Biogeography-based optimization (BBO) is a new evolutionary algorithm inspired by biogeography, which involves the study of the migration of biological species between habitats. Previous work has shown that various migration models of BBO result in significant changes in performance. Sinusoidal migration models have been shown to provide the best performance so far. Motivated by biogeography theory and previous results, in this paper a generalized sinusoidal migration model curve is proposed. A previously derived BBO Markov model is used to analyze the effect of migration models on optimization performance, and new theoretical results which are confirmed with simulation results are obtained. The results show that the generalized sinusoidal migration model is significantly better than other models for simple but representative problems, including a unimodal one-max problem, a multimodal problem, and a deceptive problem. In addition, performance comparison is further investigated through 23 benchmark functions with a wide range of dimensions and diverse complexities, to verify the superiority of the generalized sinusoidal migration model.