Probability Collectives: A distributed optimization approach for constrained problems

A complex system may be controlled and optimized in a more efficient and manageable fashion by treating it as a distributed Multi-Agent System (MAS). But the major challenge in such an approach is to make the agents work in a coordinated way to optimize the system objective via optimizing their individual local goals. This paper describes the modified Probability Collectives (PC) as an evolutionary and distributed approach to achieve the system objective. The approach is validated solving a combinatorial optimization problem such as the Single Depot Multiple Traveling Salesmen Problem (MTSP). Moreover, as constraint handling in evolutionary systems has remained a challenge for years, an effort towards developing a generalized technique incorporating constraints into the PC approach is also attempted. It is validated by solving the practical problem of a spring design. The optimum results are obtained at a reasonable computational cost.