Objectives  As solving the robust optimization (RO) problem with interval uncertainty is unduly time-consuming when the nested differential evolution algorithm is directly used, a new RO design method is proposed.

  Methods  In the proposed method, individuals' response values that have been accurately calculated within the critical distance are used to approximately predict the response values of other individuals and evaluate the robustness indexes accordingly. The accurate information of individuals' response values, which is gradually expanded in the evolutionary procedure, is also used to selectively re-evaluate the past robustness of individuals, and the critical distance is adaptively reduced on the basis of the robustness misjudgment rate.

  Results  Two numerical and one engineering examples are tested to demonstrate the applicability of the proposed algorithm. The results show that the proposed algorithm saves more than 94% of computational resources, while the estimated error is less than 2.5%.

  Conclusions  The proposed method can greatly reduce the calculation time of individuals' response values in the evolution process and maintain the adaptive balance between the accuracy and cost of robustness evaluation by using previous optimization knowledge, providing a new idea and method for RO design with interval uncertainty.