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A variable neighborhood search algorithm for the multimode set covering problem

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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.

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Notes

  1. The density or coverage degree of a subset is the number (%) of elements of the ground set included in the subset, i.e., the number (%) of rows covered by the column.

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Authors and Affiliations

  1. Department of Computer Science, University of Milano, Via Comelico 39, 20135 , Milan, Italy

    Fabio Colombo & Roberto Cordone

  2. Department of Informatics, Systems and Communication, University of Milano “Bicocca”, Viale Sarca 336, 20122 , Milan, Italy

    Guglielmo Lulli

Authors
  1. Fabio Colombo
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  2. Roberto Cordone
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  3. Guglielmo Lulli
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Corresponding author

Correspondence to Roberto Cordone.

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Colombo, F., Cordone, R. & Lulli, G. A variable neighborhood search algorithm for the multimode set covering problem. J Glob Optim 63, 461–480 (2015). https://doi.org/10.1007/s10898-013-0094-6

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  • DOI: https://doi.org/10.1007/s10898-013-0094-6

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