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Reactive VNS algorithm for the maximum k-subset intersection problem

Author

Listed:
  • Fabio C. S. Dias

    (Federal University of Ceará)

  • Wladimir Araújo Tavares

    (Federal University of Ceará)

  • José Robertty de Freitas Costa

    (Federal University of Ceará)

Abstract

This paper proposes a reactive VNS metaheuristic for the maximum intersection of k-subsets problem (kMIS). The kMIS is defined as: Given a set of elements, a subset family of the first set and an integer k. The problem consists of finding k subset so that the intersection is maximum. Our VNS metaheuristic incorporates strategies used in GRASP metaheuristics, such as the GRASP construction phase and the Reactive GRASP. Both were used in the shaking phase as a reactive components to VNS. We also propose what we call teh Dynamic Step, a new way to increase the VNS neighborhood. All of these strategies, as well as the Skewed VNS, were added to our Reactive VNS algorithm for kMIS. Computational results showed that the new algorithm outperforms the state-of-the-art algorithm.

Suggested Citation

  • Fabio C. S. Dias & Wladimir Araújo Tavares & José Robertty de Freitas Costa, 2020. "Reactive VNS algorithm for the maximum k-subset intersection problem," Journal of Heuristics, Springer, vol. 26(6), pages 913-941, December.
    • Handle: RePEc:spr:joheur:v:26:y:2020:i:6:d:10.1007_s10732-020-09452-y
    DOI: 10.1007/s10732-020-09452-y
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    References listed on IDEAS

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    Cited by:

    1. Alejandra Casado & Sergio Pérez-Peló & Jesús Sánchez-Oro & Abraham Duarte, 2022. "A GRASP algorithm with Tabu Search improvement for solving the maximum intersection of k-subsets problem," Journal of Heuristics, Springer, vol. 28(1), pages 121-146, February.

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