IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v302y2022i3p925-953.html
   My bibliography  Save this article

A three-phase search approach with dynamic population size for solving the maximally diverse grouping problem

Author

Listed:
  • Yang, Xiao
  • Cai, Zonghui
  • Jin, Ting
  • Tang, Zheng
  • Gao, Shangce

Abstract

The maximally diverse grouping problem (MDGP) aims to assign a given set of elements into a number of groups with size restrictions for the sake of maximizing the sum of diversity in these groups. MDGP is an NP-hard combinatorial optimization problem, possessing widespread application and practical importance. This paper introduces a novel hybrid algorithm, called a three-phase search approach with dynamic population size (TPSDP), for solving the problem. The proposed algorithm devises the search process into three phases with distinct functions which are iterated: (1) an undirected perturbation phase to improve the population diversity, (2) a restructure phase using a distinctive crossover operator to increase the information interaction among solutions, and (3) a directed perturbation phase to discover the adjacent local optima around current solutions. TPSDP also combines a dynamic population size strategy to reserve limited computing resources for potential solutions. The results of experiments and the Friedman test show that the overall performance of the proposed TPSDP is highly competitive with or better than previous state-of-the-art MDGP algorithms on 500 instances taken from five popular benchmark sets. Furthermore, an additional experiment of parameter analysis and a discussion of critical ingredients are presented. The source code of TPSDP is provided at https://toyamaailab.github.io/sourcedata.html.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:302:y:2022:i:3:p:925-953
    DOI: 10.1016/j.ejor.2022.02.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221722000881
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2022.02.003?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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. J Desrosiers & N Mladenović & D Villeneuve, 2005. "Design of balanced MBA student teams," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(1), pages 60-66, January.
    9. 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.
    10. 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.
    11. 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, 2024. "Efficient neighborhood evaluation for the maximally diverse grouping problem," Annals of Operations Research, Springer, vol. 341(2), pages 1247-1265, October.

    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. 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.
    2. Arne Schulz, 2024. "Efficient neighborhood evaluation for the maximally diverse grouping problem," Annals of Operations Research, Springer, vol. 341(2), pages 1247-1265, October.
    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. 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.
    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. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Johnes, Jill, 2015. "Operational Research in education," European Journal of Operational Research, Elsevier, vol. 243(3), pages 683-696.
    11. 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.
    12. Saber, Hussein M. & Ghosh, Jay B., 2001. "Assigning students to academic majors," Omega, Elsevier, vol. 29(6), pages 513-523, December.
    13. Fernández, Elena & Kalcsics, Jörg & Nickel, Stefan, 2013. "The maximum dispersion problem," Omega, Elsevier, vol. 41(4), pages 721-730.
    14. 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.
    15. Theresa M. Roeder & Robert M. Saltzman, 2014. "Schedule-Based Group Assignment Using Constraint Programming," INFORMS Transactions on Education, INFORMS, vol. 14(2), pages 63-72, 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. 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).
    18. Gralka, Sabine, 2018. "Stochastic frontier analysis in higher education: A systematic review," CEPIE Working Papers 05/18, Technische Universität Dresden, Center of Public and International Economics (CEPIE).
    19. 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.
    20. Zhiqiang Zhang & Zhongwen Li & Xiaobing Qiao & Weijun Wang, 2019. "An Efficient Memetic Algorithm for the Minimum Load Coloring Problem," Mathematics, MDPI, vol. 7(5), pages 1-20, May.

    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:302:y:2022:i:3:p:925-953. 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.