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A variable neighborhood search algorithm for the multimode set covering problem

Author

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  • Fabio Colombo
  • Roberto Cordone
  • Guglielmo Lulli

Abstract

This paper introduces the multi-mode set covering problem, which consists of a plurality of set covering problems linked by cardinality constraints. We propose a variable neighborhood search algorithm and a greedy randomized adaptive search procedure based on a common local search routine. This routine applies a penalized relaxation of the covering constraints, tuned by self-adapting parameters, and visits a sequence of neighborhoods in a nested strategy. We compare the two heuristics with each other and with a time-limited run of a general-purpose integer linear programming solver, on a benchmark set of instances with heterogeneous structure. Both heuristics outperform the solver, though with interesting differences with respect to the various classes of instances. In particular, the variable neighborhood search algorithm proves more effective and less dependent on the specific features of the instances. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Fabio Colombo & Roberto Cordone & Guglielmo Lulli, 2015. "A variable neighborhood search algorithm for the multimode set covering problem," Journal of Global Optimization, Springer, vol. 63(3), pages 461-480, November.
    • Handle: RePEc:spr:jglopt:v:63:y:2015:i:3:p:461-480
    DOI: 10.1007/s10898-013-0094-6
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    References listed on IDEAS

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    1. Lan, Guanghui & DePuy, Gail W. & Whitehouse, Gary E., 2007. "An effective and simple heuristic for the set covering problem," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1387-1403, February.
    2. Yagiura, Mutsunori & Kishida, Masahiro & Ibaraki, Toshihide, 2006. "A 3-flip neighborhood local search for the set covering problem," European Journal of Operational Research, Elsevier, vol. 172(2), pages 472-499, July.
    3. Beasley, J. E., 1987. "An algorithm for set covering problem," European Journal of Operational Research, Elsevier, vol. 31(1), pages 85-93, July.
    4. Marcelo Prais & Celso C. Ribeiro, 2000. "Reactive GRASP: An Application to a Matrix Decomposition Problem in TDMA Traffic Assignment," INFORMS Journal on Computing, INFORMS, vol. 12(3), pages 164-176, August.
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    Cited by:

    1. Lazar Mrkela & Zorica Stanimirović, 2022. "A variable neighborhood search for the budget-constrained maximal covering location problem with customer preference ordering," Operational Research, Springer, vol. 22(5), pages 5913-5951, November.

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