Sequential space conversion for design optimization

Benefiting from ‘random work’ and high sampling efficiency, subset simulation optimization (SSO) is competitive in both convergence and global exploration among stochastic optimization methods; however, it may become trapped in local optima owing to the geometry-oriented feature of subset simulation. This article proposes a sequential space conversion optimization method to handle problems with complex or misleading geometric characteristics, by linking an optimization problem with a corresponding reliability problem inspired by SSO. It first locates the most likely optimal domain by space conversion based on the control variate, then drags the later simulation layers towards the optimal domain by sequential space conversion using a Bayesian formula and control variate. Potentially independent update regions are enabled, with the characteristics of fluctuation and jumping during convergence of the stochastic optimization, which can avoid being trapped in local optima guided by specific geometry. The performance of the proposed method is then tested.