Skip to main content
SpringerLink
Log in

Multi-commodity k-splittable survivable network design problems with relays

  • Published:
Telecommunication Systems Aims and scope Submit manuscript

Abstract

The network design problem is a well known optimization problem with applications in telecommunication, infrastructure designs and military operations. This paper devises the first formulation and solution methodology for the multi-commodity k-splittable two-edge disjoint survivable network design problem with capacitated edges and relays. This problem realistically portrays telecommunications network design but has not been solved previously due to its computational difficulty. Edge capacity is considered as either a discrete or a continuous variable. An exact method and a practical heuristic method are presented, and computational results are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Altin, A., Belotti, P., & Pinar, M. C. (2010). OSPF routing with optimal oblivious performance ratio under polyhedral demand uncertainty. Optimization and Engineering, 11(3), 395–422.

    Article  Google Scholar 

  2. Atamturk, A., & Rajan, D. (2002). On splittable and unsplittable flow capacitated network design arc-set polyhedra. Mathematical Programming, 92(2), 315–333.

    Article  Google Scholar 

  3. Atamturk, A., & Rajan, D. (2008). Partition inequalities for capacitated survivable network design based on directed p-cycles. Discrete Optimization, 5(2), 415–433.

    Article  Google Scholar 

  4. Azodolmolky, S., Angelou, M., Tomkos, I., Panayiotou, T., Ellinas, G., & Antoniades, N. (2012). Impairment-aware optical networking: A survey. In N. N. Antoniades, G. Ellinas, & I. Roudas (Eds.), WDM Systems and Networks, Optical Networks (pp. 443–479). New York: Springer.

    Chapter  Google Scholar 

  5. Azodolmolky, S., Klinkowski, M., Marin, E., Careglio, D., Pareta, J. S., & Tomkos, I. (2009). A survey on physical layer impairments aware routing and wavelength assignment algorithms in optical networks. Computer Networks, 53(7), 926–944.

    Article  Google Scholar 

  6. Beshir, A., Kuipers, F., Orda, A., & Van Mieghem, P. (2012). Survivable routing and regenerator placement in optical networks. In 4th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT) (pp. 684–690).

  7. Cabral, E., Erkut, E., Laporte, G., & Patterson, R. (2007). The network design problem with relays. European Journal of Operational Research, 180(2), 834–844.

    Article  Google Scholar 

  8. Chen, S., Ivana, L., & Raghavan, S. (2010). The regenerator location problem. Networks, 55(3), 205–220.

    Google Scholar 

  9. Cherubini, D., Fanni, A., Mereu, A., Frangioni, A., Murgia, C., Scutella, M., & Zuddas, P. (2011). Linear programming models for traffic engineering in 100% survivable networks under combined IS-IS/OSPF and MPLS-TE. Computers & Operations Research, 38(12), 1805–1815.

  10. Costa, A., Cordeau, J. F., & Gendron, B. (2009). Benders, metric and cutset inequalities for multicommodity capacitated network design. Computational Optimization and Applications, 42(3), 371–392.

    Article  Google Scholar 

  11. Dahl, G., & Stoer, M. (1998). A cutting plane algorithm for multicommodity survivable network design problems. INFORMS Journal on Computing, 10(1), 1–11.

    Article  Google Scholar 

  12. Dey, S. K., & Adhya, A. (2011). Dynamic connection allocation in WDM network with limited grooming and regeneration facilities. High Capacity Optical Networks and Enabling Technologies (HONET), 2011, 65–70.

    Article  Google Scholar 

  13. Frangioni, A., & Gendron, B. (2009). 0–1 reformulations of the multicommodity capacitated network design problem. Discrete Applied Mathematics, 157(6), 1229–1241.

    Article  Google Scholar 

  14. Gagnaire, M., & Zahr, S. (2009). Impairment-aware routing and wavelength assignment in translucent networks: State of the art. IEEE Communications Magazine, 47(5), 55–61.

    Article  Google Scholar 

  15. Garcia-Manrubia, B., Pavon-Marino, P., Aparicio-Pardo, R., Klinkowski, M., & Careglio, D. (2011). Offline impairment-aware RWA and regenerator placement in translucent optical networks. Journal of Lightwave Technology, 29(3), 265–277.

    Article  Google Scholar 

  16. Garg, M., & Smith, J. (2008). Models and algorithms for the design of survivable multicommodity flow networks with general failure scenarios. Omega, 36(6), 1057–1071.

    Article  Google Scholar 

  17. Huang, S., Martel, C., & Mukherjee, B. (2011). Survivable multipath provisioning with differential delay constraint in telecom mesh networks. IEEE/ACM Transactions on Networking, 19(3), 657–669.

    Article  Google Scholar 

  18. Katrinis, K., & Tzanakaki, A. (2011). On the dimensioning of WDM optical networks with impairment-aware regeneration. IEEE/ACM Transactions on Networking, 19(3), 735–746.

    Article  Google Scholar 

  19. Kewcharoenwong, P., & Uster, H. (2014). Benders decomposition algorithms for the fixed-charge relay network design in telecommunications. Telecommunication Systems, 56(4), 441–453.

    Article  Google Scholar 

  20. Klincewicz, J. (2006). Optimization issues in quality of service. In M. Resende & P. Pardalos (Eds.), Handbook of optimization in telecommunications (pp. 435–458). New York: Springer.

    Chapter  Google Scholar 

  21. Klinkowski, M. (2012). On the effect of regenerator placement on spectrum usage in translucent elastic optical networks. In 14th International Conference on Transparent Optical Networks (ICTON) (pp. 1–6).

  22. Konak, A. (2012). Network design problem with relays: A genetic algorithm with a path-based crossover and a set covering formulation. European Journal of Operational Research, 218(3), 829–837.

    Article  Google Scholar 

  23. Konak, A., Kulturel-Konak, S., & Smith, A. E. (2009). Two-edge disjoint survivable network design problem with relays. In J. Chinneck, B. Kristjansson, & M. Saltzman (Eds.), Operations research and cyber-infrastructure, operations research/computer science interfaces series (Vol. 47, pp. 279–292). New York: Springer.

  24. Laporte, G., & Pascoal, M. M. (2011). Minimum cost path problems with relays. Computers & Operations Research, 38(1), 165–173.

    Article  Google Scholar 

  25. Marin, A. (2005). Formulating and solving splittable capacitated multiple allocation hub location problems. Computers & Operations Research, 32(12), 3093–3109.

    Article  Google Scholar 

  26. Martinelli, F., Andriolli, N., Castoldi, P., & Cerutti, I. (2014). All-optical regenerator placement in WSON. In International Conference on Optical Network Design and Modeling (pp. 299–304).

  27. Martinelli, F., Andriolli, N., Castoldi, P., & Cerutti, I. (2014). Genetic approach for optimizing the placement of all-optical regenerators in WSON. Journal of Optical Communications and Networking, 6(11), 1028–1037.

    Article  Google Scholar 

  28. Pioro, M., Szentesi, A., Harmatos, J., Juttner, A., Gajowniczek, P., & Kozdrowski, S. (2002). On open shortest path first related network optimisation problems. Performance Evaluation, 48(1–4), 201–223.

    Article  Google Scholar 

  29. Rahman, Q., Bandyopadhyay, S., & Aneja, Y. (2015). Optimal regenerator placement in translucent optical networks. Optical Switching and Networking, 15, 134–147.

    Article  Google Scholar 

  30. Rajan, D., & Atamturk, A. (2004). A directed cycle-based column-and-cut generation method for capacitated survivable network design. Networks, 43(4), 201–211.

    Article  Google Scholar 

  31. Ramirez-Marquez, J., Rocco, S., & Claudio, M. (2009). Stochastic network interdiction optimization via capacitated network reliability modeling and probabilistic solution discovery. Reliability Engineering & System Safety, 94(5), 913–921.

    Article  Google Scholar 

  32. Santos, D., de Sousa, A., & Alvelos, F. (2013). A hybrid column generation with GRASP and path relinking for the network load balancing problem. Computers & Operations Research, 40(12), 3147–3158.

    Article  Google Scholar 

  33. Tipper, D. (2014). Resilient network design: Challenges and future directions. Telecommunication Systems, 56(1), 5–16.

    Article  Google Scholar 

  34. Tomaszewski, A. M., Pióro, M., & Zotkiewicz, M. (2010). On the complexity of resilient network design. Networks, 55(2), 108–118.

    Google Scholar 

  35. Truffot, J., & Duhamel, C. (2008). A branch and price algorithm for the \(k\)-splittable maximum flow problem. Discrete Optimization, 5(3), 629–646.

    Article  Google Scholar 

  36. Varvarigos, E., & Christodoulopoulos, K. (2014). Algorithmic aspects in planning fixed and flexible optical networks with emphasis on linear optimization and heuristic techniques. Journal of Lightwave Technology, 32(4), 681–693.

    Article  Google Scholar 

  37. Xu, D., Chiang, M., & Rexford, J. (2007). DEFT: Distributed exponentially-weighted flow splitting. In 26th IEEE International Conference on Computer Communications (INFOCOM 2007) (pp. 71–79).

  38. Xu, J., Chiu, S., & Glover, F. (1997). Tabu search for dynamic routing communications network design. Telecommunication Systems, 8(1), 55–77.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of International Logistics Management, Yasar University, Bornova, Izmir, 35100, Turkey

    Ozgur Kabadurmus

  2. Department of Industrial and Systems Engineering, Auburn University, Auburn, AL, 36849, USA

    Alice E. Smith

Authors
  1. Ozgur Kabadurmus
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alice E. Smith
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ozgur Kabadurmus.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kabadurmus, O., Smith, A.E. Multi-commodity k-splittable survivable network design problems with relays. Telecommun Syst 62, 123–133 (2016). https://doi.org/10.1007/s11235-015-0067-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11235-015-0067-9

Keywords

Search

Navigation