A comparative study on kernel smoothers in Differential Evolution with estimated comparison method for reducing function evaluations

As a new research topic for reducing the number of function evaluations effectively in function optimization, an idea of utilizing a rough approximation model, which is an approximation model with low accuracy and without learning process, has been proposed. Although the approximation errors between true function values and their 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 feature of the rough model, we have proposed the estimated comparison method, which omits the function evaluations when the result of comparison can be judged by approximation values. In this study, kernel smoothers are adopted as rough approximation models. Various types of benchmark functions are solved by differential evolution (DE) with the estimated comparison method and the results are compared with those obtained by DE. It is shown that the estimated comparison method is general purpose method for reducing function evaluations and can work well with kernel smoothers. It is also shown that the potential model, which is a rough approximation model proposed by us, has better ability of function reduction than kernel smoothers.