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Shortest path problem with forbidden paths: The elementary version

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  • Di Puglia Pugliese, Luigi
  • Guerriero, Francesca

Abstract

This paper addresses the elementary shortest path problem with forbidden paths. The main aim is to find the shortest paths from a single origin node to every other node of a directed graph, such that the solution does not contain any path belonging to a given set (i.e., the forbidden set). It is imposed that no cycle can be included in the solution. The problem at hand is formulated as a particular instance of the shortest path problem with resource constraints and two different solution approaches are defined and implemented. One is a Branch & Bound based algorithm, the other is a dynamic programming approach. Different versions of the proposed solution strategies are developed and tested on a large set of test problems.

Suggested Citation

  • Di Puglia Pugliese, Luigi & Guerriero, Francesca, 2013. "Shortest path problem with forbidden paths: The elementary version," European Journal of Operational Research, Elsevier, vol. 227(2), pages 254-267.
    • Handle: RePEc:eee:ejores:v:227:y:2013:i:2:p:254-267
    DOI: 10.1016/j.ejor.2012.11.010
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    References listed on IDEAS

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    1. Desrochers, Martin & Soumis, Francois, 1988. "A reoptimization algorithm for the shortest path problem with time windows," European Journal of Operational Research, Elsevier, vol. 35(2), pages 242-254, May.
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    3. Villeneuve, Daniel & Desaulniers, Guy, 2005. "The shortest path problem with forbidden paths," European Journal of Operational Research, Elsevier, vol. 165(1), pages 97-107, August.
    4. de Queiros Vieira Martins, Ernesto, 1984. "An algorithm for ranking paths that may contain cycles," European Journal of Operational Research, Elsevier, vol. 18(1), pages 123-130, October.
    5. Eliécer Gutiérrez & Andrés Medaglia, 2008. "Labeling algorithm for the shortest path problem with turn prohibitions with application to large-scale road networks," Annals of Operations Research, Springer, vol. 157(1), pages 169-182, January.
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    Cited by:

    1. Melchiori, Anna & Sgalambro, Antonino, 2020. "A branch and price algorithm to solve the Quickest Multicommodity k-splittable Flow Problem," European Journal of Operational Research, Elsevier, vol. 282(3), pages 846-857.
    2. Wang, Li & Yang, Lixing & Gao, Ziyou, 2016. "The constrained shortest path problem with stochastic correlated link travel times," European Journal of Operational Research, Elsevier, vol. 255(1), pages 43-57.
    3. Di Puglia Pugliese, Luigi & Ferone, Daniele & Festa, Paola & Guerriero, Francesca, 2020. "Shortest path tour problem with time windows," European Journal of Operational Research, Elsevier, vol. 282(1), pages 334-344.
    4. Shi, Ning & Zhou, Shaorui & Wang, Fan & Tao, Yi & Liu, Liming, 2017. "The multi-criteria constrained shortest path problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 101(C), pages 13-29.
    5. Luigi Di Puglia Pugliese & Francesca Guerriero, 2016. "On the shortest path problem with negative cost cycles," Computational Optimization and Applications, Springer, vol. 63(2), pages 559-583, March.

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