IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v265y2015icp602-618.html
   My bibliography  Save this article

An enhanced K-SP algorithm with pruning strategies to solve the constrained shortest path problem

Author

Listed:
  • Sedeño-Noda, Antonio
  • Alonso-Rodríguez, Sergio

Abstract

We propose an exact method to solve the constrained shortest path (CSP) problem. The new approach takes advantage of the binary partition strategy of a recent K shortest paths (K-SP) algorithm that allows posing numerous additional path constraints in the model without extra difficulty. We adapt and incorporate several pruning strategies from the literature on the CSP problem in this scheme and obtain a robust and scalable algorithm. The method is compared with the current best algorithm to solve the CSP problem and produces significant speedups in a wide range of network configurations. An example is given where the CSP problem is solved in road networks containing a million nodes and arcs.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:602-618
    DOI: 10.1016/j.amc.2015.05.109
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315007407
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2015.05.109?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Pascoal, Marta M.B. & Sedeño-Noda, Antonio, 2012. "Enumerating K best paths in length order in DAGs," European Journal of Operational Research, Elsevier, vol. 221(2), pages 308-316.
    2. D. Klingman & A. Napier & J. Stutz, 1974. "NETGEN: A Program for Generating Large Scale Capacitated Assignment, Transportation, and Minimum Cost Flow Network Problems," Management Science, INFORMS, vol. 20(5), pages 814-821, January.
    3. 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.
    4. 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.
    5. Namorado Climaco, Joao Carlos & Queiros Vieira Martins, Ernesto, 1982. "A bicriterion shortest path algorithm," European Journal of Operational Research, Elsevier, vol. 11(4), pages 399-404, December.
    6. Refael Hassin, 1992. "Approximation Schemes for the Restricted Shortest Path Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 36-42, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Granat, Janusz & Guerriero, Francesca, 2003. "The interactive analysis of the multicriteria shortest path problem by the reference point method," European Journal of Operational Research, Elsevier, vol. 151(1), pages 103-118, November.
    3. Xie, Chi & Travis Waller, S., 2012. "Parametric search and problem decomposition for approximating Pareto-optimal paths," Transportation Research Part B: Methodological, Elsevier, vol. 46(8), pages 1043-1067.
    4. 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.
    5. F. Guerriero & R. Musmanno, 2001. "Label Correcting Methods to Solve Multicriteria Shortest Path Problems," Journal of Optimization Theory and Applications, Springer, vol. 111(3), pages 589-613, December.
    6. Trivella, Alessio & Corman, Francesco & Koza, David F. & Pisinger, David, 2021. "The multi-commodity network flow problem with soft transit time constraints: Application to liner shipping," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 150(C).
    7. 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.
    8. Gutierrez, Genaro J. & Kouvelis, Panagiotis & Kurawarwala, Abbas A., 1996. "A robustness approach to uncapacitated network design problems," European Journal of Operational Research, Elsevier, vol. 94(2), pages 362-376, October.
    9. Minghe Sun, 2005. "Warm-Start Routines for Solving Augmented Weighted Tchebycheff Network Programs in Multiple-Objective Network Programming," INFORMS Journal on Computing, INFORMS, vol. 17(4), pages 422-437, November.
    10. Li, Jianping & Ge, Yu & He, Shuai & Lichen, Junran, 2014. "Approximation algorithms for constructing some required structures in digraphs," European Journal of Operational Research, Elsevier, vol. 232(2), pages 307-314.
    11. Shisheng Li & T.C.E. Cheng & C.T. Ng & Jinjiang Yuan, 2017. "Two‐agent scheduling on a single sequential and compatible batching machine," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(8), pages 628-641, December.
    12. Gerald G. Brown & W. Matthew Carlyle, 2020. "Solving the Nearly Symmetric All-Pairs Shortest-Path Problem," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 279-288, April.
    13. Michael Zabarankin & Stan Uryasev & Robert Murphey, 2006. "Aircraft routing under the risk of detection," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(8), pages 728-747, December.
    14. 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.
    15. Li Guan & Jianping Li & Weidong Li & Junran Lichen, 2019. "Improved approximation algorithms for the combination problem of parallel machine scheduling and path," Journal of Combinatorial Optimization, Springer, vol. 38(3), pages 689-697, October.
    16. Chen, Bi Yu & Chen, Xiao-Wei & Chen, Hui-Ping & Lam, William H.K., 2020. "Efficient algorithm for finding k shortest paths based on re-optimization technique," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 133(C).
    17. Balaji Gopalakrishnan & Seunghyun Kong & Earl Barnes & Ellis Johnson & Joel Sokol, 2011. "A least-squares minimum-cost network flow algorithm," Annals of Operations Research, Springer, vol. 186(1), pages 119-140, June.
    18. 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.
    19. Festa, P. & Guerriero, F. & Laganà, D. & Musmanno, R., 2013. "Solving the shortest path tour problem," European Journal of Operational Research, Elsevier, vol. 230(3), pages 464-474.
    20. Yves Pochet & Mathieu Van Vyve, 2004. "A General Heuristic for Production Planning Problems," INFORMS Journal on Computing, INFORMS, vol. 16(3), pages 316-327, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:602-618. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.