An efficient robust optimization method with random and interval uncertainties

This paper develops a new mixed uncertainty robust optimization (MURO) method with both random and interval uncertainties. Existing strategies in literature always treat the system performance as a sequence of probability distribution with the interval factors varying within their domains. Moreover, the robust design objective and constraints are modeled in the form of combination of interval mean and interval deviations of performances, which cannot offer a quantitative robustness measurement of a design. The new MURO method is based on the sensitivity region concept and a hybrid robustness index is developed to represent the possibility that the uncertain vector locates within the worst-case sensitivity region (WCSR). This proposed index can offer a more quantitative and intuitive way to evaluate the robustness of a design. With the hybrid indices, the traditional robust optimization problem can be converted to an ordinary optimization with the robustness index constraints. Two numerical examples and two engineering examples with different combinations of interval and random factors are illustrated to demonstrate the applicability and efficiency of the proposed algorithm. The comparison results show that the new method can reduce the conservatism of previous method significantly with fewer computational efforts.