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A hybrid metaheuristic for the minimum labeling spanning tree problem

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  • Silva, Thiago Gouveia da
  • Queiroga, Eduardo
  • Ochi, Luiz Satoru
  • Cabral, Lucídio dos Anjos Formiga
  • Gueye, Serigne
  • Michelon, Philippe

Abstract

An edge-labeled graph (ELG) is a graph in which each edge has a label associated. Given G, an ELG, the minimum labeling spanning tree problem (MLSTP) is an NP-hard problem that consists in finding a spanning tree in G by using a minimum number of labels. The MLSTP has applications in areas such as computer networks, multimodal transportation networks, and data compression. This paper introduces new concepts, presents a revised version of the maximum vertex covering algorithm and provides a tighter bound to its time complexity. Further, a new MIP-based metaheuristic is proposed for solving the MLSTP, the multi-start local branching (MSLB). It combines the efficiency of the proposed constructive heuristics with the capacity of exploration of a new local search method based on MIP. The computational experiments performed show that the MSLB is superior to the current state-of-the-art metaheuristics in respect to quality of the solutions and processing times.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:274:y:2019:i:1:p:22-34
    DOI: 10.1016/j.ejor.2018.09.044
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    References listed on IDEAS

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    1. Andreas M. Chwatal & Günther R. Raidl, 2011. "Solving the Minimum Label Spanning Tree Problem by Mathematical Programming Techniques," Advances in Operations Research, Hindawi, vol. 2011, pages 1-38, June.
    2. Sergio Consoli & Kenneth Darby-Dowman & Nenad Mladenović & José Moreno-Pérez, 2009. "Variable neighbourhood search for the minimum labelling Steiner tree problem," Annals of Operations Research, Springer, vol. 172(1), pages 71-96, November.
    3. 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.
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