IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v233y2014i1p84-93.html
   My bibliography  Save this article

Branch-and-price algorithm for the Resilient Multi-level Hop-constrained Network Design

Author

Listed:
  • Souza, Fernanda S.H.
  • Gendreau, Michel
  • Mateus, Geraldo R.

Abstract

In this work, we investigate the Resilient Multi-level Hop-constrained Network Design (RMHND) problem, which consists of designing hierarchical telecommunication networks, assuring resilience against random failures and maximum delay guarantees in the communication. Three mathematical formulations are proposed and algorithms based on the proposed formulations are evaluated. A Branch-and-price algorithm, which is based on a delayed column generation approach within a Branch-and-bound framework, is proven to work well, finding optimal solutions for practical telecommunication scenarios within reasonable time. Computational results show that algorithms based on the compact formulations are able to prove optimality for instances of limited size in the scenarios of interest while the proposed Branch-and-price algorithm exhibits a much better performance.

Suggested Citation

  • Souza, Fernanda S.H. & Gendreau, Michel & Mateus, Geraldo R., 2014. "Branch-and-price algorithm for the Resilient Multi-level Hop-constrained Network Design," European Journal of Operational Research, Elsevier, vol. 233(1), pages 84-93.
    • Handle: RePEc:eee:ejores:v:233:y:2014:i:1:p:84-93
    DOI: 10.1016/j.ejor.2013.08.024
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221713006899
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2013.08.024?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. Anantaram Balakrishnan & Thomas L. Magnanti & Prakash Mirchandani, 1994. "Modeling and Heuristic Worst-Case Performance Analysis of the Two-Level Network Design Problem," Management Science, INFORMS, vol. 40(7), pages 846-867, July.
    2. Anantaram Balakrishnan & Thomas L. Magnanti & Prakash Mirchandani, 1994. "A Dual-Based Algorithm for Multi-Level Network Design," Management Science, INFORMS, vol. 40(5), pages 567-581, May.
    3. Cynthia Barnhart & Christopher A. Hane & Pamela H. Vance, 2000. "Using Branch-and-Price-and-Cut to Solve Origin-Destination Integer Multicommodity Flow Problems," Operations Research, INFORMS, vol. 48(2), pages 318-326, April.
    4. Anantaram Balakrishnan & Thomas L. Magnanti & Prakash Mirchandani, 1998. "Designing Hierarchical Survivable Networks," Operations Research, INFORMS, vol. 46(1), pages 116-136, February.
    5. Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser & Martin W. P. Savelsbergh & Pamela H. Vance, 1998. "Branch-and-Price: Column Generation for Solving Huge Integer Programs," Operations Research, INFORMS, vol. 46(3), pages 316-329, June.
    6. Obreque, Carlos & Donoso, Macarena & Gutiérrez, Gabriel & Marianov, Vladimir, 2010. "A branch and cut algorithm for the hierarchical network design problem," European Journal of Operational Research, Elsevier, vol. 200(1), pages 28-35, January.
    7. Luis Gouveia & João Telhada, 2001. "An Augmented Arborescence Formulation for the Two-Level Network Design Problem," Annals of Operations Research, Springer, vol. 106(1), pages 47-61, September.
    8. Current, John R. & ReVelle, Charles S. & Cohon, Jared L., 1986. "The hierarchical network design problem," European Journal of Operational Research, Elsevier, vol. 27(1), pages 57-66, October.
    9. Balakrishnan, Anantaram. & Magnanti, Thomas L. & Mirchandani, Prakash., 1991. "The multi-level network design problem," Working papers 3366-91., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    10. BOTTON, Quentin & FORTZ, Bernard & GOUVEIA, Luis & POSS, Michael, 2011. "Benders decomposition for the hop-constrained survivable network design problem," LIDAM Discussion Papers CORE 2011037, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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. Gollowitzer, Stefan & Gouveia, Luis & Ljubić, Ivana, 2013. "Enhanced formulations and branch-and-cut for the two level network design problem with transition facilities," European Journal of Operational Research, Elsevier, vol. 225(2), pages 211-222.
    2. Obreque, Carlos & Donoso, Macarena & Gutiérrez, Gabriel & Marianov, Vladimir, 2010. "A branch and cut algorithm for the hierarchical network design problem," European Journal of Operational Research, Elsevier, vol. 200(1), pages 28-35, January.
    3. Eduardo Álvarez-Miranda & Ivana Ljubić & S. Raghavan & Paolo Toth, 2015. "The Recoverable Robust Two-Level Network Design Problem," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 1-19, February.
    4. Masashi Miyagawa, 2009. "Optimal hierarchical system of a grid road network," Annals of Operations Research, Springer, vol. 172(1), pages 349-361, November.
    5. Miyagawa, Masashi, 2011. "Hierarchical system of road networks with inward, outward, and through traffic," Journal of Transport Geography, Elsevier, vol. 19(4), pages 591-595.
    6. Masashi Miyagawa, 2014. "Optimal allocation of area in hierarchical road networks," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 53(2), pages 617-630, September.
    7. Bigotte, João F. & Krass, Dmitry & Antunes, António P. & Berman, Oded, 2010. "Integrated modeling of urban hierarchy and transportation network planning," Transportation Research Part A: Policy and Practice, Elsevier, vol. 44(7), pages 506-522, August.
    8. Cruz, F. R. B. & Smith, J. MacGregor & Mateus, G. R., 1999. "Algorithms for a multi-level network optimization problem," European Journal of Operational Research, Elsevier, vol. 118(1), pages 164-180, October.
    9. Chardy, M. & Costa, M.-C. & Faye, A. & Trampont, M., 2012. "Optimizing splitter and fiber location in a multilevel optical FTTH network," European Journal of Operational Research, Elsevier, vol. 222(3), pages 430-440.
    10. Amy Cohn & Michael Magazine & George Polak, 2009. "Rank‐Cluster‐and‐Prune: An algorithm for generating clusters in complex set partitioning problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(3), pages 215-225, April.
    11. Kang, Jangha & Park, Kyungchul & Park, Sungsoo, 2009. "Optimal multicast route packing," European Journal of Operational Research, Elsevier, vol. 196(1), pages 351-359, July.
    12. 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.
    13. Ng, T.S. & Lee, L.H. & Chew, E.P., 2006. "Build-pack planning for hard disk drive assembly with approved vendor matrices and stochastic demands," European Journal of Operational Research, Elsevier, vol. 175(2), pages 1117-1140, December.
    14. van de Leensel, R.L.J.M. & Flippo, O.E. & Koster, Arie M.C.A. & Kolen, A.W.J., 1996. "A dynamic programming algorithm for the local access network expansion problem," Research Memorandum 027, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    15. Baris Yildiz & Martin Savelsbergh, 2019. "Provably High-Quality Solutions for the Meal Delivery Routing Problem," Transportation Science, INFORMS, vol. 53(5), pages 1372-1388, September.
    16. Zhixing Luo & Hu Qin & T. C. E. Cheng & Qinghua Wu & Andrew Lim, 2021. "A Branch-and-Price-and-Cut Algorithm for the Cable-Routing Problem in Solar Power Plants," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 452-476, May.
    17. Hadi W. Purnomo & Jonathan F. Bard, 2007. "Cyclic preference scheduling for nurses using branch and price," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(2), pages 200-220, March.
    18. Anantaram Balakrishnan & Thomas L. Magnanti & Prakash Mirchandani, 1998. "Designing Hierarchical Survivable Networks," Operations Research, INFORMS, vol. 46(1), pages 116-136, February.
    19. Crainic, Teodor Gabriel & Gendron, Bernard & Akhavan Kazemzadeh, Mohammad Rahim, 2022. "A taxonomy of multilayer network design and a survey of transportation and telecommunication applications," European Journal of Operational Research, Elsevier, vol. 303(1), pages 1-13.
    20. Jans, Raf, 2010. "Classification of Dantzig-Wolfe reformulations for binary mixed integer programming problems," European Journal of Operational Research, Elsevier, vol. 204(2), pages 251-254, July.

    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:ejores:v:233:y:2014:i:1:p:84-93. 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: http://www.elsevier.com/locate/eor .

    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.