A fast incremental Kriging-assisted algorithm for online optimization

The Kriging model is a popular surrogate for black-box function optimization due to its ability to provide uncertainty estimates. However, its high training cost has traditionally limited its use in online optimization. In this study, we present a fast incremental Kriging-assisted online optimization algorithm, specifically designed to address this limitation. Different hyperparameter computation strategies are formulated and tailored for real-time and non-real-time applications. The update formulas of the Cholesky decomposition of correlation matrix are derived for the correlation matrix updating, enabling efficient incremental model construction with computational complexity of O((N-1)²) when adding and removing samples. The samples farthest from the current step will be removed. The expected improvement (EI) criterion guides the selection of new samples, while the correlation matrix and the optimal sample from the previous step are transferred to the current step. An optimal Latin hypercube design (OLHD) ensures the uniform candidate sampling and consistent computational cost for EI calculation. The effectiveness of the proposed algorithm has been demonstrated through four numerical experiments. The results show that it can efficiently perform online optimization and parameter identification in both time-varying and recursive systems, exhibiting clear advantages over some existing algorithms. Moreover, the method maintains robust performance even under variations in initial values, noise, and model errors.