Interval differential evolution with dimension-reduction interval analysis method for uncertain optimization problems

Abstract

• A new optimization method is proposed to directly solve uncertain problems with interval parameters. • Dimension-reduction interval analysis calculates intervals of objective function and constraints caused by uncertainty. • The satisfaction value of interval possibility degree model utilizes to handle the uncertain constraints. • The interval preferential rule directly realizes the ranking of different design vectors. • The computational accuracy and efficiency of proposed method is verified. A constrained nonlinear interval optimization method under the framework of differential evolution algorithm is developed to solve the uncertain structural optimization problems with interval uncertainties. The proposed method is a direct optimization method based on the interval differential evolution and dimension-reduction interval analysis. The interval preferential rule based on the satisfaction value of interval possibility degree model is used to realize the direct interval ranking of different design vectors. At each evolutionary generation, the outer optimizer by differential evolution optimizer searches for the best solution within the design space. The dimension-reduction interval analysis is employed to calculate the intervals of objective and constraints for each design vector in the inner layer. This operation transforms the original nesting optimization problem into a single loop one which improves the computational efficiency of the proposed method. Finally, the effectiveness of the presented direct method is verified by two numerical examples and an engineering application.