A Game-Theoretic Equilibrium Optimization Model for Collaborative Manufacturing Systems
Keywords:
Game theory, nash equilibrium, variational inequality, equilibrium optimization, multi-agent systems, collaborative manufacturing.Abstract
Equilibrium optimization in collaborative decision making of distributed systems entails complicated interactions between various agents having different objectives and constrained by common resources. In this paper, an optimization game-theoretic framework based on equilibrium analysis is proposed. Based on the Nash equilibrium concept, a novel formulation of equilibrium analysis is derived that turns the equilibrium concept into a variational inequality problem to enable theoretical analysis of the solution existence, uniqueness, and convergence. An equilibrium-based projected iterative approach is devised to find the optimal solution subject to feasibility constraints. Mathematical properties of the proposed framework are investigated from the point of view of equilibrium theory. The effectiveness of the proposed framework is evaluated based on numerical analysis using collaborative manufacturing decision-making as an example. Multiple agents are considered to find optimal resource allocation strategies while operating under dynamic circumstances. The numerical evaluation shows better convergence properties, fewer optimization conflicts, and better resource collaboration than other optimization frameworks.
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