Finding the maximum flow in a flow network is a challenging task that has been dealt with in many algorithms; most of these algorithms are based on the Ford-Fulkerson method. Traditional methods for calculating the maximum flow often rely on static configurations in a network and may not be suited for complex networks that have changing demands. In this research, we propose an innovative approach to optimize edge capacities in a flow network; the goal is to maximize the flow in a flow network. We are integrating the Ford-Fulkerson method with the Moth-Flame Optimization (MFO) algorithm, which is a metaheuristic algorithm inspired by the moth’s behavior, to find optimal edge capacities and maximize the flow in a flow network. This integration allows a dynamic adjustment of edge capacities to achieve optimal network flow.