Virtual Nash optimization algorithms inspired by the balance between blocking the interference among design variables and motivating their coordinated development
摘要
Mutual interference among large-scale design variables can have a large impact on both optimization efficiency and the quality of the optimal solution. The authors of this paper have investigated the effects of design variables with different characteristics. It is found in this paper that even variables with the same characteristics can strongly interfere with each other in the optimization process. An approach to block the interference among variables is proposed by introducing the virtual Nash equilibrium to divide the variables into different groups in the optimization and to isolate the interference among optimization variables in different groups. Detailed virtual Nash optimization algorithms are also provided and the characteristics and essence of the virtual Nash equilibrium solution are discussed. Furthermore, by reasonably controlling two parameters in the algorithm, i.e., the number of subgroups and the frequency of elite information exchange, the mechanism by which the method of this paper improves the optimization efficiency is reasonably explained, i.e., reasonably adjusting the balance between blocking the interference among variables and enhancing the coordinated development of variables is the key point for improving the optimization efficiency. Once this balance is disrupted, the efficiency becomes poor instead. Finally, it was used to solve the inverse design of three-dimensional aerodynamic shapes to verify the efficiency of the algorithm and the effectiveness of theoretical analysis in this paper.