Probability Collectives: A multi-agent approach for solving combinatorial optimization problems

Complex systems generally have many components. It is not possible to understand such complex systems only by knowing the individual components and their behavior. This is because any move by a component affects the further decisions/moves by other components and so on. In a complex system, as the number of components grows, complexity also grows exponentially, making the entire system to be seen as a collection of subsystems or a Multi-Agent System (MAS). The major challenge is to make these agents work in a coordinated way, optimizing their local utilities and contributing the maximum towards optimization of the global objective. This paper discusses the theory of Collective Intelligence (COIN) using the modified version of Probability Collectives (PC) to achieve the global goal. The paper successfully demonstrated this approach by optimizing the Rosenbrock function in which the coupled variables are seen as autonomous agents working collectively to achieve the function optimum. To demonstrate the PC approach on combinatorial optimization problems, two test cases of the Multi-Depot Multiple Traveling Salesmen Problem (MDMTSP) with 3 depots, 3 vehicles and 15 nodes are solved. In these cases, the vehicles are considered as autonomous agents collectively searching the minimum cost path. PC is successfully accompanied with insertion, elimination and swapping heuristic techniques. The optimum results to the Rosenbrock function and both the MDMTSP test cases are obtained at reasonable computational costs.