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An improved solution algorithm for the constrained shortest path problem

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  • Santos, Luis
  • Coutinho-Rodrigues, João
  • Current, John R.

Abstract

The shortest path problem is one of the classic network problems. The objective of this problem is to identify the least cost path through a network from a pre-determined starting node to a pre-determined terminus node. It has many practical applications and can be solved optimally via efficient algorithms. Numerous modifications of the problem exist. In general, these are more difficult to solve. One of these modified versions includes an additional constraint that establishes an upper limit on the sum of some other arc cost (e.g., travel time) for the path. In this paper, a new optimal algorithm for this constrained shortest path problem is introduced. Extensive computational tests are presented which compare the algorithm to the two most commonly used algorithms to solve it. The results indicate that the new algorithm can solve optimally very large problem instances and is generally superior to the previous ones in terms of solution time and computer memory requirements. This is particularly true for the problem instances that are most difficult to solve. That is, those on large networks and/or where the additional constraint is most constraining.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:transb:v:41:y:2007:i:7:p:756-771
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    Cited by:

    1. Sedeño-Noda, Antonio & Alonso-Rodríguez, Sergio, 2015. "An enhanced K-SP algorithm with pruning strategies to solve the constrained shortest path problem," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 602-618.
    2. Li, Xiangyong & Lin, Shaochong & Tian, Peng & Aneja, Y.P., 2017. "Models and column generation approach for the resource-constrained minimum cost path problem with relays," Omega, Elsevier, vol. 66(PA), pages 79-90.
    3. Marinakis, Yannis & Migdalas, Athanasios & Sifaleras, Angelo, 2017. "A hybrid Particle Swarm Optimization – Variable Neighborhood Search algorithm for Constrained Shortest Path problems," European Journal of Operational Research, Elsevier, vol. 261(3), pages 819-834.
    4. 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.
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    6. 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.
    7. Qian Ye & Hyun Kim, 2019. "Partial Node Failure in Shortest Path Network Problems," Sustainability, MDPI, vol. 11(22), pages 1-21, November.
    8. Axel Parmentier, 2019. "Algorithms for non-linear and stochastic resource constrained shortest path," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(2), pages 281-317, April.
    9. Luigi Di Puglia Pugliese & Francesca Guerriero, 2013. "A Reference Point Approach for the Resource Constrained Shortest Path Problems," Transportation Science, INFORMS, vol. 47(2), pages 247-265, May.
    10. 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.
    11. Walteros, Jose L. & Vogiatzis, Chrysafis & Pasiliao, Eduardo L. & Pardalos, Panos M., 2014. "Integer programming models for the multidimensional assignment problem with star costs," European Journal of Operational Research, Elsevier, vol. 235(3), pages 553-568.
    12. Lowry, Michael B. & Furth, Peter & Hadden-Loh, Tracy, 2016. "Prioritizing new bicycle facilities to improve low-stress network connectivity," Transportation Research Part A: Policy and Practice, Elsevier, vol. 86(C), pages 124-140.
    13. Santos, Luís & Coutinho-Rodrigues, João & Current, John R., 2010. "An improved ant colony optimization based algorithm for the capacitated arc routing problem," Transportation Research Part B: Methodological, Elsevier, vol. 44(2), pages 246-266, February.
    14. Vedat Bayram & Hande Yaman, 2018. "Shelter Location and Evacuation Route Assignment Under Uncertainty: A Benders Decomposition Approach," Transportation Science, INFORMS, vol. 52(2), pages 416-436, March.
    15. Mark M. Nejad & Lena Mashayekhy & Daniel Grosu & Ratna Babu Chinnam, 2017. "Optimal Routing for Plug-In Hybrid Electric Vehicles," Transportation Science, INFORMS, vol. 51(4), pages 1304-1325, November.
    16. David Corredor-Montenegro & Nicolás Cabrera & Raha Akhavan-Tabatabaei & Andrés L. Medaglia, 2021. "On the shortest $$\alpha$$ α -reliable path problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 287-318, April.
    17. Luigi Di Puglia Pugliese & Francesca Guerriero, 2012. "A computational study of solution approaches for the resource constrained elementary shortest path problem," Annals of Operations Research, Springer, vol. 201(1), pages 131-157, December.

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