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Variable neighbourhood search for the minimum labelling Steiner tree problem

Author

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  • Sergio Consoli
  • Kenneth Darby-Dowman
  • Nenad Mladenović
  • José Moreno-Pérez

Abstract

We present a study on heuristic solution approaches to the minimum labelling Steiner tree problem, an NP-hard graph problem related to the minimum labelling spanning tree problem. Given an undirected labelled connected graph, the aim is to find a spanning tree covering a given subset of nodes of the graph, whose edges have the smallest number of distinct labels. Such a model may be used to represent many real world problems in telecommunications and multimodal transportation networks. Several metaheuristics are proposed and evaluated. The approaches are compared to the widely adopted Pilot Method and it is shown that the Variable Neighbourhood Search that we propose is the most effective metaheuristic for the problem, obtaining high quality solutions in short computational running times. Copyright Springer Science+Business Media, LLC 2009

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:172:y:2009:i:1:p:71-96:10.1007/s10479-008-0507-y
    DOI: 10.1007/s10479-008-0507-y
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    Citations

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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. Ghoshal, Sudishna & Sundar, Shyam, 2020. "Two heuristics for the rainbow spanning forest problem," European Journal of Operational Research, Elsevier, vol. 285(3), pages 853-864.
    5. 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.
    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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