This paper explores the use of genetic algorithms for the design of networks, where the demands on the network fluctuate in time. For varying network constraints, we find the best network using the standard genetic algorithm operators such as inversion, mutation and crossover. We also examine how the choice of genetic algorithm operators affects the quality of the best network found. Such networks typically contain redundancy in servers, where several servers perform the same task and pleiotropy, where servers perform multiple tasks. We explore this trade-off between pleiotropy versus redundancy on the cost versus reliability as a measure of the quality of the network.