The application of evolutionary games on complex networks has made a great difference. In this paper, an optimized evolutionary game method based on public goods games (PGG) is put forward to describe and evaluate time-varying mixed membership networks. Considering the heterogeneous topology, a new preferential rule is proposed to quantify the process of choosing and updating the payoff of individuals in the public goods games. Each individual is allocated with a weight to restrict the influence. The optimal parameter is obtained by minimizing the entropy of nodes topological potential, an efficient way to depict the effect among individuals, which is inspired by Gaussian potential of data field. It demonstrates that an appropriate constraint on individuals does make it more like to approach to the reality, and when it comes to specific conditions, the proposed model achieves well performance.