An interior-point Benders based branch-and-cut algorithm for mixed integer programs

We present an interior-point branch-and-cut algorithm for structured integer programs based on Benders decomposition and the analytic center cutting plane method (ACCPM). We show that the ACCPM based Benders cuts are both pareto-optimal and valid for any node of the branch-and-bound tree. The valid cuts are added to a pool of cuts that is used to warm-start the solution of the nodes after branching. The algorithm is tested on two classes of problems: the capacitated facility location problem and the multicommodity capacitated fixed charge network design problem. For the capacitated facility location problem, the proposed approach was on average 2.5 times faster than Benders-branch-and-cut and 11 times faster than classical Benders decomposition. For the multicommodity capacitated fixed charge network design problem, the proposed approach was 4 times faster than Benders-branch-and-cut while classical Benders decomposition failed to solve the majority of the tested instances.