Efficient and scalable design of Protected Working Capacity Envelope

The Protected Working Capacity Envelope (PWCE) concept was proposed by Grover (2004) in order to simplify network and operation management in survivable WDM networks. In this paper, we focus on PCWE with p-cycles and investigate a new design method, highly efficient and scalable, for designing survivable WDM networks. Traditional design methods proceed in two steps: A first step where a large (sometimes huge) number of cycles is enumerated followed by a second step where the selection of the most promising p-cycles is made with the help of combinatorial optimization tools. We develop a new (single step) method based on large scale optimization tools, i.e., column generation techniques, where the generation of cycles is dynamic and embedded within the optimization process. The key advantage of column generation (CG) techniques is that no a priori cycle enumeration step is required ahead of the optimization process: The generation of the relevant cycles, only one or few at a time, is embedded in the optimization process. We conducted intensive computational experiments. Not only do we considered several network instances with quite different topology characteristics, but we also compared our CG-based model and solution method with several existing models and methods from the literature. Results obtained in the experiments on five different network instances, show that the CG-based model and method outperform by far the results of all previous studies, both with respect to the scalability (much smaller computing times for large network instances) but also with respect to the quality of the solutions.