Backup Path Restoration Design using Path Generation Technique

In this work, we present a flow restoration based network design problem where we assume the knowledge of possible failure situations. We use the idea of a situation disjoint path couple (nominal path, backup path) which are constructed in such a way that atleast one of them is operational in any given failure situation for a flow. We present a linear programming formulation of the problem and use path generation technique (based on column generation) to solve the same for large networks. The path generation approach is an iterative method that allows us to add path couples with greater discretion, based on dual Lagrangean multipliers in every iteration. We consider four different scenarios that differ in the way we compute and add new path couples at every iteration. We present the results of our approach for an example network. From our observations, we conclude that path generation approach is an effective method to solve the backup path restoration design problem.