Multi-objective optimization design methods based on game theory

Abstract

The paper presents the game description of multi-objective optimization design problem and takes the design objectives as different players. By calculating the affecting factors of the design variables to objective functions and fuzzy clustering, the design variables are divided into different strategic spaces owned by each player. Then it uses Nash equilibrium game model, coalition cooperative game model and evolutionary game model to solve multi-objective optimization design problem and gives corresponding solving steps. According to the specific game model, a mapping relationship between the game players' payoff and the objective functions is proposed. Each player takes payoff function of its own as its objective and undertakes single-objective optimization in its own strategy space. Then this player obtains the best strategy versus other players. The best strategies of all players consist of the strategy permutation of a round game and it obtains the final game solutions through multi-round games according to the convergence criterion. Taking two objectives design of four bar joist rack structures for example, the results show that the computational precision of the coalition cooperative game model is the best ,which illustrates that cooperative game has the advantages over non-cooperative game in fulfilling polytropic win-win and collective benefit; while the coalition cooperative game model is the worst from the computational efficiency view, which shows that cooperation spends more time negotiating so as to obtain win-win; considering these factors comprehensively , evolutionary game model is better at computational precision and efficiency.