tabu search for maximally diverse grouping," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1067-1086.
    4. Schulz, Arne, 2021. "The balanced maximally diverse grouping problem with block constraints," European Journal of Operational Research, Elsevier, vol. 294(1), pages 42-53.
    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.
    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. Arne Schulz, 2024. "Efficient neighborhood evaluation for the maximally diverse grouping problem," Annals of Operations Research, Springer, vol. 341(2), pages 1247-1265, October.
    8. 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.
    9. Fred Glover & Gary Kochenberger & Weihong Xie & Jianbin Luo, 2019. "Diversification methods for zero-one optimization," Journal of Heuristics, Springer, vol. 25(4), pages 643-671, October.
    10. Saber, Hussein M. & Ghosh, Jay B., 2001. "Assigning students to academic majors," Omega, Elsevier, vol. 29(6), pages 513-523, December.
    11. 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.
    12. Jill Johnes, 2018. "University rankings: What do they really show?," Scientometrics, Springer;Akadémiai Kiadó, vol. 115(1), pages 585-606, April.
    13. 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.
    14. 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.
    15. Rafael Martí & Abraham Duarte & Manuel Laguna, 2009. "Advanced Scatter Search for the Max-Cut Problem," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 26-38, February.
    16. Carla Haelermans & John Ruggiero, 2017. "Non-parametric estimation of the cost of adequacy in education: the case of Dutch schools," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(4), pages 390-398, April.
    17. Giorgia Zotti, 2024. "Regional Differences in Italian School Efficiency: A Conditional DEA Approach," SERIES 05-2024, Dipartimento di Economia e Finanza - Università degli Studi di Bari "Aldo Moro", revised Nov 2024.
    18. Joan Crespo & Jesús Peiró-Palomino & Emili Tortosa-Ausina, 2020. "Does university performance have an economic payoff for their home regions? Evidence for the Spanish provinces," Working Papers 2020/20, Economics Department, Universitat Jaume I, Castellón (Spain).
    19. Giménez, Víctor & Thieme, Claudio & Prior, Diego & Tortosa-Ausina, Emili, 2022. "Evaluation and determinants of preschool effectiveness in Chile," Socio-Economic Planning Sciences, Elsevier, vol. 81(C).
    20. Dmitry Krass & Anton Ovchinnikov, 2006. "The University of Toronto’s Rotman School of Management Uses Management Science to Create MBA Study Groups," Interfaces, INFORMS, vol. 36(2), pages 126-137, April.

    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:eee:ejores:v:254:y:2016:i:3:p:780-800. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.