RWA in WDM rings: An efficient formulation based on maximal independent set decomposition

WDM rings are now capable of supporting more than 100 wavelengths over a single fiber. Conventional link and path formulations for the RWA problem are inefficient due to the inherent symmetry in wavelength assignment and the fact that the problem size increases fast with the number of wavelengths. Although a formulation based on maximal independent sets (MIS) does not have these drawbacks, it suffers from the exponential growth in the number of variables with the increasing network size. We develop a new ILP formulation based on the idea of partitioning the path set and representing the maximal independent sets in the original network using the independent sets calculated in each of these partitions. This formulation trades off the number of variables with the number of constraints and, as a result, achieves a much better scalability in terms of network dimension. The proposed approach is compared with existing formulations on ring networks of various sizes and it is demonstrated that the new formulation achieves more than two orders of magnitude decrease in running time, making it possible to (1) solve optimally large network instances for any number of wavelengths, which cannot be solved with classical formulations, and (2) perform extensive “what-if” analysis to evaluate the sensitivity of the optimal solutions to uncertainties in forecast traffic scenarios.