Flexible Manufacturing Systems (FMS) are advanced production environments integrating automated machine tools and material handling devices such as mobile robots with the aim to form a high efficiency, flexibility and adaptability production system. In FMS, material handling system is crucial to ensure the production flow to be in high efficiency. The problem of achieving efficient scheduling in FMS is considered a challenging combinatorial optimization problem which mainly caused by asymmetric travel times, machine and mobile robot constraints and precedence constraints. This paper investigates the metaheuristic approaches consist of Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) to solve the scheduling problem of dual mobile robot system in a Job-Shop FMS environment. The scheduling algorithms are formulated with the objective to achieve a minimal completion time (or makespan) while maintaining the order of task execution and transportation task by mobile robots. Multiple layouts were applied to both algorithms for evaluation and analysis purposes. The results have indicated that GA delivered a better performance in terms of providing a solution with lover makespan whereas PSO demonstrated faster convergence with minimized computational times.