Parallel constrained Bayesian optimization via batched Thompson sampling with enhanced active learning process for reliability-based design optimization

This paper proposes an effective and robust decoupled approach for addressing reliability-based design optimization (RBDO) problems. The method iteratively performs a parallel constrained Bayesian optimization (PCBO) with deterministic parameters based on the most probable point (MPP) underpinning limit-state functions (LSFs) sequentially updated through an enhanced active learning-based reliability evaluation process. During the deterministic optimization process, the PCBO integrates with a trust region approach that considers a collection of simultaneous local optimization runs, each guided by an independent Gaussian process (GP) model. The trust region approach leverages a well-established selection strategy in reinforcement learning, known as the multi-armed bandit, to allocate samples across local trust regions and decide which local optimization runs to continue. In particular, batched Thompson sampling is adopted as an acquisition function to determine the optimal design by selecting a batch of candidate points from local trust regions via sampling from the posterior of the independent GP models, with the batch evaluations executed in parallel. In the reliability analysis, the GP model estimates, from the optimal design offered by the PCBO, the spectrum of LSFs under random parameters, and hence allows an efficient failure probability estimation through a cross-entropy (CE) method with Gaussian mixture (GM) clustering without direct performance function evaluations. By leveraging information from the GM clustering, an enhanced active learning mechanism is developed to strategically refine the GP model by generating multiple informative points in the clustered regions with the largest uncertainty and high-reliability sensitivity, thus improving the accuracy of failure probability predictions. Eventually, an invertible cross-entropy (iCE) method is proposed to decouple the reliability analysis from the optimization process, enabling the update of the new MPP assigned for the PCBO to identify the new optimal design. The proposed method significantly alleviates computational costs for both deterministic design optimization and reliability analysis and quickly converges to the optimal RBDO design. Three numerical examples are provided to illustrate the efficiency and robustness of the proposed approach in addressing the RBDO problem.