Reducing function evaluations in Differential Evolution using rough approximation-based comparison

Abstract

In this study, we propose to utilize a rough approximation model, which is an approximation model with low accuracy and without learning process, to reduce the number of function evaluations effectively. Although the approximation errors between the true function values and the approximation values estimated by the rough approximation model are not small, the rough model can estimate the order relation of two points with fair accuracy. In order to use this nature of the rough model, we propose estimated comparison which omits the function evaluations when the result of comparison can be judged by approximation values. The advantage of the estimated comparison method is shown by comparing the results obtained by differential evolution (DE) and DE with estimated comparison method in various types of benchmark functions.