<p>The performance of differential evolution algorithms is sensitive to the population size, and most existing population size control methods continuously reduce the population during the iteration process, which decreases the exploration ability and makes it difficult to prevent a premature convergence of the algorithm. To improve the exploration ability of the differential evolution algorithm, this paper proposes a cosine-exponential population size adaptive (CEPSA) method. In the iterative process, CEPSA enables the population size to decrease or increase. The CEPSA periodically enhances the diversity of the population in the iterative process of the algorithm, which improves the exploration ability of the algorithm and prevents it from premature convergence. Based on the CEPSA, this paper proposes a new variant of the differential evolution algorithm, which is known as CEDE. In the experiment, the performance of CEDE was verified via the CEC 2014 and CEC 2017 benchmark test sets and several real-world engineering problems. CEDE was compared with 11 variants of differential evolution and six metaheuristic algorithms. The experimental results show that CEDE was significantly better than the compared algorithms. In addition, we conducted a sensitivity analysis on the parameters of CEDE, and the experimental results show that CEDE was not sensitive to the parameters, indicating that CEDE can be easily applied to various optimization problems.</p>