Abstract—The collective intelligent behaviors of insects or animal groups in nature have maintained the survival of the species for thousands of years. In this paper, a novel swarm intelligence algorithm called the social group entropy optimization (SGEO) algorithm is proposed for solving optimization tasks. The proposed algorithm is based on the social group model, the status optimization model, and the entropy model, which are the main contributions of this paper. First, the social group model and the feedback mechanism between Leaders and Followers are developed to reduce the probability of local optimum. Second, the status optimization model is described to reveal the changing rule about the population behavior states, to support the conversion between different social behaviors during evolution, to promote the algorithm to optimize quickly, and to avoid local optimization. Third, the entropy model is introduced to analyze the entropy of social groups, the change rule of difference entropy, and to set the information entropy as behavior’s criterion of state optimization. In addition, the mathematical model of the SGEO is deduced from the group theory, matter dynamics, and the information entropy theory. The convergence and parallelism of it have been analyzed and verified theoretically. Moreover, to test the effectiveness of the SGEO, it is used to solve benchmark functions’problems that are commonly considered within the literature of evolutionary algorithms. Experimental results are compared with those of three other state-of-the-art algorithms. The superior performance of the SGEO validates its effectiveness and efficiency for the optimization problems, especially for the high-dimension problems.