We propose and evaluate two methods for accelerating differential evolution and interactive differential evolution (IDE). The first acceleration method, which we call DE/gravity, aims to realize performance similar to that of paired-comparison-based IDE/best while removing the requirement that the IDE user must choose the best individual among all displayed individuals. The second acceleration method generates not only a conventional trial vector but also a second and third trial vector. It calculates a moving average vector, X moving, for the population between generations, and compares a given target vector with the three trial vectors of a conventional trial vector, a target vector + Xmoving, and a trial vector + Xmoving, and uses the best one among the four vectors as offspring in the next generation. We evaluate these acceleration methods and a conventional method by applying them to Gaussian mixture models and demonstrate the effectiveness of our proposed methods.