SOLVING CONSTRAINED OPTIMIZATION PROBLEMS USING PROBABILITY COLLECTIVES AND A PENALTY FUNCTION APPROACH

The best option to deal with a complex system that is too cumbersome to be treated in a centralized way is to decompose it into a number of sub-systems and optimize them in a distributed and decentralized way to reach the desired system objective. These sub-systems can be viewed as a multi-agent system (MAS) with self-learning agents. Furthermore, another challenge is to handle the constraints involved in real world optimization problems. This paper demonstrates the theory of probability collectives (PC) in the collective intelligence (COIN) framework, supplemented with a penalty function approach for constraint handling. The method of deterministic annealing in statistical physics, game theory and Nash equilibrium are at the core of the PC optimization methodology. Three benchmark problems have been solved with the optimum results obtained at reasonable computational cost. The evident strengths and weaknesses are also discussed to determine the future direction of research.