A cross-entropy method accelerated derivative-free RBDO algorithm

Many engineering applications require optimization of the system performance subject to reliability constraints, which are commonly referred to as the reliability based design and optimization (RBDO) problems. In this work we propose a derivative-free algorithm to solve the RBDO problems. In particular, we focus on the type of RBDO problems where the objective function is deterministic and easy to evaluate, whereas the reliability constraints involve very small failure probabilities. The algorithm consists of solving a set of subproblems, in which simple surrogate models of the reliability constraints are constructed and used in solving the subproblems. Moreover, we employ a cross-entropy (CE) method with sample reweighting to evaluate the rare failure probabilities, which constructs the surrogate for the reliability constraints by performing only a single full CE simulation in each iteration. Finally we demonstrate the performance of the proposed method with both academic and practical examples.