Uncertainties, inevitable in nature, can be classified as probability based and interval based uncertainties, in terms of its representations. Corresponding optimization strategies have been proposed to deal with these two types of uncertainties individually. However, it is more likely that both types of uncertainty occur in one single problem and so it is trivial to treat all uncertainties the same. In this paper a novel formulation for reliability based design optimization (RBDO) under mixed probability and interval uncertainties is proposed, in which the objective variation or the objective robustness is also concerned. Furthermore, it is proposed to efficiently solve the worst case parameter resulted from the interval uncertainty by utilizing the Utopian solution presented in a single-looped robust optimization approach, in which the inner optimization problem can be solved by performing matrix operations. The remaining problem can be solved utilizing any existing RBDO method. This work applies the performance measure approach to search for the most probable failure point (MPFP) and sequential quadratic programming (SQP) to solve the entire problem. Two engineering examples are given to demonstrate the applicability of the proposed approach and to illustrate the necessity to consider the objective robustness under certain circumstances.

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