Efficient Constrained Optimization by the $$\varepsilon $$ Constrained Differential Evolution with Rough Approximation

Abstract

It has been 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 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. The estimated comparison, which omits the function evaluations when the result of the comparison can be judged by the approximation values, proposed to use this nature of the rough model. In this chapter, a constrained optimization method is proposed by combining the \(\varepsilon \) constrained method and the estimated comparison, where rough approximation is used not only for an objective function but also for constraint violation. The proposed method is an efficient constrained optimization algorithm that can find near-optimal solutions in a small number of function evaluations. The advantage of the method is shown by solving well-known nonlinear constrained problems.