How Much Wavelength Conversion Allows a Reduction in the Blocking Rate

We study the problem of routing and wavelength assignment (RWA) in a WDM optical network under different hop assumptions, i.e., with and without wavelength converters, considering the objective of minimizing the blocking rate. We design a heuristic with two interactive phases, one for the routing and one for the wavelength assignment, which generalizes a previous algorithm by Noronha and Ribeiro [Eur. J. Oper. Res. 171, 797 (2006)] based on a Tabu Search scheme using a partition coloring reformulation for uniform traffic and single-hop connections. Considering nonuniform traffic, we explore a reformulation of the RWA problem as a generalized partition coloring problem and develop a Tabu Search algorithm to solve it. We also explore how to integrate multihop connections, with the addition of conversion features at some or at all optical nodes. Experiments are done on several traffic and network instances. Most heuristic solutions are excellent as illustrated by the very small gap between the values provided by the heuristic and the optimal values of the linear relaxation. We next show that conversion features, although often considered an added value, are of little help in improving on the blocking rate except for some very particular traffic instances, even on realistic network topologies.