IDEAS home Printed from https://ideas.repec.org/a/spr/joheur/v26y2020i6d10.1007_s10732-020-09453-x.html
   My bibliography  Save this article

A tabu search for the design of capacitated rooted survivable planar networks

Author

Listed:
  • Alain Hertz

    (Polytechnique and GERAD)

  • Thomas Ridremont

    (Polytechnique and GERAD
    ENSTA ParisTech and CEDRIC-CNAM)

Abstract

Consider a rooted directed graph G with a subset of vertices called terminals, where each arc has a positive integer capacity and a non-negative cost. For a given positive integer k, we say that G is k-survivable if every of its subgraphs obtained by removing at most k arcs admits a feasible flow that routes one unit of flow from the root to every terminal. We aim at determining a k-survivable subgraph of G of minimum total cost. We focus on the case where the input graph G is planar and propose a tabu search algorithm whose main procedure takes advantage of planar graph duality properties. In particular, we prove that it is possible to test the k-survivability of a planar graph by solving a series of shortest path problems. Experiments indicate that the proposed tabu search algorithm produces optimal solutions in a very short computing time, when these are known.

Suggested Citation

  • Alain Hertz & Thomas Ridremont, 2020. "A tabu search for the design of capacitated rooted survivable planar networks," Journal of Heuristics, Springer, vol. 26(6), pages 829-850, December.
    • Handle: RePEc:spr:joheur:v:26:y:2020:i:6:d:10.1007_s10732-020-09453-x
    DOI: 10.1007/s10732-020-09453-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10732-020-09453-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10732-020-09453-x?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. Geir Dahl & Mechthild Stoer, 1998. "A Cutting Plane Algorithm for Multicommodity Survivable Network Design Problems," INFORMS Journal on Computing, INFORMS, vol. 10(1), pages 1-11, February.
    2. Quentin Botton & Bernard Fortz & Luis Gouveia & Michael Poss, 2013. "Benders Decomposition for the Hop-Constrained Survivable Network Design Problem," INFORMS Journal on Computing, INFORMS, vol. 25(1), pages 13-26, 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. Juan Ma & Foad Mahdavi Pajouh & Balabhaskar Balasundaram & Vladimir Boginski, 2016. "The Minimum Spanning k -Core Problem with Bounded CVaR Under Probabilistic Edge Failures," INFORMS Journal on Computing, INFORMS, vol. 28(2), pages 295-307, May.
    2. Yogesh Agarwal, 2013. "Design of Survivable Networks Using Three- and Four-Partition Facets," Operations Research, INFORMS, vol. 61(1), pages 199-213, February.
    3. Okan Arslan & Ola Jabali & Gilbert Laporte, 2020. "A Flexible, Natural Formulation for the Network Design Problem with Vulnerability Constraints," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 120-134, January.
    4. Maher, Stephen J., 2021. "Implementing the branch-and-cut approach for a general purpose Benders’ decomposition framework," European Journal of Operational Research, Elsevier, vol. 290(2), pages 479-498.
    5. Clavijo López, Christian & Crama, Yves & Pironet, Thierry & Semet, Frédéric, 2024. "Multi-period distribution networks with purchase commitment contracts," European Journal of Operational Research, Elsevier, vol. 312(2), pages 556-572.
    6. Filippi, C. & Guastaroba, G. & Speranza, M.G., 2021. "On single-source capacitated facility location with cost and fairness objectives," European Journal of Operational Research, Elsevier, vol. 289(3), pages 959-974.
    7. Yogesh K. Agarwal, 2002. "Design of Capacitated Multicommodity Networks with Multiple Facilities," Operations Research, INFORMS, vol. 50(2), pages 333-344, April.
    8. Vatsa, Amit Kumar & Jayaswal, Sachin, 2015. "A New Formulation and Benders' Decomposition for Multi-period facility Location Problem with Server Uncertainty," IIMA Working Papers WP2015-02-07, Indian Institute of Management Ahmedabad, Research and Publication Department.
    9. Jyotirmoy Dalal & Halit Üster, 2018. "Combining Worst Case and Average Case Considerations in an Integrated Emergency Response Network Design Problem," Transportation Science, INFORMS, vol. 52(1), pages 171-188, January.
    10. Ljubić, Ivana & Mutzel, Petra & Zey, Bernd, 2017. "Stochastic survivable network design problems: Theory and practice," European Journal of Operational Research, Elsevier, vol. 256(2), pages 333-348.
    11. Garg, Manish & Smith, J. Cole, 2008. "Models and algorithms for the design of survivable multicommodity flow networks with general failure scenarios," Omega, Elsevier, vol. 36(6), pages 1057-1071, December.
    12. Jose L. Andrade-Pineda & David Canca & Pedro L. Gonzalez-R, 2017. "On modelling non-linear quantity discounts in a supplier selection problem by mixed linear integer optimization," Annals of Operations Research, Springer, vol. 258(2), pages 301-346, November.
    13. Vatsa, Amit Kumar & Jayaswal, Sachin, 2016. "A new formulation and Benders decomposition for the multi-period maximal covering facility location problem with server uncertainty," European Journal of Operational Research, Elsevier, vol. 251(2), pages 404-418.
    14. Ioannis Gamvros & Bruce Golden & S. Raghavan, 2006. "The Multilevel Capacitated Minimum Spanning Tree Problem," INFORMS Journal on Computing, INFORMS, vol. 18(3), pages 348-365, August.
    15. Michał Pióro & Yoann Fouquet & Dritan Nace & Michael Poss, 2016. "Optimizing Flow Thinning Protection in Multicommodity Networks with Variable Link Capacity," Operations Research, INFORMS, vol. 64(2), pages 273-289, April.
    16. M Riis & A J V Skriver & S F Møller, 2005. "Internet protocol network design with uncertain demand," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(10), pages 1184-1195, October.
    17. Rahmaniani, Ragheb & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2017. "The Benders decomposition algorithm: A literature review," European Journal of Operational Research, Elsevier, vol. 259(3), pages 801-817.
    18. Ozgur Kabadurmus & Alice E. Smith, 2016. "Multi-commodity k-splittable survivable network design problems with relays," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 62(1), pages 123-133, May.
    19. Anantaram Balakrishnan & Prakash Mirchandani & Harihara Prasad Natarajan, 2009. "Connectivity Upgrade Models for Survivable Network Design," Operations Research, INFORMS, vol. 57(1), pages 170-186, February.
    20. Gouveia, Luis & Leitner, Markus & Ruthmair, Mario, 2017. "Extended formulations and branch-and-cut algorithms for the Black-and-White Traveling Salesman Problem," European Journal of Operational Research, Elsevier, vol. 262(3), pages 908-928.

    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:joheur:v:26:y:2020:i:6:d:10.1007_s10732-020-09453-x. 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.