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Greedy Randomized Adaptive Search and Variable Neighbourhood Search for the minimum labelling spanning tree problem

Author

Listed:
  • Consoli, S.
  • Darby-Dowman, K.
  • Mladenovic, N.
  • Moreno Pérez, J.A.

Abstract

This paper studies heuristics for the minimum labelling spanning tree (MLST) problem. The purpose is to find a spanning tree using edges that are as similar as possible. Given an undirected labelled connected graph, the minimum labelling spanning tree problem seeks a spanning tree whose edges have the smallest number of distinct labels. This problem has been shown to be NP-hard. A Greedy Randomized Adaptive Search Procedure (GRASP) and a Variable Neighbourhood Search (VNS) are proposed in this paper. They are compared with other algorithms recommended in the literature: the Modified Genetic Algorithm and the Pilot Method. Nonparametric statistical tests show that the heuristics based on GRASP and VNS outperform the other algorithms tested. Furthermore, a comparison with the results provided by an exact approach shows that we may quickly obtain optimal or near-optimal solutions with the proposed heuristics.

Suggested Citation

  • Consoli, S. & Darby-Dowman, K. & Mladenovic, N. & Moreno Pérez, J.A., 2009. "Greedy Randomized Adaptive Search and Variable Neighbourhood Search for the minimum labelling spanning tree problem," European Journal of Operational Research, Elsevier, vol. 196(2), pages 440-449, July.
    • Handle: RePEc:eee:ejores:v:196:y:2009:i:2:p:440-449
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    References listed on IDEAS

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    1. Hansen, Pierre & Mladenovic, Nenad, 2001. "Variable neighborhood search: Principles and applications," European Journal of Operational Research, Elsevier, vol. 130(3), pages 449-467, May.
    2. Stefan Voßs & Andreas Fink & Cees Duin, 2005. "Looking Ahead with the Pilot Method," Annals of Operations Research, Springer, vol. 136(1), pages 285-302, April.
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    Cited by:

    1. Zhaowei Miao & Feng Yang & Ke Fu & Dongsheng Xu, 2012. "Transshipment service through crossdocks with both soft and hard time windows," Annals of Operations Research, Springer, vol. 192(1), pages 21-47, January.
    2. Thiago Gouveia da Silva & Serigne Gueye & Philippe Michelon & Luiz Satoru Ochi & Lucídio dos Anjos Formiga Cabral, 2019. "A polyhedral approach to the generalized minimum labeling spanning tree problem," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 7(1), pages 47-77, March.
    3. Silva, Thiago Gouveia da & Queiroga, Eduardo & Ochi, Luiz Satoru & Cabral, Lucídio dos Anjos Formiga & Gueye, Serigne & Michelon, Philippe, 2019. "A hybrid metaheuristic for the minimum labeling spanning tree problem," European Journal of Operational Research, Elsevier, vol. 274(1), pages 22-34.
    4. Clímaco, João C.N. & Eugénia Captivo, M. & Pascoal, Marta M.B., 2010. "On the bicriterion - minimal cost/minimal label - spanning tree problem," European Journal of Operational Research, Elsevier, vol. 204(2), pages 199-205, July.
    5. Raffaele Cerulli & Ciriaco D'Ambrosio & Domenico Serra & Carmine Sorgente, 2024. "The Budgeted Labeled Minimum Spanning Tree Problem," Mathematics, MDPI, vol. 12(2), pages 1-22, January.
    6. Pierre Hansen & Nenad Mladenović & José Moreno Pérez, 2010. "Variable neighbourhood search: methods and applications," Annals of Operations Research, Springer, vol. 175(1), pages 367-407, March.

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