A novel multi-fidelity sequential optimization method based on multi-level Gaussian process

Multi-fidelity optimization algorithms can efficiently find the optimum of the high-fidelity system with assistance of lower-fidelity and cheaper simulation(s). However, existing methods do not utilize this “assistance” sufficiently, where they generally tend to query high-fidelity systems during the optimization procedure. In this paper, we propose a novel sequential criterion based on multi-level Gaussian process (MLGP) and name it the multi-level expected improvement criterion (LEI). LEI is an extended version of the expected improvement criterion (EI) with a closed form, which integrates the correlation index, cost ratio, and constraint handling terms, hence determining both location and fidelity level of the next sample. Specifically, the correlation index is a function of the prediction error for each fidelity, which can reflect the metamodeling accuracy of low-fidelity and the desirable sampling site for high-fidelity system. We have proved that low-fidelity samples can improve the accuracy of MLGP modeling while the LEI criterion can improve the robustness and accuracy of optimization theoretically. Furthermore, the LEI criterion can easily be extended to multiple fidelity scenarios. The numerical results show that the proposed algorithm saves the sample size for high fidelity with higher optimization efficiency and stronger robustness.

Authors

• Zecong Liu
• Liang Yan
• Xiaojun Duan National University of Defense Technology
• Yike Xiao
• Bo Liu Peking University
• Jiangtao Chen

Keywords

• Multi-fidelity
• Surrogate model
• Multi-level Gaussian process
• Bayesian optimization