Efficient constrained optimization by the ε constrained differential evolution with rough approximation using kernel regression

Abstract

We have proposed 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 in unconstrained optimization. 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 have proposed estimated comparison which omits the function evaluations when the result of the comparison can be judged by approximation values. In this study, we propose to utilize the estimated comparison in constrained optimization and propose the eDEkr, which is the combination of the e constrained method and the estimated comparison using kernel regression. The eDEkr is a very efficient constrained optimization algorithm that can find high-quality solutions in a very small number of function evaluations. It is shown that the eDEkr can find near optimal solutions stably in a very small number of function evaluations compared with various other methods on well-known nonlinear constrained problems.