In the current industrial fields, automatic guided vehicles (AGVs) are widely employed to constitute the flexible manufacturing system (FMS), owing to their great advantages of routing flexibility and high efficiency. However, one main challenge lies in the coupling process of the design problem of the unidirectional guide-path network (UGN) and the task scheduling problem of AGVs. To reduce the complexity, most pertinent literatures only handle these problems one by one, based on the stepwise design methods, thereby neglecting the constraint conditions and the optimization objectives caused by the FMS environment. The motivation of the paper is to bring the coupling factors into the integrated design and solution process. Firstly, an integrated design model of designing UGN and scheduling AGVs simultaneously is proposed, with the objective of minimizing the makespan (i.e., the maximum completion time of all handling tasks), in the consideration of the practical constraints, e.g., the job handling and processing sequence constraints and the AGV number constraint. Secondly, a dual-population collaborative evolutionary genetic algorithm (CEGA) is developed to solve the problems of designing and scheduling in a parallel way. The solutions of the integrated model, i.e., the potential strongly connected UGN and the feasible processing and handling sequence, are, respectively, coded as two different subpopulations with independent and concurrent evolution processes. The neighbourhood search operation, the niche technique, and the elitism strategy are combined to improve the convergence speed and maintain the population diversity. The experimental results show that the integrated design model can formulate the problem more accurately, and the CEGA algorithm is computationally efficient with high solution quality.