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Optimality conditions in preference-based spanning tree problems

Author

Listed:
  • Alonso, Sergio
  • Domínguez-Ríos, Miguel Ángel
  • Colebrook, Marcos
  • Sedeo-Noda, Antonio

Abstract

Spanning tree problems defined in a preference-based environment are addressed. In this approach, optimality conditions for the minimum-weight spanning tree problem (MST) are generalized for use with other, more general preference orders. The main goal of this paper is to determine which properties of the preference relations are sufficient to assure that the set of 'most-preferred' trees is the set of spanning trees verifying the optimality conditions. Finally, algorithms for the construction of the set of spanning trees fulfilling the optimality conditions are designed, improving the methods in previous papers.

Suggested Citation

  • Alonso, Sergio & Domínguez-Ríos, Miguel Ángel & Colebrook, Marcos & Sedeo-Noda, Antonio, 2009. "Optimality conditions in preference-based spanning tree problems," European Journal of Operational Research, Elsevier, vol. 198(1), pages 232-240, October.
    • Handle: RePEc:eee:ejores:v:198:y:2009:i:1:p:232-240
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    References listed on IDEAS

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    1. Perny, Patrice & Spanjaard, Olivier, 2005. "A preference-based approach to spanning trees and shortest paths problems***," European Journal of Operational Research, Elsevier, vol. 162(3), pages 584-601, May.
    2. Ramos, R. M. & Alonso, S. & Sicilia, J. & Gonzalez, C., 1998. "The problem of the optimal biobjective spanning tree," European Journal of Operational Research, Elsevier, vol. 111(3), pages 617-628, December.
    3. Knowles, Joshua D. & Corne, David W., 2002. "Enumeration of Pareto optimal multi-criteria spanning trees - a proof of the incorrectness of Zhou and Gen's proposed algorithm," European Journal of Operational Research, Elsevier, vol. 143(3), pages 543-547, December.
    4. Colebrook, Marcos & Sicilia, Joaquin, 2007. "A polynomial algorithm for the multicriteria cent-dian location problem," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1008-1024, June.
    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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