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.

多保真优化（MFO）在工程设计中受到了广泛的关注，它通过大量的低保真（LF）而廉价的样品来增加少量的昂贵的高保真（HF）样本，从而提高了优化性能。影响MFO有效性的关键因素是如何在迭代过程中为HF和LF模拟自适应分配样本。为了解决MFO中的此类样本分配问题，我们提出了一个名为Filter-GEI的新填充准则，该准则在广义预期改进（GEI）采集函数的基础上强加了自适应滤波器功能。特别是，通过考虑HF和LF模型之间的相关性，Filter-GEI可以有效地分配HF和LF样本，从而在本地搜索和全局搜索之间实现良好的平衡。此外，考虑到并行计算，Filter-GEI在每次迭代中填充多个HF和LF样本，随着计算能力的提高，它可以进一步提高其效率。通过对涡轮叶片设计的五个数学玩具问题和一个工程问题的测试，该算法的有效性得到了很好的证明。