Automatic guided vehicle system (AGVs) plays a vital role in material handling operations for a flexible manufacturing system (FMS).Optimum AGVs fleet size selection is one of the most sig-nificant decisions in effective design and control of automated material handling system. The fleet size estimation and optimization of AGVs requires an in-depth understanding of the various factors that AGVs in the FMS relies on. In this paper, an investigation for fleet size optimization of AGVs in different layouts of FMS by application of the analytical method and grey wolf optimization al-gorithm (GWO) is carried out. Layout design is one of the significant factors for optimization of AGV’s fleet size in any FMS. Results yield from analytical and grey wolf optimization algorithm are compared and validated for the different sizes of FMS layouts by computational experiments.