Comparison of ILP formulations for the RWA problem

Abstract

We present a review of the integer linear programming (ILP) formulations that have been proposed for the routing and wavelength assignment problem in WDM optical networks assuming asymmetrical 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 widely differ. We propose improvements for some of the formulations that result in further reductions in the number of variables and constraints. 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 observe that LP relaxation bounds often provide solutions with a value very close to the optimal ILP one. We solve exactly for the first time several RWA (Routing and Wavelength Assignment) realistic instances, including those proposed by Krishnaswamy and Sivarajan [R. Krishnaswamy, K. Sivarajan, Algorithms for routing and wavelength assignment based on solutions of LP-relaxation, IEEE Communications Letters 5 (10) (2001) 435–437], with a proof of the optimality.