We use the convergence points estimated by our proposed method as elite individuals for evolutionary computation and evaluate the acceleration effect and analyze the effect and computational cost. The worst individuals in population are replaced with the convergence points estimated from the moving vectors between parent individuals and their offspring; i.e. these convergence points are used as elite individuals. Differential evolution (DE) and 14 benchmark functions are used in our evaluation experiments. The experimental results show that use of the estimated convergence points as elite can accelerate DE search in spite of the calculation cost of the convergence points. We finally analyze the components of the proposed estimation method to improve cost-performance.