Macro-Agent Evolutionary Model for decomposable function optimization

This paper analyzes the numerical optimization problems from the viewpoint of multiagent systems. First, Macro-Agent Evolutionary Model (MacroAEM) is proposed with the intrinsic properties of decomposable functions in mind. In this model, a subfunction forms a macro-agent, and 3 new behaviors, namely competition, cooperation, and selfishness, are developed for macro-agents to optimizing objective functions. Second, MacroAEM model is integrated with multiagent genetic algorithm, which results a new algorithm, Hierarchical MultiAgent Genetic Algorithm (HMAGA). The convergence of HMAGA is analyzed theoretically and the results show that HMAGA converges to the global optima. In experiments, HMAGA is applied to a kind of complicated decomposable function, namely Rosenbrock function. The results show that HMAGA achieves a good performance, especially for the high-dimensional functions. In addition, the analyses on time complexity demonstrate that HMAGA has a good scalability.