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Experiments with LAGRASP heuristic for set k-covering

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Abstract

The set k-covering problem (SC k P) is a variant of the classical set covering problem, in which each object is required to be covered at least k times. We describe a hybrid Lagrangean heuristic, named LAGRASP, which combines subgradient optimization and GRASP with path-relinking to solve the SC k P. Computational experiments carried out on 135 test instances show experimentally that by properly tuning the parameters of LAGRASP, it is possible to obtain a good trade-off between solution quality and running times. Furthermore, LAGRASP makes better use of the dual information provided by subgradient optimization and is able to discover better solutions and to escape from locally optimal solutions even after the stabilization of the lower bounds, whereas other strategies fail to find new improving solutions.

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Authors and Affiliations

  1. Department of Informatics and Applied Mathematics, Universidade Federal do Rio Grande do Norte, Campus Universitário, Lagoa Nova, Natal, RN, 59072-970, Brazil

    Luciana S. Pessoa

  2. Algorithms and Optimization Research Department, AT&T Labs Research, 180 Park Avenue, Room C241, Florham Park, NJ, 07932, USA

    Mauricio G. C. Resende

  3. Department of Computer Science, Universidade Federal Fluminense, Rua Passo da Pátria, 156, Niterói, RJ, 24210-240, Brazil

    Celso C. Ribeiro

Authors
  1. Luciana S. Pessoa
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  2. Mauricio G. C. Resende
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  3. Celso C. Ribeiro
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Correspondence to Luciana S. Pessoa.

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Pessoa, L.S., Resende, M.G.C. & Ribeiro, C.C. Experiments with LAGRASP heuristic for set k-covering. Optim Lett 5, 407–419 (2011). https://doi.org/10.1007/s11590-011-0312-4

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  • DOI: https://doi.org/10.1007/s11590-011-0312-4

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