A Lagrangean relaxation approach to the maximizing-number-of-connection problem in WDM networks

The emergence of WDM (wavelength-division multiplexing) technology has provided great convenience in designing a wavelength routing optical network. We study the routing and wavelength assignment (RWA) problem with the objective of maximizing the number of connections in an all-optical WDM network, where the physical topology and network resource, as well as the connection demand matrix, are given. The paper provides an effective approach with reasonable computational complexity and good performance to solve this problem. We employ a decomposition approach using Lagrangean relaxation (LR) to simplify the solution procedure. The overall problem is decomposed into semi-lightpath level subproblems for the decision of the rejection and the wavelength and route selection from source to destination. We propose the MMCSLP (modified minimum cost semi-lightpath) algorithm to solve the specific form of the subproblem. At the higher level, Lagrange multipliers are updated iteratively by a subgradient method. Also, a heuristic algorithm is proposed to generate a feasible RWA scheme based on the dual solution. The performance of this approach on sample networks is compared with other recently proposed methods. The optimization results indicate that our algorithm can achieve a very good near-optimum solution, and it shows a great advantage in computational complexity.