A Hierarchical Optimization Algorithm Based on Self-organizing Evolutionary Game Model

Hierarchical optimization is utilized to address problems with varying levels of priority among decision makers. It has wide applications in supply chain management, resource allocation optimization, hierarchical production operations, and other domains. To accommodate the vast array of structures encountered in hierarchical optimization problems, this study introduces an innovative optimization framework based on self-organizing evolutionary game models. Initially drawing inspiration from the Nash game and the Stackelberg game, the priority relationship in hierarchical optimization problems is translated into the leader-follower relationship in the game model. Subsequently, optimization methods based on the evolutionary algorithm are proposed for both the Nash and Stackelberg games. Finally, a self-organized optimization framework grounded in the game models is presented, which can be extended to hierarchical optimization problems involving more than two layers and multiple decision makers in each layer. This framework enables adaptive adjustments for various types of hierarchical optimization problems. Based on the specific structure of the problem and the proposed framework, corresponding optimization algorithms can be developed. The experimental results demonstrate that algorithms based on this framework are adept at solving a wide range of hierarchical optimization problems and consistently yield satisfactory equilibrium solutions.