Robust Solutions for the DWDM Routing and Provisioning Problem: Models and Algorithms

The dense wavelength division multiplexing routing and provisioning problem with uncertain demands and a fixed budget is modeled as a multicriteria optimization problem. To obtain a robust design for this problem, the primary objective is to minimize a regret function that models the total amount of over and/or under provisioning in the network resulting from uncertainty in a demand forecast. Point-to-point demands are given by a set of scenarios each with a known probability, and regret is modeled as a quadratic function. The secondary objective is to minimize the equipment cost that achieves the optimal value for regret. We propose a two-phase robust optimization strategy that uses a pair of integer linear programs having a large number of continuous variables, but only two integer variables for each link. In an empirical study, the two-phase robust optimization strategy is compared to alternative techniques using a mean-value model, a worst-case model, and a two-stage stochastic integer program with recourse model. Both the worst-case model and the stochastic programming model exhibited a bias toward low-cost designs (well below the budget) at the expense of high expected over/under provisioning. For a tight budget, the mean-value model fails miserably yielding no design for comparison. The two-phase robust strategy produces the optimal design for a given budget that is the best compromise between expected regret and equipment cost.