Recently robots have gained great attention due to their ability to operate in dynamic and complex environments with moving obstacles. The path planning of a moving robot in a dynamic environment is to find the shortest and safe possible path from the starting point towards the desired target point. A dynamic environment is a robot's environment that consists of some static and moving obstacles. Therefore, this problem can be considered as an optimization problem and thus it is solved via optimization algorithms. In this paper, three approaches for determining the optimal pathway of a robot in a dynamic environment were proposed. These approaches are; the particle swarming optimization (PSO), ant colony optimization (ACO), and hybrid PSO and ACO. These used to carry out the path planning tasks effectively. A set of certain constraints must be met simultaneously to achieve the goals; the shortest path, the least time, and free from collisions. The results are calculated for the two algorithms separately and then that of the hybrid algorithm is calculated. The effectiveness and superiority of the hybrid algorithm were verified on both PSO and ACO algorithms.