Comparison of ILP formulations for the RWA problem

We present a review of the various integer linear programming (ILP) formulations that have been proposed for the routing and wavelength assignment problem in WDM optical networks with a unified and simplified notation under asymmetrical assumptions on the traffic. We show that all formulations proposed under asymmetrical traffic assumptions, both link and path formulations, are equivalent in terms of the upper bound value provided by the optimal solution of their linear programming relaxation, although their number of variables and constraints differ. We also propose some improvements for some of the formulations that result in the elimination of potential looping lightpaths and lead to further reductions in the number of variables and constraints. We next discuss the easiness of adding a constraint on the number of hops (i.e., how to take into account the node/link attenuating effect) depending on the formulations. Under the objective of minimizing the blocking rate, we propose an experimental comparison of the best lower and upper bounds that are available. We then discuss the easiness of exact ILP solution depending on the formulations. We solve exactly for the first time some RWA (Routing and Wavelength Assignment) instances, including those proposed by Krishnaswamy and Sivarajan (2001), with a proof of the optimality. The conclusion is that LP relaxations bounds often provide solutions with a value very close to the optimal ILP one.