A multi-fidelity Bayesian optimization approach based on the expected further improvement

Sampling efficiency is important for simulation-based design optimization. While Bayesian optimization (BO) has been successfully applied in engineering problems, the cost associated with large-scale simulations has not been fully addressed. Extending the standard BO approaches to multi-fidelity optimization can utilize the information of low-fidelity models to further reduce the optimization cost. In this work, a multi-fidelity Bayesian optimization approach is proposed, in which hierarchical Kriging is used for constructing the multi-fidelity metamodel. The proposed approach quantifies the effect of HF and LF samples in multi-fidelity optimization based on a new concept of expected further improvement. A novel acquisition function is proposed to determine both the location and fidelity level of the next sample simultaneously, with the consideration of balance between the value of information provided by the new sample and the associated sampling cost. The proposed approach is compared with some state-of-the-art methods for multi-fidelity global optimization with numerical examples and an engineering case. The results show that the proposed approach can obtain global optimal solutions with reduced computational costs.