This paper formulates the network topology and capacity expansion problem in a telecommunications network and suggests a family of heuristics and a dual-based lower bounding procedure for solving it. They include schemes exploiting special subproblem structures, decomposition of the problem using Lagrangian relaxation, and a global search strategy. Carefully designed experiments show that the procedure generates solutions within forty percent of the lower bound in most cases. To evaluate the solution quality more accurately, additional experiments have been performed, using a random search strategy for the topological variables with capacity expansion optimized. It is shown that the global heuristic solutions dominate solutions that use the random search strategy for topological variables. Following the computational experiments, a tighter formulation is suggested which can improve the lower bounds. The paper concludes with a discussion of further research areas.