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Solving the maximum min-sum dispersion by alternating formulations of two different problems

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  • Amirgaliyeva, Zhazira
  • Mladenović, Nenad
  • Todosijević, Raca
  • Urošević, Dragan

Abstract

The maximum min-sum dispersion problem aims to maximize the minimum accumulative dispersion among the chosen elements. It is known to be strongly NP-hard problem. In this paper we present heuristic where the objective functions of two different problems are shifted within variable neighborhood search framework. Though this heuristic can be seen as an extended variant of variable formulation search approach that takes into account alternative formulations of one problem, the important difference is that it allows using alternative formulations of more than one optimization problem. Here we use one alternative formulation that is of max-sum type of the originally max–min type maximum diversity problem. Computational experiments on the benchmark instances used in the literature show that the suggested approach improves the best known results for most instances in a shorter computing time.

Suggested Citation

  • Amirgaliyeva, Zhazira & Mladenović, Nenad & Todosijević, Raca & Urošević, Dragan, 2017. "Solving the maximum min-sum dispersion by alternating formulations of two different problems," European Journal of Operational Research, Elsevier, vol. 260(2), pages 444-459.
    • Handle: RePEc:eee:ejores:v:260:y:2017:i:2:p:444-459
    DOI: 10.1016/j.ejor.2016.12.039
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    References listed on IDEAS

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    2. Prokopyev, Oleg A. & Kong, Nan & Martinez-Torres, Dayna L., 2009. "The equitable dispersion problem," European Journal of Operational Research, Elsevier, vol. 197(1), pages 59-67, August.
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    Cited by:

    1. Jiawei Song & Yang Wang & Haibo Wang & Qinghua Wu & Abraham P. Punnen, 2019. "An effective multi-wave algorithm for solving the max-mean dispersion problem," Journal of Heuristics, Springer, vol. 25(4), pages 731-752, October.
    2. Alessandro Hill & Eduardo Lalla-Ruiz & Stefan Voß & Marcos Goycoolea, 2019. "A multi-mode resource-constrained project scheduling reformulation for the waterway ship scheduling problem," Journal of Scheduling, Springer, vol. 22(2), pages 173-182, April.
    3. Martí, Rafael & Martínez-Gavara, Anna & Pérez-Peló, Sergio & Sánchez-Oro, Jesús, 2022. "A review on discrete diversity and dispersion maximization from an OR perspective," European Journal of Operational Research, Elsevier, vol. 299(3), pages 795-813.
    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. Sergey Kovalev & Isabelle Chalamon & Fabio J. Petani, 2023. "Maximizing single attribute diversity in group selection," Annals of Operations Research, Springer, vol. 320(1), pages 535-540, January.
    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.

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