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Metaheuristics for the linear ordering problem with cumulative costs

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  • Duarte, Abraham
  • Martí, Rafael
  • Álvarez, Ada
  • Ángel-Bello, Francisco

Abstract

The linear ordering problem with cumulative costs (LOPCC) is a variant of the well-known linear ordering problem, in which a cumulative propagation makes the objective function highly non-linear. The LOPCC has been recently introduced in the context of mobile-phone telecommunications. In this paper we propose two metaheuristic methods for this NP-hard problem. The first one is based on the GRASP methodology, while the second one implements an Iterated Greedy-Strategic Oscillation procedure. We also propose a post-processing based on Path Relinking to obtain improved outcomes. We compare our methods with the state-of-the-art procedures on a set of 218 previously reported instances. The comparison favors the Iterated Greedy – Strategic Oscillation with the Path Relinking post-processing, which is able to identify 87 new best objective function values.

Suggested Citation

  • Duarte, Abraham & Martí, Rafael & Álvarez, Ada & Ángel-Bello, Francisco, 2012. "Metaheuristics for the linear ordering problem with cumulative costs," European Journal of Operational Research, Elsevier, vol. 216(2), pages 270-277.
    • Handle: RePEc:eee:ejores:v:216:y:2012:i:2:p:270-277
    DOI: 10.1016/j.ejor.2011.07.036
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    References listed on IDEAS

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    1. Righini, Giovanni, 2008. "A branch-and-bound algorithm for the linear ordering problem with cumulative costs," European Journal of Operational Research, Elsevier, vol. 186(3), pages 965-971, May.
    2. Abraham Duarte & Manuel Laguna & Rafael Martí, 2011. "Tabu search for the linear ordering problem with cumulative costs," Computational Optimization and Applications, Springer, vol. 48(3), pages 697-715, April.
    3. Thomas A. Feo & Mauricio G. C. Resende & Stuart H. Smith, 1994. "A Greedy Randomized Adaptive Search Procedure for Maximum Independent Set," Operations Research, INFORMS, vol. 42(5), pages 860-878, October.
    4. Mauricio G.C. Resende & Celso C. Ribeiro, 2010. "Greedy Randomized Adaptive Search Procedures: Advances, Hybridizations, and Applications," International Series in Operations Research & Management Science, in: Michel Gendreau & Jean-Yves Potvin (ed.), Handbook of Metaheuristics, chapter 0, pages 283-319, Springer.
    5. Ruiz, Ruben & Stutzle, Thomas, 2007. "A simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem," European Journal of Operational Research, Elsevier, vol. 177(3), pages 2033-2049, March.
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    Cited by:

    1. Carlos García-Martínez & Fred Glover & Francisco Rodriguez & Manuel Lozano & Rafael Martí, 2014. "Strategic oscillation for the quadratic multiple knapsack problem," Computational Optimization and Applications, Springer, vol. 58(1), pages 161-185, May.
    2. J. Terán-Villanueva & Héctor Fraire Huacuja & Juan Carpio Valadez & Rodolfo Pazos Rangel & Héctor Puga Soberanes & José Martínez Flores, 2015. "A heterogeneous cellular processing algorithm for minimizing the power consumption in wireless communications systems," Computational Optimization and Applications, Springer, vol. 62(3), pages 787-814, December.
    3. García-Martínez, C. & Rodriguez, F.J. & Lozano, M., 2014. "Tabu-enhanced iterated greedy algorithm: A case study in the quadratic multiple knapsack problem," European Journal of Operational Research, Elsevier, vol. 232(3), pages 454-463.

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