A performance measure approach for risk optimization

In recent years, several approaches have been proposed for solving reliability-based design optimization (RBDO), where the probability of failure is a design constraint. The same cannot be said about risk optimization (RO), where probabilities of failure are part of the objective function. In this work, we propose a performance measure approach (PMA) for RO problems. We first demonstrate that RO problems can be solved as a sequence of RBDO sub-problems. The main idea is to take target reliability indexes (i.e., probabilities of failure) as design variables. This allows the use of existing RBDO algorithms to solve RO problems. The idea also extends the literature concerning RBDO to the context of RO. Here, we solve the resulting RBDO sub-problems using the PMA. Sensitivity expressions required by the proposed approach are also presented. The proposed approach is compared to an algorithm that employs the first-order reliability method (FORM) for evaluation of the probabilities of failure. The numerical examples show that the proposed approach is efficient and more stable than direct employment of FORM. This behavior has also been observed in the context of RBDO, and was the main reason for the development of PMA. Consequently, the proposed approach can be seen as an extension of PMA approaches to RO, which result in more stable optimization algorithms.