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Multiobjective shortest path problems with lexicographic goal-based preferences

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  • Pulido, Francisco Javier
  • Mandow, Lawrence
  • Pérez de la Cruz, José Luis

Abstract

Multiobjective shortest path problems are computationally harder than single objective ones. In particular, execution time is an important limiting factor in exact multiobjective search algorithms. This paper explores the possibility of improving search performance in those cases where the interesting portion of the Pareto front can be initially bounded. We introduce a new exact label-setting algorithm that returns the subset of Pareto optimal paths that satisfy a set of lexicographic goals, or the subset that minimizes deviation from goals if these cannot be fully satisfied. Formal proofs on the correctness of the algorithm are provided. We also show that the algorithm always explores a subset of the labels explored by a full Pareto search. The algorithm is evaluated over a set of problems with three objectives, showing a performance improvement of up to several orders of magnitude as goals become more restrictive.

Suggested Citation

  • Pulido, Francisco Javier & Mandow, Lawrence & Pérez de la Cruz, José Luis, 2014. "Multiobjective shortest path problems with lexicographic goal-based preferences," European Journal of Operational Research, Elsevier, vol. 239(1), pages 89-101.
    • Handle: RePEc:eee:ejores:v:239:y:2014:i:1:p:89-101
    DOI: 10.1016/j.ejor.2014.05.008
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    1. Matthias Müller-Hannemann & Karsten Weihe, 2006. "On the cardinality of the Pareto set in bicriteria shortest path problems," Annals of Operations Research, Springer, vol. 147(1), pages 269-286, October.
    2. Gabrel, Virginie & Vanderpooten, Daniel, 2002. "Enumeration and interactive selection of efficient paths in a multiple criteria graph for scheduling an earth observing satellite," European Journal of Operational Research, Elsevier, vol. 139(3), pages 533-542, June.
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    4. Martins, Ernesto Queiros Vieira, 1984. "On a multicriteria shortest path problem," European Journal of Operational Research, Elsevier, vol. 16(2), pages 236-245, May.
    5. Machuca, E. & Mandow, L. & Pérez de la Cruz, J.L. & Ruiz-Sepulveda, A., 2012. "A comparison of heuristic best-first algorithms for bicriterion shortest path problems," European Journal of Operational Research, Elsevier, vol. 217(1), pages 44-53.
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