Abstract: The joint problem of selecting a route for each communicating node pair and a capacity value for each link in computer communication network is studied in this paper. Given the network topology and traffic characteristics as well as a set of candidate routes and a set of candidate capacities for each link, it is required to obtain the least costly feasible design where the costs include both capacity and queuing components. Genetic algorithms are used in order to obtain verifiable good solutions to the problem. This method has been tested on ARPA and RING. Extensive computational results indicate that the method is very effective.