In this paper, we present a traffic grooming problem of the SONET-WDM ring. The objective is to minimize the total cost of optical add-drop multiplexers (OADMs) and inter-ring hub equipment, while satisfying intra-ring and inter-ring capacities. We develop integer programming (IP) formulations for the problem and devise some reformulations for enhancing the mathematical representation of the proposed IP model. By investigating the polyhedral structure of the problem, we develop some valid inequalities that provide a tight lower bound for the problem. Dealing with the inherent computational complexity of the problem, we also devise an effective tabu search procedure for finding a feasible solution of good quality within reasonable computation time. Computational results are provided to demonstrate the relative strength of the proposed formulations, and to reveal the efficacy of the lower and upper bound procedures for solving the problem.
SONET-WDM ring Traffic grooming Integer programming Tabu search
This is a preview of subscription content, log in to check access.
Haupt, R.L., Haupt, S.E.: Practical Genetic Algorithms. John Wiley & Sons (2004)Google Scholar
Kang D., Lee K., Park S., Park K. and Kim S. (2000). Design of local networks using USHRs. Telecommun. Syst. 14: 197–217
Klincewicz J.G. (1998). Hub location in backbone/tributary network design: A review. Location Sci. 6: 307–333
Laguna, M., Marti, R.: Scatter Search: Methodology and Implementations in C. Kluwer Academic Publisher (2003)Google Scholar
Lee Y.H., Sherali H.D., Han J.H. and Kim S.I. (2000). A branch-and-cut algorithm for solving an intra-ring SONET design problem. Networks 35: 223–232
Martello S. and Toth P. (1990). Knapsack Problems: Algorithms and Computer Implementations. John Wiley & Sons, New York
Nemhauser G. and Wolsey L.A. (1988). Integer and Combinatorial Optimization. John Wiley & Sons, New York
Ramaswami R. and Sivarajan K.N. (1998). Optical Networks: A Practical Perspective. Morgan Kaufman Publishers, California
Sherali H.D., Smith J.C. and Lee Y.H. (2000). Enhanced model representation for an intra-ring SONET design problem allowing demand splitting. INFORMS J. Comput. 12: 284–298
Thomadsen T. and Stidsen T. (2005). Hierarchical ring network design using branch-and-price. Telecommun. Syst. 29: 61–76
Wang J., Cho W. and Mukherjee B. (2001). Improved approaches for cost-effective traffic grooming in WDM ring networks: non-uniform traffic and bi-directional ring. IEEE/OSA J. Lightwave Technol. 19: 1645–1653