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A GRASP algorithm with Tabu Search improvement for solving the maximum intersection of k-subsets problem

Author

Listed:
  • Alejandra Casado

    (Universidad Rey Juan Carlos)

  • Sergio Pérez-Peló

    (Universidad Rey Juan Carlos)

  • Jesús Sánchez-Oro

    (Universidad Rey Juan Carlos)

  • Abraham Duarte

    (Universidad Rey Juan Carlos)

Abstract

The selection of individuals with similar characteristics from a given population have always been a matter of interest in several scientific areas: data privacy, genetics, art, among others. This work is focused on the maximum intersection of k-subsets problem (kMIS). This problem tries to find a subset of k individuals with the maximum number of features in common from a given population and a set of relevant features. The research presents a Greedy Randomized Adaptive Search Procedure (GRASP) where the local improvement is replaced by a complete Tabu Search metaheuristic with the aim of further improving the quality of the obtained solutions. Additionally, a novel representation of the solution is considered to reduce the computational effort. The experimental comparison carefully analyzes the contribution of each part of the algorithm to the final results as well as performs a thorough comparison with the state-of-the-art method. Results, supported by non-parametric statistical tests, confirms the superiority of the proposal.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joheur:v:28:y:2022:i:1:d:10.1007_s10732-022-09490-8
    DOI: 10.1007/s10732-022-09490-8
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    References listed on IDEAS

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    1. Thomas A. Feo & Mauricio G. C. Resende & Stuart H. Smith, 1994. "A Greedy Randomized Adaptive Search Procedure for Maximum Independent Set," Operations Research, INFORMS, vol. 42(5), pages 860-878, October.
    2. 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.
    3. Manuel Laguna & Thomas A. Feo & Hal C. Elrod, 1994. "A Greedy Randomized Adaptive Search Procedure for the Two-Partition Problem," Operations Research, INFORMS, vol. 42(4), pages 677-687, August.
    4. Peeters, M.J.P., 2003. "The maximum edge biclique problem is NP-complete," Other publications TiSEM 3e340431-37b3-4bc5-9b14-9, Tilburg University, School of Economics and Management.
    5. Larisa Komosko & Mikhail Batsyn & Pablo San Segundo & Panos M. Pardalos, 2016. "A fast greedy sequential heuristic for the vertex colouring problem based on bitwise operations," Journal of Combinatorial Optimization, Springer, vol. 31(4), pages 1665-1677, May.
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    Cited by:

    1. Casado, A. & Bermudo, S. & López-Sánchez, A.D. & Sánchez-Oro, J., 2023. "An iterated greedy algorithm for finding the minimum dominating set in graphs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 41-58.

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