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Exploiting Set-Based Structures to Accelerate Dynamic Programming Algorithms for the Elementary Shortest Path Problem with Resource Constraints

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Abstract

In this paper we consider a label-setting dynamic-programming algorithm for the Elementary Shortest Path Problem with Resource Constraints (ESPPRC). We use a pseudo resource to guarantee that labels are permanent. We observe that storing the states based on the subset of nodes visited by the associated path can improve the performance of the algorithm significantly. To this end we use a variant of a prefix tree to store the states and show by computational experiments that the performance of the dynamic programming algorithm is improved significantly when the number of undominated states is large.

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  • Range, Troels Martin, 2013. "Exploiting Set-Based Structures to Accelerate Dynamic Programming Algorithms for the Elementary Shortest Path Problem with Resource Constraints," Discussion Papers on Economics 17/2013, University of Southern Denmark, Department of Economics.
    • Handle: RePEc:hhs:sdueko:2013_017
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    File URL: https://www.sdu.dk/-/media/files/om_sdu/institutter/ivoe/disc_papers/disc_2013/dpbe17_2013.pdf
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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.
    2. Martin Desrochers & Jacques Desrosiers & Marius Solomon, 1992. "A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows," Operations Research, INFORMS, vol. 40(2), pages 342-354, April.
    3. Marius M. Solomon, 1987. "Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints," Operations Research, INFORMS, vol. 35(2), pages 254-265, April.
    4. Stefan Irnich & Daniel Villeneuve, 2006. "The Shortest-Path Problem with Resource Constraints and k -Cycle Elimination for k (ge) 3," INFORMS Journal on Computing, INFORMS, vol. 18(3), pages 391-406, August.
    5. Santos, Luis & Coutinho-Rodrigues, João & Current, John R., 2007. "An improved solution algorithm for the constrained shortest path problem," Transportation Research Part B: Methodological, Elsevier, vol. 41(7), pages 756-771, August.
    6. Stefan Irnich & Guy Desaulniers, 2005. "Shortest Path Problems with Resource Constraints," Springer Books, in: Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), Column Generation, chapter 0, pages 33-65, Springer.
    7. Moshe Dror, 1994. "Note on the Complexity of the Shortest Path Models for Column Generation in VRPTW," Operations Research, INFORMS, vol. 42(5), pages 977-978, October.
    8. Michael Drexl & Stefan Irnich, 2012. "Solving Elementary Shortest-Path Problems as Mixed-Integer Programs," Working Papers 1201, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
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    More about this item

    Keywords

    Elementary shortest path problem; resource constraints; dynamic programming; prefix tree;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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