In this paper, an improved ACDE (Adaptive Cauchy Differential Evolution) algorithm with faster convergence speed, called ACDE2, is suggested. The baseline ACDE algorithm uses a "DE/rand/1" mutation strategy to provide good population diversity, and it is appropriate for solving multimodal optimization problems. However, the convergence speed of the mutation strategy is slow, and it is therefore not suitable for solving unimodal optimization problems. The ACDE2 algorithm uses a "DE/current-to-best/1" mutation strategy in order to provide a fast convergence speed, where a control parameter initialization operator is used to avoid converging to local optimization. The operator is executed after every predefined number of generations or when every individual fails to evolve, which assigns a value with a high level of exploration property to the control parameter of each individual, providing additional population diversity. Our experimental results show that the ACDE2 algorithm performs better than some state-of-the-art DE algorithms, particularly in unimodal optimization problems.