Relax-and-Cut for Capacitated Network Design

We present an evaluation of a Lagrangean-based branch-and-bound algorithm with additional valid inequalities for the capacitated network design problem. The focus is on two types of valid inequalities, the cover inequalities and local cuts. We show how these inequalities can be considered in a Lagrangean relaxation without destroying the computationally simple structure of the subproblems. We present an extensive computational study on a large set of benchmark data. The results show that the presented algorithm outperforms many other exact and heuristical solvers in terms of running time and solution quality.