Design of Hierarchical Ring-Mesh Optical Networks Considering Cabling Cost

케이블 비용을 고려한 링메쉬 구조의 광통신망 설계

  • Han, Jung-Hee (Department of Business Administration, Kangwon National University)
  • 한정희 (강원대학교 경영대학 경영학과)
  • Received : 2009.01.11
  • Accepted : 2010.05.13
  • Published : 2010.05.31


In this paper, we deal with a hierarchical ring-mesh optical network design problem. The objective is to minimize the total cost of optical add-drop multiplexers (OADMs) handling intra-ring traffic, optical cross-connects (OXCs) handling inter-ring traffic, and cabling cost among OADMs and among OXCs, while satisfying intra-ring and inter-ring capacities. We develop an integer programming (IP) formulation for the problem and devise some cutting planes that partially break the symmetry of rings. Dealing with the inherent computational complexity of the problem, we devise an effective heuristic procedure that finds a good quality feasible solution within reasonable computing times. Computational results demonstrate the efficacy of the proposed solution procedure; the developed symmetry breaking inequalities significantly reduce the computing time to find an optimal solution for small size problems, and the heuristic procedure finds a better feasible solution than that CPLEX, a commercial optimization software, finds for large size problems.


  1. Sherali, H. D., J. C. Smith, and Y. H. Lee, "Enhanced model representation for an intra-ring SONET design problem allowing demand splitting", INFORMS Journal on Computing, Vol. 12, pp. 284-298, 2000.
  2. Thomadsen, T. and T. Stidsen, "Hierarchical ring network design using branch-and-price", Telecommunication Systems, Vol. 29, pp. 61-76, 2005.
  3. Wang, J., W. Cho, and B. Mukherjee, "Improved approaches for cost-effective traffic grooming in WDM ring networks: non-uniform traffic and bi-directional ring", IEEE/OSA Journal of Lightwave Technology, Vol. 19, pp. 1645-1653, 2001.
  4. Aringhieri, R. and M. Dell''Amico, "Comparing metaheuristic algorithms for SONET network design problems", Journal of Heuristics, Vol. 11, pp. 35-57, 2005.
  5. Chang, M. and S. Chang, "A heuristic method for self-healing ring design in a single-homing cluster", Telecommunication Systems, Vol. 14, pp. 175-195, 2000.
  6. Cho, W., J. Wang, and B. Mukherjee, "Improved approaches for cost-effective traffic grooming in WDM ring networks: uniform-traffic case", Photonic Network Communications, Vol. 3, pp. 245-254, 2001.
  7. Chung, S, H. Kim, Y. Yoon, and D. Tcha, "Cost-minimizing construction of a unidirectional SHR with diverse protection", IEE/ACM Transactions on Networking, Vol. 4, pp. 921- 928, 1996.
  8. Fortz, B, P. Soriano, and C. Wynants, "A tabu search algorithm for self-healing ring network design", European Journal of Operational Research, Vol. 151, pp. 280-295, 2003.
  9. Gerstel, O., R. Ramaswami, and G. Sasaki, "Cost-effective traffic grooming in WDM rings", IEEE/ACM Transactions on Networking, Vol. 8, pp. 618-630, 2000.
  10. Goldschmidt, O., A. Laugier, and E. Olinick, "SONET/SDH ring assignment with capacity constraints", Discrete Applied Mathematics, Vol. 129, pp. 99-128, 2003.
  11. Grover, W. and R. Martens, "Combined ring-mesh optical transport networks", Cluster Computing, Vol. 7, pp. 245-258, 2004.
  12. Kang, D., K. Lee, S. Park, K. Park, and S. Kim, "Design of local networks using USHRs", Telecommunication Systems, Vol. 14, pp. 197- 217, 2000.
  13. Kim, Y., Y. Lee, and J. Han, "A ring-mesh topology design problem for optical transport network", Journal of Heuristics, Vol. 14, pp. 83- 202, 2008.
  14. Lee C. and S. Koh, "Assignment of add-drop multiplexer rings and digital cross-connect systems mesh in telecommunication networks", Journal of the Operational Research Society, Vol. 52, pp. 440-448, 2001.
  15. Lee Y., H. Sherali, J. Han, and S. Kim, "A branch-and-cut algorithm for solving an intra-ring SONET design problem", Networks, Vol. 35, pp. 223-232, 2000.<223::AID-NET6>3.0.CO;2-J