A Lagrangean decomposition approach for the routing and wavelength assignment in multifiber WDM networks

This paper addresses the problem of routing and wavelength assignment (RWA) in multifiber WDM networks assuming neither a special topology nor wavelength converters. Given a set of connection requests, the number of fibers deployed on each link, and the number of wavelengths a fiber can support, we seek to maximize the number of lightpaths that can be established. We formulate the problem as an integer linear program (ILP), whose validity is proven by showing that the selected lightpaths can indeed be realized by properly configuring the optical switches. Furthermore, using a Lagrangean decomposition approach, the problem formulation is significantly simplified. The main advantage of our approach is that, independent of the number of wavelengths, provably optimal solutions to the problem can be obtained by considering only one wavelength in the formulation, leading to highly efficient and scalable algorithms. Although our formulation is path-flow based rather than link-flow based, we prove that, even if all, possibly exponentially many, paths are considered, its linear programming (LP) relaxation can always be solved in polynomial time. We use the branch-and-bound algorithm in the CPLEX optimization package to solve the resulting ILP formulation. Computational results confirm the high efficiency of the Lagrangean decomposition approach.