Trust-Region Bayesian Optimization for High-Dimensional Black-Box Problems: Integrating Deep Kernel Learning with Adaptive Gradient Mechanisms

The traditional Bayesian optimization (BO) algorithm faces significant performance bottlenecks when addressing high-dimensional black-box optimization problems. To mitigate this challenge, the present paper introduces a novel trust region Bayesian optimization algorithm. Firstly, in the design of the BO surrogate model, we employ a combination of deep neural networks and kernel methods to enhance the Gaussian process regression (GPR) model. This approach improves GPR’s capacity to identify and fit the nonlinear characteristics of black-box functions while also increasing regression accuracy. Secondly, in formulating the BO acquisition function, an adaptive gradient trust region adjustment method is utilized to bolster BO’s search capabilities within high-dimensional solution spaces. Concurrently, a hybrid sampling strategy is implemented to generate more diverse sampling points, thereby enhancing BO’s ability to escape local optima. The proposed algorithm has been validated on three 60D multimodal complex functions as well as two engineering application problems and compared with other advanced variants of BO. Experimental results demonstrate that our proposed algorithm exhibits superior iterative convergence, rapidly approaches optimal values for black-box problems with fewer function evaluations, and achieves higher computational accuracy. These findings confirm both the feasibility and effectiveness of the improved BO approach presented in this paper.