Compact ILP formulations for the routing and wavelength assignment problem in the design of optical transport networks with regenerators

This paper addresses two variants of the routing and wavelength assignment problem arising in the context of optical transport networks. In both variants, we address the case where the physical coverage of the fiber network is such that regenerators, to be placed on intermediate nodes of the lightpaths, have to be used to reach full connectivity between network nodes. In the first variant, we aim to minimize the solution cost given by the sum of the costs of all electrical–optical–electrical converter components. In the second variant, among all minimum cost solutions, we aim to optimize the network load balancing by minimizing the highest assigned wavelength. For each problem variant, we start by defining a basic integer linear programming compact formulation. Then, we improve each formulation using variable reformulation and variable elimination techniques. Finally, we present computational results showing that the reformulated formulations with variable elimination let us obtain provable optimal solutions for problem instances of relevant size within reasonable runtimes.