This paper considers the problem of designing a network to transport material from sources of supply to sites where demand occurs. However, the demand at each site is uncertain. We formulate the problem as a robust discrete optimization problem. The minimax objective is to find a robust solution that has the best worst-case performance over a set of possible scenarios. However, this is a difficult optimization problem. This paper describes a two-space genetic algorithm that is a general technique to solve such minimax optimization problems. This algorithm maintains two populations. The first population represents solutions. The second population represents scenarios. An individual in one population is evaluated with respect to the individuals in the other population. The populations evolve simultaneously, and they converge to a robust solution and a worst-case scenario. Experimental results show that the two-space genetic algorithm can find robust solutions to the minimax network design problem. Since robust discrete optimization problems occur in many areas, the algorithm will have a wide variety of applications.