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Basic variable neighborhood search for the minimum sitting arrangement problem

Author

Listed:
  • Eduardo G. Pardo

    (Universidad Rey Juan Carlos)

  • Antonio García-Sánchez

    (Universidad Politécnica de Madrid)

  • Marc Sevaux

    (Universitè de Bretagne-Sud)

  • Abraham Duarte

    (Universidad Rey Juan Carlos)

Abstract

The minimum sitting arrangement (MinSA) problem is a linear layout problem consisting in minimizing the number of errors produced when a signed graph is embedded into a line. This problem has been previously tackled by theoretical and heuristic approaches in the literature. In this paper we present a basic variable neighborhood search (BVNS) algorithm for solving the problem. First, we introduce a novel constructive scheme based on the identification of cliques from the input graph, when only the positive edges are considered. The solutions obtained by the constructive procedure are then used as a starting point for the proposed BVNS algorithm. Efficient implementations of the several configurations of the local search procedure within the BVNS are described. The algorithmic proposal is then compared with previous approaches in the state of the art for the MinSA over different sets of referred instances. The obtained results supported by non-parametric statistical tests, indicate that BVNS can be considered as the new state-of-the-art algorithm for the MinSA.

Suggested Citation

  • Eduardo G. Pardo & Antonio García-Sánchez & Marc Sevaux & Abraham Duarte, 2020. "Basic variable neighborhood search for the minimum sitting arrangement problem," Journal of Heuristics, Springer, vol. 26(2), pages 249-268, April.
    • Handle: RePEc:spr:joheur:v:26:y:2020:i:2:d:10.1007_s10732-019-09432-x
    DOI: 10.1007/s10732-019-09432-x
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    References listed on IDEAS

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    1. Abraham Duarte & Juan Pantrigo & Eduardo Pardo & Nenad Mladenovic, 2015. "Multi-objective variable neighborhood search: an application to combinatorial optimization problems," Journal of Global Optimization, Springer, vol. 63(3), pages 515-536, November.
    2. Pierre Hansen & Nenad Mladenović & Raca Todosijević & Saïd Hanafi, 2017. "Variable neighborhood search: basics and variants," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(3), pages 423-454, September.
    3. Juan Pantrigo & Rafael Martí & Abraham Duarte & Eduardo Pardo, 2012. "Scatter search for the cutwidth minimization problem," Annals of Operations Research, Springer, vol. 199(1), pages 285-304, October.
    4. Eduardo G. Pardo & Mauricio Soto & Christopher Thraves, 2015. "Embedding signed graphs in the line," Journal of Combinatorial Optimization, Springer, vol. 29(2), pages 451-471, February.
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    Cited by:

    1. Cavero, Sergio & Pardo, Eduardo G. & Duarte, Abraham, 2023. "Efficient iterated greedy for the two-dimensional bandwidth minimization problem," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1126-1139.

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