Resolution of a WDM network design problem using a decomposition approach and a size reduction method

Multicommodity flow models have been proposed in the literature to formulate different network design problems as Mixed Integer Linear Programming (MILP) problems. The formulations are important because there are algorithms that find the optimal solution to these problems. However, MILP problems are NP-hard, which makes the solution of design problem instances of non trivial size numerically intractable. In this article we propose a method to tackle the inherent complexity of a WDM network design problem formulated as a multicommodity flow problem. The method allows to solve WDM network design problems of medium size. We first decompose the design problem into two subproblems that can be solved separately. Multicommodity flow models are used to formulate each subproblem as a MILP problem. We then prune the variables' space associated to each subproblem by eliminating from the formulation useless variables. The solution to the design problem is obtained by solving the subproblems sequentially. To take into account the dependency between subproblems, we introduce a feedback mechanism to exchange information between the algorithms that solve the subproblems.