Solving the Capacitated Local Access Network Design Problem

We propose an exact solution method for a routing and capacity installation problem in networks. Given an input graph, the problem is to route traffic from a set of source nodes to a sink node and to install transmission facilities on the edges of the graph to accommodate the flow at minimum cost. We give a branch and bound algorithm that solves relaxations obtained by approximating the non-continuous cost function by its convex envelope. The approximations are refined by branching on the flow ranges on selected edges. Our computational experiments indicate that this method is effective in solving moderatesize problems and provides very good candidate solutions early in the branch and bound tree.