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Multi-agent modeling and simulation are crucial for many applications including military ones, such as battlefield modeling and simulation. In a dynamic time-varying environment multi-agent reinforcement learning for agent path-planning, where mobile agents and obstacles move randomly, becomes a challenging problem. This is due to the fact that what a given agent learned, during its past states in time, prior to achieving its current present state may become obsolete and irrelevant at the current agent state. This is due to the agent's time-varying changes in its dynamic time-varying environment. In particular, in such dynamic environment it is desired to have agent(s) not only be equipped with intelligence to avoid other agents and moving obstacles but also be able to learn the shortest path to the goal in a minimum amount of runs. This paper presents a reinforcement-learning-based technique which allows an agent (s) to converge to the shortest path in a small number of runs of two. We use a combination of potential field and reinforcement learning to solve this problem. When used alone these two approaches have their limitations. Here we propose an approach that we name “dissolving potential field” and “selective reinforcement learning” in a time-varying agent's environment. The paper describes a method based on these two approaches combined, such that it guides the agent(s) to accomplish its (their) goals in a dynamically varying and changing environment.