Parallel multi-fidelity expected improvement method for efficient global optimization

Multi-fidelity optimization (MFO) has received extensive attentions in engineering design, which resorts to augmenting the small number of expensive high-fidelity (HF) samples by a large number of low-fidelity (LF) but cheap samples to improve the optimization performance. A key factor that influences the effectiveness of MFO is how to adaptively assign samples for HF and LF simulations in the iteration process. To address such sample assignment issue in MFO, we propose a new infill criterion named Filter-GEI, which imposes an adaptive filter function on top of the generalized expected improvement (GEI) acquisition function. In particular, by taking the correlations between HF and LF models into account, the Filter-GEI can efficiently allocate HF and LF samples to achieve a good balance in between the local and global search. Furthermore, considering parallel computing, the Filter-GEI infills multiple HF and LF samples in each iteration, which can further improve its efficiency as computing power increases. Through tests on five mathematical toy problems and one engineering problem for the turbine blade design, the effectiveness of the proposed algorithm has been well demonstrated.