Backup path restoration design using path generation technique

In this work, we study 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 pair (nominal path, backup path) which are constructed in such a way that at least one of them is operational in any given failure situation for a flow. We present an approximate linear programming formulation of the problem and show how path generation technique (based on column generation) can be used to solve it. The path generation approach is an iterative method that allows us to add new path pairs based on dual Lagrangean multipliers in every iteration. We consider four different scenarios that differ in the way we compute and add new path pairs 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.