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On the bicriterion - minimal cost/minimal label - spanning tree problem

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  • Clímaco, João C.N.
  • Eugénia Captivo, M.
  • Pascoal, Marta M.B.

Abstract

We address a bicriterion spanning tree problem relevant in some application fields such as telecommunication networks or transportation networks. Each edge is assigned with a cost value and a label (such as a color). The first criterion intends to minimize the total cost of the spanning tree (the summation of its edge costs), while the second intends to get the solution with a minimal number of different labels. Since these criteria, in general, are conflicting criteria we developed an algorithm to generate the set of non-dominated spanning trees. Computational experiments are presented and results discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:204:y:2010:i:2:p:199-205
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    References listed on IDEAS

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    1. Namorado Climaco, Joao Carlos & Queiros Vieira Martins, Ernesto, 1982. "A bicriterion shortest path algorithm," European Journal of Operational Research, Elsevier, vol. 11(4), pages 399-404, December.
    2. 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.
    3. Eugene L. Lawler, 1972. "A Procedure for Computing the K Best Solutions to Discrete Optimization Problems and Its Application to the Shortest Path Problem," Management Science, INFORMS, vol. 18(7), pages 401-405, March.
    4. 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.
    5. Zhou, Gengui & Gen, Mitsuo, 1999. "Genetic algorithm approach on multi-criteria minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 114(1), pages 141-152, April.
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    Cited by:

    1. Andrew Ensor & Felipe Lillo, 2016. "Colored-Edge Graph Approach for the Modeling of Multimodal Transportation Systems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(01), pages 1-21, February.
    2. José M. F. Craveirinha & João C. N. Clímaco & Lúcia M. R. A. Martins & Marta M. B. Pascoal, 2016. "An exact method for constructing minimal cost/minimal SRLG spanning trees over optical networks," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 62(2), pages 327-346, June.

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