Primary/Secondary Path Generation Problem: Reformulation, Solutions and Comparisons

This paper considers the primary and secondary path generation problem in traffic engineering. We first present a standard MILP model. Since its size and integrality gap are very large, we then apply a Benders decomposition to isolate the failure case capacity constraints, related linearisation variables and linearisation constraints. The disaggregated Benders cuts are generated, which is actually the set of violated failure case capacity constraints with their linearisation variables and the required linearisation constraints. This corresponds to adding the failure case capacity constraints, their linearisation variables and linearisation constraints only as they are needed. Some results on generated test cases for different network topologies are given. In comparison with the standard MILP formulation, we reduce execution times on average by a factor of 1000 using the Benders decomposition. We also compare with a scheme of accepting demands one-by-one, which can handle more large-scale problems at the cost of loosing optimality.