The Sequential Optimization and Reliability Assessment (SORA) method is a single loop method containing a sequence of cycles of decoupled deterministic optimization and reliability assessment for improving the efficiency of probabilistic optimization. However, the original SORA method as well as some other existing single loop methods is not efficient for solving problems with changing variance. In this paper, to enhance the SORA method, three formulations are proposed by taking the effect of changing variance into account. These formulations are distinguished by the different strategies of Inverse Most Probable Point (IMPP) approximation. Mathematical examples and a pressure vessel design problem are used to test and compare the effectiveness of the proposed formulations. The “Direct Linear Estimation Formulation” is shown to be the most effective and efficient approach for dealing with problems with changing variance. The gained insight can be extended and utilized to other optimization strategies that require MPP or IMPP estimations.

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