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Particle swarm optimization (PSO) has the disadvantages of easily getting trapped in local optima and a low search accuracy. Scores of approaches have been used to improve the diversity, search accuracy, and results of PSO, but the balance between exploration and exploitation remains sub-optimal. Many scholars have divided the population into multiple sub-populations with the aim of managing it in space. In this paper, a multi-stage search strategy that is dominated by mutual repulsion among particles and supplemented by attraction was proposed to control the traits of the population. From the angle of iteration time, the algorithm was able to adequately enhance the entropy of the population under the premise of satisfying the convergence, creating a more balanced search process. The study acquired satisfactory results from the CEC2017 test function by improving the standard PSO and improved PSO.

The swarm intelligence algorithm has become an important method to solve optimization problems because of its excellent self-organization, self-adaptation, and self-learning characteristics. However, when a traditional swarm intelligence algorithm faces high and complex multi-peak problems, population diversity is quickly lost, which leads to the premature convergence of the algorithm. In order to solve this problem, dimension entropy is proposed as a measure of population diversity, and a diversity control mechanism is proposed to guide the updating of the swarm intelligence algorithm. It maintains the diversity of the algorithm in the early stage and ensures the convergence of the algorithm in the later stage. Experimental results show that the performance of the improved algorithm is better than that of the original algorithm.

The reconnection of broken edges is an effective way to avoid drawback for the commons in past studies. Inspired by this, we proposed a public goods game model under the edges rules, where we evaluate the weight of edges by their nodes’ payoff. The results proved that the game obtains a larger range of cooperation with a small gain factor by this proposed model by consulting Monte Carlo simulations (MCS) and real experiments. Furthermore, as the following the course of game and discussing the reason of cooperation, in the research, we found that the distribution entropy of the excess average degree is able to embody and predict the presence of cooperation.