Abstract
This paper deals with a ring-mesh network design problem arising from the deployment of an optical transport network. The problem seeks to find an optimal clustering of traffic demands in the network such that the total cost of optical add-drop multiplexer (OADM) and optical cross-connect (OXC) is minimized, while satisfying the OADM ring capacity constraint, the node cardinality constraint, and the OXC capacity constraint. We formulate the problem as an integer programming model and propose several alternative modeling techniques designed to improve the mathematical representation of the problem. We then develop various classes of valid inequalities to tighten the mathematical formulation of the problem and describe an algorithmic approach that coordinates tailored routines with a commercial solver CPLEX. We also propose an effective tabu search procedure for finding a good feasible solution as well as for providing a good incumbent solution for the column generation based heuristic procedure that enhances the solvability of the problem. Computational results exhibit the viability of the proposed method.
Similar content being viewed by others
References
Clouqueur, M., Grover, W., Leung, D., Shai, O.: Mining the rings: strategies for ring-to mesh evolution. Design of Reliable Communication Networks (DRCN 2001), Budapest, Hungry, October 2001
Glover, F., Laguna, M.: Tabu Search. Kluwer Academic, Boston (1997)
Goldschmidt, O., Laugier, A., Olinick, E.: SONET/SDH ring assignment with capacity constraints. Discret. Appl. Math. 129, 99–128 (2003)
Grover, W.D., Martens, R.: Combined ring-mesh optical transport network. Clust. Comput. 7, 245–258 (2004)
Kennington, J., Olinick, E., Orthynski, A., Spiride, G.: Wavelength routing and assignment in a survivable WDM mesh networks. Oper. Res. 51, 67–79 (2003)
Labbe, M., Yaman, H., Gourdin, E.: A branch and cut algorithm for hub location problems with single assignment. Math. Program. Ser. A 102, 371–405 (2005)
Lee, Y., Han, J., Kang, K.: A fiber routing problem in designing optical transport networks with wavelength division multiplexed systems. Photonic Netw. Commun. 5, 247–257 (2003)
Lee, Y., Sherali, H.D., Han, J., Kim, S.: A branch-and-cut algorithm for solving and intra-ring synchronous optical network design problem. Networks 35, 223–232 (2000)
Nemhauser, G., Wolsey, L.: Integer and Combinatorial Optimization. Wiley, New York (1988)
Sherali, H.D., Smith, J.C.: Improving discrete model representation via symmetry considerations. Manag. Sci. 47, 1394–1407 (2001)
Smith, J.C., Schaefer, A.J., Yen, J.W.: A stochastic integer programming approach to solving a synchronous optical network ring design problem. Networks 44, 290–3046 (2004)
Stidsen, T., Glenstrup, A.: Quantifying optimal mesh and ring design costs. Nav. Res. Logist. 51, 1–14 (2004)
Sutter, A., Vanderbeck, F., Wolsey, L.: Optimal placement of add/drop multiplexers: heuristic and exact algorithms. Oper. Res. 46(5), 719–728 (1998)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kim, Y., Lee, Y. & Han, J. A ring-mesh topology design problem for optical transport networks. J Heuristics 14, 183–202 (2008). https://doi.org/10.1007/s10732-007-9034-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10732-007-9034-2