Abstract
In translucent networks, signal regenerators that operate based on optical/electrical/optical (O/E/O) conversion are employed to handle the problems of physical impairments and resulting signal quality issues in long-distance transmissions. Regenerators are placed at the relay nodes in a translucent network in such a way that the optical signals are not transmitted farther than a threshold distance without a 3R regeneration (reamplification-reshaping-retiming).
In this study, we consider a fixed-charge relay network design (FCRND) problem whose applications are found mainly in long distance translucent optical telecommunication networks. From a modeling perspective, FCRND combines prominent features of the uncapacitated single-assignment hub location (location of relays points) and the fixed-charge network design problems (choice of transmission links in the network and routing of signals) while additionally considering distance-based coverage constraints. We devise Benders decomposition based solution methodologies in which the algorithmic performance is further enhanced by devising strengthened and disaggregated Benders cuts, surrogate constraints for the master problem, and an upper bound heuristic to both obtain and tighten optimality Benders cuts. We obtain solutions within 2.0 % of optimality in very reasonable times as we illustrate in our computational study.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Balakrishnan, A., Magnanti, T. L., & Mirchandani, P. (1997). Network design in annotated bibliographies in combinatorial optimization. In M. Dell’ Amico, F. Maffioli, & S. Martello (Eds.), Annotated bibliographies in combinatorial optimization (pp. 331–334). New York: Wiley.
Barnhart, C., Hane, C. A., Johnson, E. L., & Sigismondi, G. (1994). A column generation and partitioning approach for multi-commodity flow problems. Telecommunications Systems, 3, 239–258.
Benders, J. F. (1962). Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik, 4, 238–252.
Birkan, G., Kennington, J., Olinick, E., Ortynski, A., & Spiride, G. (2006). Practical integrated design strategies for opaque and all-optical DWDM networks: optimization models and solution procedures. Telecommunications Systems, 31, 61–83.
Cabral, E. A., Erkut, E., Laporte, G., & Patterson, R. A. (2007). The network design problem with relays. European Journal of Operational Research, 180(2), 834–844.
Cabral, E. A., Erkut, E., Laporte, G., & Patterson, R. A. (2008). Wide area telecommunication network design: application to the Alberta supernet. Journal of the Operational Research Society, 59(11), 1460–1470.
Campbell, J. F., Ernst, A. T., & Krishnamoorthy, M. (2002). Hub location problems. In Z. Drezner & H. W. Hamacher (Eds.), Facility location: applications and theory (pp. 373–407). New York: Springer.
Chen, S., Ljubić, I., & Raghavan, S. (2010). The regenerator location problem. Networks, 55, 205–220.
Flammini, M., Spaccamela, A. M., Monaco, G., Moscardelli, L., & Zaks, S. (2009). On the complexity of the regenerator placement problem in optical networks. In Proceedings of the twenty-first annual symposium on parallelism in algorithms and architectures, SPAA’09, New York, NY, USA (pp. 154–162). New York: ACM.
Geoffrion, A. M., & Graves, G. W. (1974). Multicommodity distribution system design by Benders decomposition. Management Science, 20(5), 822–844.
Kim, S. W., & Seo, S. W. (2001). Regenerator placement algorithms for connection establishment in all-optical networks. IEE Proceedings. Communications, 148(1), 25–30.
Mach, P., Bestak, R., & Becvar, Z. (2013). Optimization of association procedure in WiMAX networks with relay stations. Telecommunications Systems, 52(3), 1697–1704.
Magnanti, T. L., & Wong, R. T. (1981). Accelerating Benders decomposition: algorithmic enhancement and model selection. Operations Research, 29(3), 464–484.
Mateus, G., & Franqueira, R. (2000). Model and heuristic for a generalized access network design problem. Telecommunications Systems, 15, 257–271.
Sarkar, S., Yen, H. H., Dixit, S., & Mukherjee, B. (2009). Hybrid wireless-optical broadband access network (woban): network planning using Lagrangian relaxation. IEEE/ACM Transactions on Networking, 17(4), 1094–1105.
Shen, G., & Tucker, R. S. (2007). Translucent optical networks: the way forward [topics in optical communications]. IEEE Communications Magazine, 45(2), 48–54.
Simmons, J. M. (2006). Network design in realistic all-optical backbone networks. IEEE Communications Magazine, 44, 88–94.
Simmons, J. M. (2008). Optical network design and planning. Berlin: Springer.
Üster, H., & Kewcharoenwong, P. (2010). Strategic design and analysis of a relay network in truckload transportation. Transportation Science, 45(4), 505–523. 2011.
Üster, H., & Maheshwari, N. (2007). Strategic network design for multi-zone truckload shipments. IIE Transactions, 39(2), 177–189.
Yang, X., & Ramamurthy, B. (2002). Dynamic routing in translucent wdm optical networks. In IEEE international conference on communications, 2002, ICC 2002 (vol. 5, pp. 2796–2802).
Yang, X., & Ramamurthy, B. (2005). Sparse regeneration in translucent wavelength-routed optical networks: architecture, network design and wavelength routing. Photonic Network Communications, 10, 39–53.
Acknowledgements
The authors thank the anonymous associate editor and two referees for their helpful comments on earlier versions of this paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kewcharoenwong, P., Üster, H. Benders decomposition algorithms for the fixed-charge relay network design in telecommunications. Telecommun Syst 56, 441–453 (2014). https://doi.org/10.1007/s11235-013-9763-5
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11235-013-9763-5