Granular Risk-Based Design Optimization

Optimization considering uncertainty is an increasingly important and continuously developing uncertainty mitigation technique for modern design. Compared with its well-established branches, i.e., reliability-based design optimization (RBDO) and robust design optimization, risk-based design optimization (RDO) is just regarded as an extension of RBDO by incorporating future cost; hence, it has not received much deep theoretical study. Based on the generalized theory of uncertainty, we introduce different levels of probability granulation into RDO and propose a granular risk-based design optimization (GRDO) methodology. The risks are modeled as granular probabilities, their mean values, and standard deviations. Two multiobjective optimization (MO) formulations of GRDO are proposed and solved by multiobjective evolutionary algorithm based on decomposition aided with solution filtering criterion. Based on the results of a structural design example, the capability of GRDO on uncertainty management is validated by comparing the performances of different MO formulations, while uncertainty mitigation using GRDO is achieved by controlling the risks associated with fixed level of uncertainty. This way, GRDO is approved as a general design frame rather than just an uncertainty mitigation technique like conventional RDO.