IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v222y2014i1p279-29110.1007-s10479-013-1308-5.html
   My bibliography  Save this article

Fast approximation algorithms for routing problems with hop-wise constraints

Author

Listed:
  • Amir Elalouf

Abstract

Given a graph G(N,A) with a cost (or benefit) and a delay on each arc, the constrained routing problem (CRP) aims to find a minimum-cost or a maximum-benefit path from a given source to a given destination node, subject to an end-to-end delay constraint. The problem (with a single constraint) is NP-hard, and has been studied by many researchers who found fully polynomial approximation schemes (FPAS) for this problem. The current paper focuses on a generalized CRP version, CRP with hop-wise constraints (CRPH). In the generalized version, instead of one constraint there are up to n−1 special-type constraints, where n is the number of nodes. An FPAS based on interval partitioning is proposed for both the minimization and the maximization versions of CRPH. For G(N,A) with n nodes and m arcs, the complexity of the algorithm is O(mn 2 /ε). Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Amir Elalouf, 2014. "Fast approximation algorithms for routing problems with hop-wise constraints," Annals of Operations Research, Springer, vol. 222(1), pages 279-291, November.
  • Handle: RePEc:spr:annopr:v:222:y:2014:i:1:p:279-291:10.1007/s10479-013-1308-5
    DOI: 10.1007/s10479-013-1308-5
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-013-1308-5
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s10479-013-1308-5?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. Altannar Chinchuluun & Panos Pardalos, 2007. "A survey of recent developments in multiobjective optimization," Annals of Operations Research, Springer, vol. 154(1), pages 29-50, October.
    2. Refael Hassin, 1992. "Approximation Schemes for the Restricted Shortest Path Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 36-42, February.
    3. Christian Artigues & Dominique Feillet, 2008. "A branch and bound method for the job-shop problem with sequence-dependent setup times," Annals of Operations Research, Springer, vol. 159(1), pages 135-159, March.
    4. Henig, Mordechai I., 1986. "The shortest path problem with two objective functions," European Journal of Operational Research, Elsevier, vol. 25(2), pages 281-291, May.
    5. P. Eveborn & M. Rönnqvist, 2004. "Scheduler – A System for Staff Planning," Annals of Operations Research, Springer, vol. 128(1), pages 21-45, April.
    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. Lee, Jisun & Joung, Seulgi & Lee, Kyungsik, 2022. "A fully polynomial time approximation scheme for the probability maximizing shortest path problem," European Journal of Operational Research, Elsevier, vol. 300(1), pages 35-45.
    2. Duque, Daniel & Lozano, Leonardo & Medaglia, Andrés L., 2015. "An exact method for the biobjective shortest path problem for large-scale road networks," European Journal of Operational Research, Elsevier, vol. 242(3), pages 788-797.
    3. Thai Doan Chuong, 2021. "Optimality and duality in nonsmooth composite vector optimization and applications," Annals of Operations Research, Springer, vol. 296(1), pages 755-777, January.
    4. Lee, Soonhui & Turner, Jonathan & Daskin, Mark S. & Homem-de-Mello, Tito & Smilowitz, Karen, 2012. "Improving fleet utilization for carriers by interval scheduling," European Journal of Operational Research, Elsevier, vol. 218(1), pages 261-269.
    5. Xu Lei & Tang Shiyun & Deng Yanfei & Yuan Yuan, 2020. "Sustainable operation-oriented investment risk evaluation and optimization for renewable energy project: a case study of wind power in China," Annals of Operations Research, Springer, vol. 290(1), pages 223-241, July.
    6. Esaignani Selvarajah & Rui Zhang, 2014. "Supply chain scheduling to minimize holding costs with outsourcing," Annals of Operations Research, Springer, vol. 217(1), pages 479-490, June.
    7. Randeep Bhatia & Sudipto Guha & Samir Khuller & Yoram J. Sussmann, 1998. "Facility Location with Dynamic Distance Functions," Journal of Combinatorial Optimization, Springer, vol. 2(3), pages 199-217, September.
    8. Geng, Zhichao & Yuan, Jinjiang, 2023. "Single-machine scheduling of multiple projects with controllable processing times," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1074-1090.
    9. Walter J. Gutjahr & Alois Pichler, 2016. "Stochastic multi-objective optimization: a survey on non-scalarizing methods," Annals of Operations Research, Springer, vol. 236(2), pages 475-499, January.
    10. Boaz Golany & Moshe Kress & Michal Penn & Uriel G. Rothblum, 2012. "Network Optimization Models for Resource Allocation in Developing Military Countermeasures," Operations Research, INFORMS, vol. 60(1), pages 48-63, February.
    11. Thai Doan Chuong, 2022. "Second-order cone programming relaxations for a class of multiobjective convex polynomial problems," Annals of Operations Research, Springer, vol. 311(2), pages 1017-1033, April.
    12. Carolina Almeida & Richard Gonçalves & Elizabeth Goldbarg & Marco Goldbarg & Myriam Delgado, 2012. "An experimental analysis of evolutionary heuristics for the biobjective traveling purchaser problem," Annals of Operations Research, Springer, vol. 199(1), pages 305-341, October.
    13. 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.
    14. Seyyed Amir Babak Rasmi & Ali Fattahi & Metin Türkay, 2021. "SASS: slicing with adaptive steps search method for finding the non-dominated points of tri-objective mixed-integer linear programming problems," Annals of Operations Research, Springer, vol. 296(1), pages 841-876, January.
    15. David Bergman & Merve Bodur & Carlos Cardonha & Andre A. Cire, 2022. "Network Models for Multiobjective Discrete Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 990-1005, March.
    16. Eduardo Álvarez-Miranda & Hesso Farhan & Martin Luipersbeck & Markus Sinnl, 2017. "A bi-objective network design approach for discovering functional modules linking Golgi apparatus fragmentation and neuronal death," Annals of Operations Research, Springer, vol. 258(1), pages 5-30, November.
    17. Wang, Honggang, 2017. "Multi-objective retrospective optimization using stochastic zigzag search," European Journal of Operational Research, Elsevier, vol. 263(3), pages 946-960.
    18. Faramroze G. Engineer & George L. Nemhauser & Martin W. P. Savelsbergh, 2011. "Dynamic Programming-Based Column Generation on Time-Expanded Networks: Application to the Dial-a-Flight Problem," INFORMS Journal on Computing, INFORMS, vol. 23(1), pages 105-119, February.
    19. Julio B. Clempner, 2018. "Computing multiobjective Markov chains handled by the extraproximal method," Annals of Operations Research, Springer, vol. 271(2), pages 469-486, December.
    20. Mong-Jen Kao & Bastian Katz & Marcus Krug & D. T. Lee & Ignaz Rutter & Dorothea Wagner, 2013. "The density maximization problem in graphs," Journal of Combinatorial Optimization, Springer, vol. 26(4), pages 723-754, November.

    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:spr:annopr:v:222:y:2014:i:1:p:279-291:10.1007/s10479-013-1308-5. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.