Reducing Function Evaluations Using Adaptively Controlled Differential Evolution with Rough Approximation Model

Abstract

In this chapter, a rough approximation model, which is an approximation model with low accuracy and without learning process, is presented in order to reduce the number of function evaluations effectively. Although the approximation errors between the true function values and the approximation values are not small, the rough model can estimate the order relation of solutions with fair accuracy. By utilizing this nature of the rough model, we have proposed estimated comparison method, in which function evaluations are omitted when the order relation of solutions can be judged by approximation values. In the method, a parameter for error margin is introduced to avoid incorrect judgment. Also, a parameter for utilizing congestion of solutions is introduced to avoid omitting promising solutions. In order to improve the stability and efficiency of the method, we propose adaptive control of the margin parameter and the congestion parameter according to the success rate of the judgment. The advantage of these improvements is shown by comparing the results obtained by Differential Evolution (DE), DE with the estimated comparison method, adaptively controlled DE with the estimated comparison method and particle swarm optimization in various types of benchmark functions.