Generalized hierarchical expected improvement method based on black-box functions of adaptive search strategy

Abstract

With the improvement of the accuracy of numerical simulation experiments, the computational costs of black–box function problems are increasing. In the process of global optimization using the Bayesian optimization method, the sampling cost and the optimization accuracy are the keys for measuring the effectiveness of the Bayesian optimization method. The expected improvement method has a closed-form of the acquisition function, which can realize the effective use of the sampled points, thereby reducing the sampling cost and improving the optimization accuracy. Therefore, this method has been widely used to solve practical engineering problems. The current expected improvement methods are based on fixed local–global search strategy. These methods have difficulty adapting to black-box functions of different complexities, and they have significant limitations in balancing local and global search capabilities. This article proposes a generalized hierarchical expected improvement (GHEI) Bayesian optimization method with an adaptive search strategy. By introducing the balance parameters to adjust the improvement functions, the local–global search criterion is further changed. On this basis, an adaptive search strategy based on the equivalent expectation to improve the optimization is proposed, and it improves the ability to deal with black-box functions of different complexities. The accuracy of the hierarchical Gaussian process model is further improved through methods such as related parameter estimation, hyperparameter determination, and basis function order selection. Comparative analysis with numerical calculation examples verified the effectiveness of the proposed method. Finally, the adaptive GHEI method is applied on the spacecraft radiation resistance equivalent test analysis, and results show that the adaptive GHEI method exhibits a strong search efficiency and applicability .