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The approach of PC optimizes any complex system by decomposing it into smaller subsystems and further treats them in a distributed and decentralized way. These subsystems can be viewed as a Multi\u2010Agent System with rational and self\u2010interested agents optimizing their local goals. However, as there is no inherent constraint handling capability in the PC approach, a real challenge is to take into account constraints and at the same time make the agents work collectively avoiding the tragedy of commons to optimize the global\/system objective. At the core of the PC optimization methodology are the concepts of Deterministic Annealing in Statistical Physics, Game Theory and Nash Equilibrium. Moreover, a rule\u2010based procedure is incorporated to handle solutions based on the number of constraints violated and drive the convergence towards feasibility. Two specially developed cases of the Circle Packing Problem with known solutions are solved and the true optimum results are obtained at reasonable computational costs. 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