IDEAS home Printed from https://ideas.repec.org/b/dau/thesis/123456789-15093.html
   My bibliography  Save this book

Survavibility in Multilayer Networks : models and Polyhedra

Editor

Listed:
  • Mahjoub, Ali Ridha

Author

Listed:
  • Taktak, Raouia

Abstract

This thesis deals with a problem related to survivability issues in multilayer IP-over-WDM networks. Given a set of traffic demands for which we know a survivable logical routing in the IP layer, the aim is determine the corresponding survivable topology in the WDM layer. We show that the problem is NP-hard even for a single demand. Moreover, we propose four integer linear programming formulations for the problem. The first one is based on the so-called cut inequalities. We consider the polyhedron associated with the formulation. We identify several families of valid inequalities and discuss their facial aspect. We also develop separation routines. Using this, we devise a Branch-and-Cut algorithm and present experimental results. The second formulation uses paths between terminals of the underlying graph as variables. We devise a Branch-and-Price algorithm based on that formulation. In addition, we investigate a natural formulation for the problem which uses only the design variables. Finally, we propose an extended compact formulation which, in addition to the design variables, uses routing variables. We show that this formulation provides a tighter bound for the problem.

Suggested Citation

  • Taktak, Raouia, 2013. "Survavibility in Multilayer Networks : models and Polyhedra," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/15093 edited by Mahjoub, Ali Ridha.
    • Handle: RePEc:dau:thesis:123456789/15093
    Note: dissertation
    as

    Download full text from publisher

    File URL: http://basepub.dauphine.fr/xmlui/bitstream/123456789/15093/2/2013PA090076.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. François Vanderbeck, 2000. "On Dantzig-Wolfe Decomposition in Integer Programming and ways to Perform Branching in a Branch-and-Price Algorithm," Operations Research, INFORMS, vol. 48(1), pages 111-128, February.
    2. Pamela H. Vance & Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser, 1997. "Airline Crew Scheduling: A New Formulation and Decomposition Algorithm," Operations Research, INFORMS, vol. 45(2), pages 188-200, April.
    3. François Vanderbeck, 2005. "Implementing Mixed Integer Column Generation," Springer Books, in: Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), Column Generation, chapter 0, pages 331-358, Springer.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Siqian Shen & Mingdi You & Yintai Ma, 2017. "Single‐commodity stochastic network design under demand and topological uncertainties with insufficient data," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(2), pages 154-173, March.

    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. Tao Wu & Zhe Liang & Canrong Zhang, 2018. "Analytics Branching and Selection for the Capacitated Multi-Item Lot Sizing Problem with Nonidentical Machines," INFORMS Journal on Computing, INFORMS, vol. 30(2), pages 236-258, May.
    2. Marc Peeters & Zeger Degraeve, 2004. "The Co-Printing Problem: A Packing Problem with a Color Constraint," Operations Research, INFORMS, vol. 52(4), pages 623-638, August.
    3. Cynthia Barnhart & Amy Cohn, 2004. "Airline Schedule Planning: Accomplishments and Opportunities," Manufacturing & Service Operations Management, INFORMS, vol. 6(1), pages 3-22, November.
    4. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    5. Paul A. Chircop & Timothy J. Surendonk & Menkes H. L. van den Briel & Toby Walsh, 2022. "On routing and scheduling a fleet of resource-constrained vessels to provide ongoing continuous patrol coverage," Annals of Operations Research, Springer, vol. 312(2), pages 723-760, May.
    6. Guglielmo Lulli & Suvrajeet Sen, 2004. "A Branch-and-Price Algorithm for Multistage Stochastic Integer Programming with Application to Stochastic Batch-Sizing Problems," Management Science, INFORMS, vol. 50(6), pages 786-796, June.
    7. Degraeve, Z. & Jans, R.F., 2003. "A New Dantzig-Wolfe Reformulation And Branch-And-Price Algorithm For The Capacitated Lot Sizing Problem With Set Up Times," ERIM Report Series Research in Management ERS-2003-010-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    8. Gamvros, Ioannis & Raghavan, S., 2012. "Multi-period traffic routing in satellite networks," European Journal of Operational Research, Elsevier, vol. 219(3), pages 738-750.
    9. Denissa Sari Darmawi Purba & Eleftheria Kontou & Chrysafis Vogiatzis, 2021. "Evacuation Route Planning for Alternative Fuel Vehicles," Papers 2109.01578, arXiv.org, revised May 2022.
    10. Gondzio, Jacek & González-Brevis, Pablo & Munari, Pedro, 2013. "New developments in the primal–dual column generation technique," European Journal of Operational Research, Elsevier, vol. 224(1), pages 41-51.
    11. 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.
    12. Chu, James C., 2018. "Mixed-integer programming model and branch-and-price-and-cut algorithm for urban bus network design and timetabling," Transportation Research Part B: Methodological, Elsevier, vol. 108(C), pages 188-216.
    13. Allman, Andrew & Zhang, Qi, 2020. "Dynamic location of modular manufacturing facilities with relocation of individual modules," European Journal of Operational Research, Elsevier, vol. 286(2), pages 494-507.
    14. Cortés, Cristián E. & Gendreau, Michel & Rousseau, Louis Martin & Souyris, Sebastián & Weintraub, Andrés, 2014. "Branch-and-price and constraint programming for solving a real-life technician dispatching problem," European Journal of Operational Research, Elsevier, vol. 238(1), pages 300-312.
    15. Timo Gschwind & Stefan Irnich, 2016. "Dual Inequalities for Stabilized Column Generation Revisited," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 175-194, February.
    16. Maenhout, Broos & Vanhoucke, Mario, 2010. "A hybrid scatter search heuristic for personalized crew rostering in the airline industry," European Journal of Operational Research, Elsevier, vol. 206(1), pages 155-167, October.
    17. Arpan Rijal & Marco Bijvank & Asvin Goel & René de Koster, 2021. "Workforce Scheduling with Order-Picking Assignments in Distribution Facilities," Transportation Science, INFORMS, vol. 55(3), pages 725-746, May.
    18. Ogbe, Emmanuel & Li, Xiang, 2017. "A new cross decomposition method for stochastic mixed-integer linear programming," European Journal of Operational Research, Elsevier, vol. 256(2), pages 487-499.
    19. Park, Jongyoon & Han, Jinil & Lee, Kyungsik, 2024. "Integer optimization models and algorithms for the multi-period non-shareable resource allocation problem," European Journal of Operational Research, Elsevier, vol. 317(1), pages 43-59.
    20. Matthias Winkenbach & Alain Roset & Stefan Spinler, 2016. "Strategic Redesign of Urban Mail and Parcel Networks at La Poste," Interfaces, INFORMS, vol. 46(5), pages 445-458, October.

    More about this item

    Keywords

    Réseaux IP-Sur-WDM; Sécurisation; Complexité; Polytope; Facette; Algorithme de coupes et branchements; Algorithme de branchements et génération de colonnes; Formulation étendue; IP-Over-WDM networks; Survivability; Complexity; Facet; Branch-And-Cut algorithm; Branch-And-Price algorithm; Extended formulation;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

    Statistics

    Access and download statistics

    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:dau:thesis:123456789/15093. 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: Alexandre Faure (email available below). General contact details of provider: https://edirc.repec.org/data/daup9fr.html .

    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.