This paper describes a general approach to the optimal design of communications networks when considering both economics and reliability. The approach uses a genetic algorithm to identify the best topology of network arcs to collectively meet cost and network reliability considerations. This approach is distinct because it is highly flexible and can readily solve many versions of the network design problem, including formulations not previously seen in the literature that more closely reflect actual design scenarios. The method is shown to be effective, computationally efficient and flexible on a suite of diverse test problems.