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Variable and large neighborhood search to solve the multiobjective set covering problem

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Abstract

In this paper, we study the multiobjective version of the set covering problem. To our knowledge, this problem has only been addressed in two papers before, and with two objectives and heuristic methods. We propose a new heuristic, based on the two-phase Pareto local search, with the aim of generating a good approximation of the Pareto efficient solutions. In the first phase of this method, the supported efficient solutions or a good approximation of these solutions is generated. Then, a neighborhood embedded in the Pareto local search is applied to generate non-supported efficient solutions. In order to get high quality results, two elaborate local search techniques are considered: a large neighborhood search and a variable neighborhood search. We intensively study the parameters of these two techniques. We compare our results with state-of-the-art results and we show that with our method, better results are obtained for different indicators.

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Notes

  1. A MOCO problem is intractable if the number of non-dominated points is exponential in the size of the instance.

  2. However, the authors claim that they generate all the supported efficient solutions, even if they use a heuristic to solve the linear weighted sum problems.

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Authors and Affiliations

  1. LIP6, Université Pierre et Marie Curie, 4, Place Jussieu, 75252 , Paris Cedex 05, France

    T. Lust

  2. Laboratory of Mathematics and Operational Research, Faculté Polytechnique de Mons, University of Mons, 20, Place du Parc, 7000 , Mons, Belgium

    D. Tuyttens

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  1. T. Lust
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  2. D. Tuyttens
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Lust, T., Tuyttens, D. Variable and large neighborhood search to solve the multiobjective set covering problem. J Heuristics 20, 165–188 (2014). https://doi.org/10.1007/s10732-013-9236-8

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