Design process of a robust flow-path network for automated guided vehicle (AGV) systems is proposed in this paper. An effectiveness of a system with a robust flow-path network does not sink against any task. However, for this robust flow-path, the number of possible tasks is very large in AGV systems, therefore it is impossible to test the promising flow-path network against all of possible tasks. The problem is solved by the method of difficult task design with genetic algorithm (GA). The effective flow-path network is designed with GA simultaneously, because the difficult tasks depend on the flow-path networks. Competitive co-evolution is applied to the simultaneous design. Results of the designing are shown through simulations and the designed flow-path network makes it possible to complete 10000 tasks that are generated randomly.