In this dissertation, we propose the study of a family of network design problems that arise in a wide range of practical settings ranging from telecommunications to data management. We investigate the use of heuristic search procedures coupled with lower bounding mechanisms to obtain high quality solutions for deterministic, stochastic and robust variants of these problems. We extend the use of well-known methods such as the sample average approximation for stochastic optimization and the Bertsimas and Sim approach for robust optimization with heuristics and lower bounding mechanisms. This is particular important for NP-complete problems where even deterministic and small instances are difficult to solve to optimality. Our extensions provide a novel way of applying these techniques while using heuristics; which from a practical perspective increases their usefulness.