Multiobjective routing in multiservice MPLS networks with traffic splitting — A network flow approach

  • Rita Girão-SilvaEmail author
  • José Craveirinha
  • João Clímaco
  • M. Eugénia Captivo


A multiobjective routing model for Multiprotocol Label Switching networks with multiple service types and traffic splitting is presented in this paper. The routing problem is formulated as a multiobjective mixed-integer program, where the considered objectives are the minimization of the bandwidth routing cost and the minimization of the load cost in the network links with a constraint on the maximal splitting of traffic trunks. Two different exact methods are developed for solving the formulated problem, one based on the classical constraint method and another based on a modified constraint method. A very extensive experimental study, with results on network performance measures in various reference test networks and in randomly generated networks, is also presented and its results are discussed.


Routing models multiobjective optimization telecommunication networks network flow approach traffic splitting 


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  1. [1]
    Aarts, E. & Lenstra, J. K. (editors) (1997). Local Search in Combinatorial Optimization. John Wiley & Sons.zbMATHGoogle Scholar
  2. [2]
    Agdeppa, R. P., Yamashita, N. & Fukushima, M. (2007). The traffic equilibrium problem with nonadditive costs and its monotone mixed complementarity problem formulation. Transportation Research Part B — Methodological, 41(8):862–874.CrossRefGoogle Scholar
  3. [3]
    Avallone, S., Manetti, V., Mariano, M. & Romano, S. P. (2007). A splitting infrastructure for load balancing and security in an MPLS network. Proceedings of the 3rd International Conference on Testbeds and Research Infrastructure for the Development of Networks and Communities (TridentCom 2007), Lake Buena Vista (FL), USA, May 21–23.Google Scholar
  4. [4]
    Bekhor, S., Toledo, T. & Toledo, J. N. (2008). Effects of choice set size and route choice models on path-based traffic assignment. Transportmetrica, 4(2):117–133.CrossRefGoogle Scholar
  5. [5]
    Bertsimas, D. & Tsitsiklis, J. (1993). Simulated annealing. Statistical Science, 8(1):10–15.CrossRefGoogle Scholar
  6. [6]
    Bovy, P. H. L. (2009). On modelling route choice sets in transportation networks: A synthesis. Transport Reviews: A Transnational Transdisciplinary Journal, 29(1):43–68.CrossRefGoogle Scholar
  7. [7]
    Brands, T. & van Eck, G. (2010). Multimodal network design and assessment — Proposal for a dynamic multi-objective approach. 11th TRAIL Congress, The Netherlands Research School on Transport, Infrastructure and Logistics, Nov.Google Scholar
  8. [8]
    Branke, J., Deb, K., Miettinen, K. & Słowiński, R. (editors) (2008). Multiobjective Optimization — Interactive and Evolutionary Approaches. Lecture Notes in Computer Science, volume 5252, Springer.zbMATHGoogle Scholar
  9. [9]
    Chen, A., Zhou, Z., Chootinan, P., Ryu, S., Yang, C. & Wong, S. C. (2011). Transport network design problem under uncertainty: A review and new developments. Transport Reviews, 31(6):743–768.CrossRefGoogle Scholar
  10. [10]
    Clímaco, J. C. N., Craveirinha, J. M. F. & Pascoal, M. M. B. (2006). An automated reference point-like approach for multicriteria shortest path problems. Journal of Systems Science and Systems Engineering, 15(3):314–329.CrossRefGoogle Scholar
  11. [11]
    Clímaco, J. C. N., Craveirinha, J. M. F. & Pascoal, M. M. B. (2007). Multicriteria routing models in telecommunication networks — Overview and a case study. In Shi, Y., Olson, D. L. & Stam, A. (editors), Advances in Multiple Criteria Decision Making and Human Systems Management: Knowledge and Wisdom, pages 17–46, IOS Press.Google Scholar
  12. [12]
    Clímaco, J. & Pascoal, M. (2009). Finding nondominated shortest pairs of disjoint simple paths. Computers & Operations Research, 36(11):2892–2898.CrossRefMathSciNetzbMATHGoogle Scholar
  13. [13]
    Cohon, J. L. (1978). Multiobjective Programming and Planning. Mathematics in Science and Engineering, Academic Press.zbMATHGoogle Scholar
  14. [14]
    Craveirinha, J., Gomes, T., Pascoal, M. & Clímaco, J. (2011). A stochastic bicriteria approach for restorable QoS routing in MPLS. Proceedings of the 2011 International Conference on Telecommunication Systems — Modeling and Analysis (ICTSM2011), pages 1–15, Prague, Czech Republic, May 26–28.Google Scholar
  15. [15]
    Craveirinha, J., Clímaco, J., Martins, L., da Silva, C. G. & Ferreira, N. (2013). A bi-criteria minimum spanning tree routing model for MPLS/Overlay networks. Telecommunication Systems, 52(1):203–215.CrossRefGoogle Scholar
  16. [16]
    Craveirinha, J. M. F., Clímaco, J. C. N., Pascoal, M. M. B. & Martins, L. M. R. A. (2007). Traffic splitting in MPLS networks — A hierarchical multicriteria approach. Journal of Telecommunications and Information Technology, (4):3–10.Google Scholar
  17. [17]
    Craveirinha, J., Girão-Silva, R. & Clímaco, J. (2008). A meta-model for multiobjective routing in MPLS networks. Central European Journal of Operations Research, 16(1):79–105.CrossRefzbMATHGoogle Scholar
  18. [18]
    Dana, A., Zadeh, A. K., Kalantari, M. E. & Badie, K. (2003). A traffic splitting restoration scheme for MPLS network using case-based reasoning. Proceedings of the 9th Asia Pacific Conference on Communications (APCC 2003), volume 2, pages 763–766, Sep. 21–24.Google Scholar
  19. [19]
    Dana, A., Khademzadeh, A., Kalantari, M. E. & Badie, K. (2004). Fault recovery in MPLS network using case-based reasoning. Modares Technical and Engineering, 16:127–138.Google Scholar
  20. [20]
    Deb, K. (2001). Multi-Objective Optimization using Evolutionary Algorithms. John Wiley & Sons.zbMATHGoogle Scholar
  21. [21]
    Dial, R. B. (1996). Bicriterion traffic assignment: Basic theory and elementary algorithms. Transportation Science, 30(2):93–111.CrossRefzbMATHGoogle Scholar
  22. [22]
    Dial, R. B. (1997). Bicriterion traffic assignment: Efficient algorithms plus examples. Transportation Research Part B — Methodological, 31(5):357–379.CrossRefGoogle Scholar
  23. [23]
    Dixit, A., Prakash, P. & Kompella, R. R. (2011). On the efficacy of fine-grained traffic splitting protocols in data center networks. Proceedings of SIGCOMM11, pages 430–431, Toronto (Ontario), Canada, Aug. 15–19.Google Scholar
  24. [24]
    Doar, M. & Leslie, I. M. (1993). How bad is naive multicast routing? Proceedings of INFOCOM, volume 1, pages 82–89, San Francisco (CA), USA.Google Scholar
  25. [25]
    Ehrgott, M. & Gandibleux, X. (2000). A survey and annotated bibliography of multiobjective combinatorial optimization. OR Spektrum, 22(4):425–460.CrossRefMathSciNetzbMATHGoogle Scholar
  26. [26]
    Elwalid, A., Jin, C., Low, S. & Widjaja, I. (2001). MATE: MPLS Adaptive Traffic Engineering. In Sengupta, B., Bauer, F. & Cavendish, D. (editors), Proceedings of the 20th Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2001), volume 3, pages 1300–1309, Anchorage (AK), USA, IEEE Computer and Communications Societies.CrossRefGoogle Scholar
  27. [27]
    Erbas, S. C. & Erbas, C. (2003). A multiobjective off-line routing model for MPLS networks. In Charzinski, J., Lehnert, R. & Tran-Gia, P. (editors), Proceedings of the 18th International Teletraffic Congress (ITC-18), pages 471–480, Berlin, Germany, Elsevier, Amsterdam.Google Scholar
  28. [28]
    Ferng, H.-W. & Peng, C.-C. (2004). Traffic splitting in a network: Split traffic models and applications. Computer Communications, 27(12):1152–1165.CrossRefGoogle Scholar
  29. [29]
    Fortz, B. & Thorup, M. (2000). Internet traffic engineering by optimizing OSPF weights. In Sidi, M., Katzela, I. & Shavitt, Y. (editors), Proceedings of the 19th Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2000), volume 2, pages 519–528, Tel Aviv, Israel, Mar. 26–30, IEEE Computer and Communications Societies.CrossRefGoogle Scholar
  30. [30]
    Fortz, B. & Thorup, M. (2002). Optimizing OSPF/IS-IS weights in a changing world. IEEE Journal on Selected Areas in Communications, 20(4):756–767.CrossRefGoogle Scholar
  31. [31]
    Gandibleux, X., Sevaux, M., Sőrensen, K. & T’Kindt, V. (editors) (2004). Metaheuristics for Multiobjective Optimisation. Lecture Notes in Economics and Mathematical Systems, volume 535, Springer.zbMATHGoogle Scholar
  32. [32]
    Gendreau, M. & Potvin, J.-Y. (2010). Tabu search. In Gendreau, M. & Potvin, J.-Y. (editors), Handbook of Metaheuristics, International Series in Operations Research & Management Science, volume 146, pages 41–59, Springer.CrossRefGoogle Scholar
  33. [33]
    Ghosh, A. & Dehuri, S. (2004). Evolutionary algorithms for multi-criterion optimization: A survey. International Journal of Computing & Information Sciences, 2(1):38–57.Google Scholar
  34. [34]
    Girão-Silva, R., Craveirinha, J. & Clímaco, J. (2009). Hierarchical multiobjective routing in Multiprotocol Label Switching networks with two service classes — A heuristic solution. International Transactions in Operational Research, 16(3):275–305.CrossRefzbMATHGoogle Scholar
  35. [35]
    Girão-Silva, R., Craveirinha, J., Clímaco, J. & Captivo, M. E. (2013). Multiobjective Routing in Multiservice MPLS Networks with Traffic Splitting — Report on a Network Flow Approach. Research Report 2/2013, INESC-Coimbra.Google Scholar
  36. [36]
    Gomes, T., Martins, L. & Craveirinha, J. (2001). An algorithm for calculating k shortest paths with a maximum number of arcs. Investigação Operacional, 21:235–244.Google Scholar
  37. [37]
    Guihaire, V. & Hao, J.-K. (2008). Transit network design and scheduling: a global review. Transportation Research Part A: Policy and Practice, 42(10):1251–1273.Google Scholar
  38. [38]
    He, J. & Rexford, J. (2008). Towards Internet-wide multipath routing. IEEE Network, 22(2):16–21.CrossRefGoogle Scholar
  39. [39]
    Huang, H.-J. & Li, Z.-C. (2007). A multiclass, multicriteria logit-based traffic equilibrium assignment model under ATIS. European Journal of Operational Research, 176(3):1464–1477.CrossRefzbMATHGoogle Scholar
  40. [40]
    Knowles, J., Oates, M. & Corne, D. (2000). Advanced multi-objective evolutionary algorithms applied to two problems in telecommunications. BT Technology Journal, 18(4):51–65.CrossRefGoogle Scholar
  41. [41]
    Krishnadas, C. S. & Roy, R. (2009). Quality of Experience (QoE) assurance by a multipath balanced traffic splitting algorithm in MPLS networks. Annales UMCS Informatica AI, 9(1):165–177.Google Scholar
  42. [42]
    Lee, G. M. & Choi, J. S. (2002). A survey of multipath routing for traffic engineering. [Online]Google Scholar
  43. [43]
    Lee, Y., Seok, Y., Choi, Y. & Kim, C. (2002). A constrained multipath traffic engineering scheme for MPLS networks. Proceedings of the IEEE International Conference on Communications (ICC 2002), New York, USA, Apr.28–May2.Google Scholar
  44. [44]
    Lee, K., Toguyeni, A., Noce, A. & Rahmani, A. (2005). Comparison of multipath algorithms for load balancing in a MPLS network. In Kim, C. (editor), Proceedings of the International Conference on Information Networking, Convergence in Broadband and Mobile Networking (ICOIN2005), Lecture Notes in Computer Science, volume 3391, pages 463–470, Jeju Island, Korea, Jan.31–Feb.2, Springer.CrossRefGoogle Scholar
  45. [45]
    Lee, K., Toguyeni, A. & Rahmani, A. (2006). Hybrid multipath routing algorithms for load balancing in MPLS based IP network. Proceedings of the 20th International Conference on Advanced Information Networking and Applications (AINA 2006), Apr.18–20.Google Scholar
  46. [46]
    Liu, Y., Bunker, J. & Ferreira, L. (2010). Transit users’ route-choice modelling in transit assignment: A review. Transport Reviews: A Transnational Transdisciplinary Journal, 30(6):753–769.CrossRefGoogle Scholar
  47. [47]
    Lo, H. K. & Chen, A. (2000a). Reformulating the traffic equilibrium problem via a smooth gap function. Mathematical and Computer Modelling, 31(2–3):179–195.CrossRefMathSciNetzbMATHGoogle Scholar
  48. [48]
    Lo, H. K. & Chen, A. (2000b). Traffic equilibrium problems with route-specific costs: formulation and algorithms. Transportation Research Part B — Methodological, 34(6):493–513.CrossRefGoogle Scholar
  49. [49]
    Lu, C.-C., Mahmassani, H. S. & Zhou, X. (2008). A bi-criterion dynamic user equilibrium traffic assignment model and solution algorithm for evaluating dynamic road pricing strategies. Transportation Research Part C, 16:371–389.CrossRefGoogle Scholar
  50. [50]
    Marcotte, P. & Patriksson, M. (2007). Traffic equilibrium. In Barnhart, C. & Laporte, G. (editors), Transportation, Handbooks in Operations Research and Management Science, volume 14, pages 623–713, North-Holland, Amsterdam.CrossRefGoogle Scholar
  51. [51]
    Mavrotas, G. (2009). Effective implementation of the ɛ-constraint method in Multi-Objective Mathematical Programming problems. Applied Mathematics and Computation, 213(2):455–465.CrossRefMathSciNetzbMATHGoogle Scholar
  52. [52]
    Medhi, D. & Tipper, D. (2000). Some approaches to solving a multi-hour broadband network capacity design problem with single-path routing. Telecommunication Systems, 13(2):269–291.CrossRefzbMATHGoogle Scholar
  53. [53]
    Messac, A., Ismail-Yahaya, A. & Mattson, C. A. (2003). The normalized normal constraint method for generating the Pareto frontier. Structural and Multidisciplinary Optimization, 25(2):86–98.CrossRefMathSciNetzbMATHGoogle Scholar
  54. [54]
    Mitra, D. & Ramakrishnan, K. G. (2001). Techniques for traffic engineering of multiservice, multipriority networks. Bell Labs Technical Journal, 6(1):139–151.CrossRefGoogle Scholar
  55. [55]
    Murugesan, G., Natarajan, A. M. & Venkatesh, C. (2008). Enhanced variable splitting ratio algorithm for effective load balancing in MPLS networks. Journal of Computer Science, 4(3):232–238.CrossRefGoogle Scholar
  56. [56]
    Nagurney, A., Dong, J. & Mokhtarian, P. L. (2002). Traffic network equilibrium and the environment: A multicriteria decision-making perspective. In Kontoghiorghes, E., Rustem, B. & Siokos, S. (editors), Computational Methods in Decision-Making, Economics and Finance, pages 501–523, Kluwer.CrossRefGoogle Scholar
  57. [57]
    Nelakuditi, S. & Zhang, Z.-L. (2001). On selection of paths for multipath routing. In Wolf, L., Hutchison, D. & Steinmetz, R. (editors), Proceedings of IWQoS 2001, Lecture Notes in Computer Science, volume 2092, pages 170–184, Karlsruhe, Germany, Springer.Google Scholar
  58. [58]
    Patriksson, M. (1994). The Traffic Assignment Problem — Models and Methods. Topics in Transportation, VSP.Google Scholar
  59. [59]
    Pióro, M., Szentesi, Á., Harmatos, J., Jüttner, A., Gajowniczek, P. & Kozdrowski, S. (2002). On open shortest path first related network optimization problems. Performance Evaluation, 48:201–223.CrossRefzbMATHGoogle Scholar
  60. [60]
    Prashker, J. N. & Bekhor, S. (2004). A review on route choice models used in the stochastic user equilibrium problem. Transport Reviews, 24(4):437–463.CrossRefGoogle Scholar
  61. [61]
    Prato, C. G. (2009). Route choice modeling: past, present and future research directions. Journal of Choice Modelling, 2(1):65–100.CrossRefMathSciNetGoogle Scholar
  62. [62]
    Raith, A., Wang, J. Y. T., Ehrgott, M. & Mitchell, S. A. (2011). Solving multi-objective traffic assignment. In ORP3 Meeting, Cádiz, Spain, Sep.13–17.Google Scholar
  63. [63]
    Ran, B. & Boyce, D. (1996). Modeling Dynamic Transportation Networks — An Intelligent Transportation System Oriented Approach. Lecture Notes in Economics and Mathematical Systems, volume 417, Springer, 2nd ed.CrossRefzbMATHGoogle Scholar
  64. [64]
    Sheffi, Y. (1985). Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods. Prentice-Hall, Inc.Google Scholar
  65. [65]
    Singh, R. K., Chaudhari, N. S. & Saxena, K. (2012). Load balancing in IP/MPLS networks: A survey. Communications and Network, 4:151–156.CrossRefGoogle Scholar
  66. [66]
    Song, J., Kim, S. & Lee, M. (2003). Dynamic load distribution in MPLS networks. In Kahng, H.-K. (editor), Proceedings of the International Conference on Information Networking, Convergence in Broadband and Mobile Networking (ICOIN2003), Lecture Notes in Computer Science, volume 2662, pages 989–999, Jeju Island, Korea, Feb.12–14, Springer.Google Scholar
  67. [67]
    Srivastava, S., Krithikaivasan, B., Medhi, D. & Pióro, M. (2003). Traffic engineering in the presence of tunneling and diversity constraints: Formulation and Lagrangean decomposition approach. In Charzinski, J., Lehnert, R. & Tran-Gia, P. (editors), Proceedings of the 18th International Teletraffic Congress (ITC-18), pages 461–470, Berlin, Germany, Elsevier, Amsterdam.Google Scholar
  68. [68]
    Srivastava, S., Agrawal, G., Pióro, M. & Medhi, D. (2005). Determining link weight system under various objectives for OSPF networks using a Lagrangian relaxation-based approach. IEEE Transactions on Network and Service Management, 2(1):9–18.CrossRefGoogle Scholar
  69. [69]
    Steuer, R. E. (1986). Multiple Criteria Optimization: Theory, Computation and Application. Probability and Mathematical Statistics. John Wiley & Sons.Google Scholar
  70. [70]
    Talbi, E.-G., Basseur, M., Nebro, A. J. & Alba, E. (2012). Multi-objective optimization using metaheuristics: non-standard algorithms. International Transactions in Operational Research, 19(1–2):283–305.CrossRefMathSciNetzbMATHGoogle Scholar
  71. [71]
    Wang, J., Patek, S., Wang, H. & Liebeherr, J. (2002). Traffic engineering with AIMD in MPLS networks. In Carle, G. & Zitterbart, M. (editors), Proceedings of the 7th IFIP/IEEE International Workshop on Protocols for High Speed Networks (PfHSN 2002), Lecture Notes in Computer Science, volume 2334, pages 192–210, Berlin, Germany, Apr.22–24, Springer.Google Scholar
  72. [72]
    Wang, J. Y. T. & Ehrgott, M. (2011). Modelling stochastic route choice with bi-objective traffic assignment. In Proceedings of International Choice Modelling Conference 2011, Leeds, UK, Jul.4–6.Google Scholar
  73. [73]
    Wang, J. Y. T. & Ehrgott, M. (2013). Modelling route choice behavior in a tolled road network with a time surplus maximisation bi-objective user equilibrium. Procedia — Social and Behavioral Sciences, 80:266–288.CrossRefGoogle Scholar
  74. [74]
    Wierzbicki, A. P. & Burakowski, W. (2011). A conceptual framework for multiple-criteria routing in QoS IP networks. International Transactions in Operational Research, 18(3):377–399.CrossRefMathSciNetGoogle Scholar
  75. [75]
    Yang, H. & Huang, H.-J. (2004). The multiclass, multi-criteria traffic network equilibrium and systems optimum problem. Transportation Research Part B — Methodological, 38:1–15.CrossRefGoogle Scholar
  76. [76]
    Zhang, Q. & Li, H. (2007). MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Transactions on Evolutionary Computation, 11(6):712–731.CrossRefGoogle Scholar
  77. [77]
    Zitzler, E. (2012). Evolutionary multiobjective optimization. In Rozenberg, G., Bäck, T. & Kok, J. N. (editors), Handbook of Natural Computing, pages 871–904, Springer.CrossRefGoogle Scholar
  78. [78]
    gt-itm (2000). Modeling Topology of Large Internetworks. Google Scholar

Copyright information

© Systems Engineering Society of China and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Rita Girão-Silva
    • 1
    • 2
    Email author
  • José Craveirinha
    • 2
  • João Clímaco
    • 2
  • M. Eugénia Captivo
    • 3
  1. 1.Department of Electrical and Computer EngineeringUniversity of CoimbraCoimbraPortugal
  2. 2.Institute of Computers and Systems Engineering of Coimbra (INESC-Coimbra)CoimbraPortugal
  3. 3.Centro de Investigação Operacional, Faculdade de CiênciasUniversidade de LisboaLisboaPortugal

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