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A comparison of different routing schemes for the robust network loading problem: polyhedral results and computation

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Abstract

We consider the capacity formulation of the Robust Network Loading Problem. The aim of the paper is to study what happens from the theoretical and from the computational point of view when the routing policy (or scheme) changes. The theoretical results consider static, volume, affine and dynamic routing, along with splittable and unsplittable flows. Our polyhedral study provides evidence that some well-known valid inequalities (the robust cutset inequalities) are facets for all the considered routing/flows policies under the same assumptions. We also introduce a new class of valid inequalities, the robust 3-partition inequalities, showing that, instead, they are facets in some settings, but not in others. A branch-and-cut algorithm is also proposed and tested. The computational experiments refer to the problem with splittable flows and the budgeted uncertainty set. We report results on several instances coming from real-life networks, also including historical traffic data, as well as on randomly generated instances. Our results show that the problem with static and volume routing can be solved quite efficiently in practice and that, in many cases, volume routing is cheaper than static routing, thus possibly representing the best compromise between cost and computing time. Moreover, unlikely from what one may expect, the problem with dynamic routing is easier to solve than the one with affine routing, which is hardly tractable, even using decomposition methods.

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References

  1. Agarwal, Y.: Design of survivable networks using three- and four-partition facets. Oper. Res. 61(1), 199–213 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  2. Agarwal, Y.K.: k-partition-based facets of the network design problem. Networks 47(3), 123–139 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. Altın, A., Amaldi, E., Belotti, P., Pınar, M.: Provisioning virtual private networks under traffic uncertainty. Networks 49(1), 100–115 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Altin, A., Yaman, H., Pinar, M c: The robust network loading problem under hose demand uncertainty: formulation, polyhedral analysis, and computations. INFORMS J. Comput. 23(1), 75–89 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Andrade, R., Lisser, A., Maculan, N.: Multi-service multi-facility network design under uncertainty. Ann. Oper. Res. 199(1), 157–178 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  6. Avella, P., Mattia, S., Sassano, A.: Metric inequalities and the network loading problem. Discrete Optim. 4, 103–114 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  7. Ayoub, J., Poss, M.: Decomposition for adjustable robust linear optimization subject to uncertainty polytope. Comput. Manag. Sci. 13(2), 219–239 (2016)

    Article  MathSciNet  Google Scholar 

  8. Babonneau, F., Vial, J.-P., Klopfenstein, O., Ouorou, A.: Robust capacity assignment solutions for telecommunications networks with uncertain demands. Networks 62(4), 255–272 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. Barahona, F.: Network design using cut inequalities. SIAM J. Optim. 6, 823–834 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ben-Ameur, W.: Between fully dynamic routing and robust stable routing. In: Proceedings of DRCN2007, pp. 1–6 (2007)

  11. Ben-Ameur, W., Kerivin, H.: Routing of uncertain traffic demands. Optim. Eng. 6, 283–313 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Ben-Ameur, W., Zotkiewicz, M.: Volume oriented routing. In: Proceedings of NETWORKS2010), pp. 1–7 (2010)

  13. Ben-Tal, A., Ghaoui, L .E., Nemirovski, A.: Robust Optimization. Princeton University Press, Princeton (2009)

    Book  MATH  Google Scholar 

  14. Ben-Tal, A., Goryashko, A., Guslitzer, E., Nemirovski, A.: Adjustable robust solutions of uncertain linear programs. Math. Program. 99(2), 351–376 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  15. Bertsimas, D., Sim, M.: The price of robustness. Oper. Res. 52(1), 35–53 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  16. Bienstock, D., Chopra, S., Günlük, O., Tsai, C.-Y.: Minimum cost capacity installation for multicommodity network flows. Math. Program. 81, 177–199 (1998)

    MathSciNet  MATH  Google Scholar 

  17. Bienstock, D., Mattia, S.: Using mixed-integer programming to solve power grid blackout problems. Discrete Optim. 4, 115–141 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  18. Bley, A., Klaehne, R., Menne, U., Raack, C., Wessaely, R.: Multi-layer network design—a model-based optimization approach. In: Proceedings of the PGTS 2008, Berlin, Germany, pp. 107–116 (2008)

  19. Cacchiani, V., Jünger, M., Liers, F., Lodi, A., Schmidt, D.R.: Single-commodity robust network design with finite and hose demand sets. Math. Program. 157(1), 297–342 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  20. Chekuri, C., Oriolo, G., Scutellà, M., Shepherd, F.: Hardness of robust network design. Networks 50(1), 50–154 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  21. CPLEX: IBM ILOG CPLEX 12.6 Reference Manual. ILOG CPLEX Division, Gentilly, France (2013)

  22. Duffield, N., Goyal, P., Greenberg, A., Mishra, P., Ramakrishnan, K., van der Merive, J.: A flexible model for resource management in virtual private networks. In: SIGCOMM Computer Communication Review 29(4), 95–108 (1999)

  23. Fingerhut, J., Suri, S., Turner, J.: Designing least-cost nonblocking broadband networks. J. Algorithms 24(2), 287–309 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  24. Fortz, B., Poss, M.: An improved benders decomposition applied to a multi-layer network design problem. Oper. Res. Lett. 37(5), 359–364 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  25. Gupta, A., Kleinberg, J., Kumar, A., Rastogi, R., Yener, B.: Provisioning a virtual private network: a network design problem for multicommodity flows. In: Proceedings of ACMSTOC 2001, pp. 389–398 (2001)

  26. Koster, A., Kutschka, M., Raack, C.: Robust network design: formulations, valid inequalities, and computations. Networks 61(2), 128–149 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  27. Lee, C., Lee, K., Park, S.: Benders decomposition approach for the robust network design problem with flow bifurcations. Networks 62(1), 1–16 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  28. Lemaréchal, C., Ouorou, A., Petrou, G.: Robust network design in telecommunications under polytope demand uncertainty. Eur. J. Oper. Res. 206(3), 634–641 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  29. Magnanti, T., Mirchandani, P., Vachani, R.: The convex hull of two core capacitated network design problems. Math. Program. 60, 233–250 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  30. Mattia, S.: Separating tight metric inequalities by bilevel programming. Oper. Res. Lett. 40(6), 568–572 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  31. Mattia, S.: Solving survivable two-layer network design problems by metric inequalities. Comput. Optim. Appl. 51(2), 809–834 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  32. Mattia, S.: A polyhedral study of the capacity formulation of the multilayer network design problem. Networks 62(1), 17–26 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  33. Mattia, S.: The robust network loading problem with dynamic routing. Comput. Optim. Appl. 54(3), 619–643 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  34. Mattia, S.: The cut property under demand uncertainty. Networks 66(2), 159–168 (2015)

    Article  MathSciNet  Google Scholar 

  35. Mattia, S., Rossi, F., Servilio, M., Smriglio, S.: Staffing and scheduling flexible call centers by two-stage robust optimization. Omega 72, 25–37 (2017)

    Article  Google Scholar 

  36. Minoux, M.: Robust network optimization under polyhedral demand uncertainty is NP-hard. Discrete Appl. Math. 158(5), 597–603 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  37. Mudchanatongsuk, S., Ordonez, F., Liu, J.: Robust solutions for network design under transportation cost and demand uncertainty. J. Oper. Res. Soc. 59, 552–562 (2008)

    Article  MATH  Google Scholar 

  38. Ordóñez, F., Zhao, J.: Robust capacity expansion of network flows. Networks 50(2), 136–145 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  39. Orlowski, S., Pióro, M., Tomaszewski, A., Wessäly, R.: SNDlib 1.0-Survivable Network Design Library. Networks 55(3), 276–286 (2010)

    Google Scholar 

  40. Ouorou, A.: Tractable approximations to a robust capacity assignment model in telecommunications under demand uncertainty. Comput. Oper. Res. 40(1), 318–327 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  41. Ouorou, A., Vial, J.-P.: A model for robust capacity planning for telecommunications networks under demand uncertainty. In: Proceedings of DRCN 2007, pp. 1–4 (2007)

  42. Pioro, M., Nace, D., Poss, M., Fouquet, Y.: Optimizing flow thinning protection in multicommodity networks with variable link capacity. Oper. Res. 64(2), 273–289 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  43. Poss, M.: A comparison of routing sets for robust network design. Optim. Lett. 8(5), 1619–1635 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  44. Poss, M., Raack, C.: Affine recourse for the robust network design problem: between static and dynamic routing. Networks 61(2), 180–198 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  45. Scutellà, M.: On improving optimal oblivious routing. Oper. Res. Lett. 37(3), 197–200 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  46. Wiesemann, W., Kuhn, D., Sim, M.: Distributionally robust convex optimization. Oper. Res. 62(6), 1358–1376 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  47. Zeng, B., Zhao, L.: Solving two-stage robust optimization problems using a column-and-constraint generation method. Oper. Res. Lett. 41(5), 457–461 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  48. Zhang, Y., Roughan, M., Duffield, N., Greenberg, A.: Fast accurate computation of large-scale IP traffic matrices from link loads. In: Proceedings of ACM SIGMETRICS, pp. 206–217 (2003)

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Authors and Affiliations

  1. Istituto di Analisi dei Sistemi ed Informatica, Consiglio Nazionale delle Ricerche, Via dei Taurini 19, 00185, Rome, Italy

    Sara Mattia

  2. UMR CNRS 5506 LIRMM, Université de Montpellier, Rue Ada 161, 34095, Montpellier cedex 5, France

    Michael Poss

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  1. Sara Mattia
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  2. Michael Poss
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Correspondence to Michael Poss.

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Mattia, S., Poss, M. A comparison of different routing schemes for the robust network loading problem: polyhedral results and computation. Comput Optim Appl 69, 753–800 (2018). https://doi.org/10.1007/s10589-017-9956-z

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  • DOI: https://doi.org/10.1007/s10589-017-9956-z

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