Organization of an agents' formation through a cellular automaton

The article deals with the algorithm for a distributed organization of the agents' formation defined by a graph and the numerical simulation of such algorithm. Agents move through terrain with many random obstacles (“random landscape”). At first, we describe the continuous statement of the two-criteria minimization problem. The first criterion is the agent's route time. The second criterion is the closeness of agents' formation to the desired one. Next, we introduce a cellular automaton simulating the movement of agents for obtaining quasi-optimal solutions of the problem. The cellular automaton has one-dimensional and two-dimensional representations. Agents use reflexion to predict the motion of other agents. Then we compare obtained solutions with optimal ones for different types of random landscapes via numerical experiment. At this point, we obtain the empirical distribution for the time of an agent's exit to finish point. Finally, we find the relation between a type of random landscape through which agents move and the quality of agents' formation.