Stochastic Subset Optimization for optimal reliability problems

Reliability-based design of a system often requires the minimization of the probability of system failure over the admissible space for the design variables. For complex systems this probability can rarely be evaluated analytically and so it is often calculated using stochastic simulation techniques, which involve an unavoidable estimation error and significant computational cost. These features make efficient reliability-based optimal design a challenging task. A new method called Stochastic Subset Optimization (SSO) is proposed here for iteratively identifying sub-regions for the optimal design variables within the original design space. An augmented reliability problem is formulated where the design variables are artificially considered as uncertain and Markov Chain Monte Carlo techniques are implemented in order to simulate samples of them that lead to system failure. In each iteration, a set with high likelihood of containing the optimal design parameters is identified using a single reliability analysis. Statistical properties for the identification and stopping criteria for the iterative approach are discussed. For problems that are characterized by small sensitivity around the optimal design choice, a combination of SSO with other optimization algorithms is proposed for enhanced overall efficiency.