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An algorithm for approximating the Pareto set of the multiobjective set covering problem

Author

Listed:
  • Lakmali Weerasena

    (Clemson University)

  • Margaret M. Wiecek

    (Clemson University)

  • Banu Soylu

    (Erciyes University)

Abstract

The multiobjective set covering problem (MOSCP), a challenging combinatorial optimization problem, has received limited attention in the literature. This paper presents a heuristic algorithm to approximate the Pareto set of the MOSCP. The proposed algorithm applies a local branching approach on a tree structure and is enhanced with a node exploration strategy specially developed for the MOSCP. The main idea is to partition the search region into smaller subregions based on the neighbors of a reference solution and then to explore each subregion for the Pareto points of the MOSCP. Numerical experiments for instances with two, three and four objectives set covering problems are reported. Results on a performance comparison with benchmark algorithms from the literature are also included and show that the new algorithm is competitive and performs best on some instances.

Suggested Citation

  • Lakmali Weerasena & Margaret M. Wiecek & Banu Soylu, 2017. "An algorithm for approximating the Pareto set of the multiobjective set covering problem," Annals of Operations Research, Springer, vol. 248(1), pages 493-514, January.
    • Handle: RePEc:spr:annopr:v:248:y:2017:i:1:d:10.1007_s10479-016-2229-x
    DOI: 10.1007/s10479-016-2229-x
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    References listed on IDEAS

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    1. Soylu, Banu, 2015. "Heuristic approaches for biobjective mixed 0–1 integer linear programming problems," European Journal of Operational Research, Elsevier, vol. 245(3), pages 690-703.
    2. Andrzej Jaszkiewicz, 2004. "A Comparative Study of Multiple-Objective Metaheuristics on the Bi-Objective Set Covering Problem and the Pareto Memetic Algorithm," Annals of Operations Research, Springer, vol. 131(1), pages 135-158, October.
    3. Florios, Kostas & Mavrotas, George, 2014. "Generation of the exact Pareto set in multi-objective traveling salesman and set covering problems," MPRA Paper 105074, University Library of Munich, Germany.
    4. Mark S. Daskin & Edmund H. Stern, 1981. "A Hierarchical Objective Set Covering Model for Emergency Medical Service Vehicle Deployment," Transportation Science, INFORMS, vol. 15(2), pages 137-152, May.
    5. Christian Prins & Caroline Prodhon & Roberto Calvo, 2006. "Two-phase method and Lagrangian relaxation to solve the Bi-Objective Set Covering Problem," Annals of Operations Research, Springer, vol. 147(1), pages 23-41, October.
    6. Alberto Caprara & Matteo Fischetti & Paolo Toth, 1999. "A Heuristic Method for the Set Covering Problem," Operations Research, INFORMS, vol. 47(5), pages 730-743, October.
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    Cited by:

    1. Lakmali Weerasena, 2022. "Advancing local search approximations for multiobjective combinatorial optimization problems," Journal of Combinatorial Optimization, Springer, vol. 43(3), pages 589-612, April.
    2. Hu, Xiaoxuan & Zhu, Waiming & Ma, Huawei & An, Bo & Zhi, Yanling & Wu, Yi, 2021. "Orientational variable-length strip covering problem: A branch-and-price-based algorithm," European Journal of Operational Research, Elsevier, vol. 289(1), pages 254-269.
    3. Lakmali Weerasena & Aniekan Ebiefung & Anthony Skjellum, 2022. "Design of a heuristic algorithm for the generalized multi-objective set covering problem," Computational Optimization and Applications, Springer, vol. 82(3), pages 717-751, July.

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