In this paper, a new Multi-Fidelity Global Optimization algorithm using a data-mining strategy named MFGO is presented to solve computationally intensive black-box problems, where Kriging is used to construct and update the high fidelity (HF) and low fidelity (LF) surrogate models. In MFGO, a data-mining strategy including four successive phases “Data-collecting, Data-clustering, Data-cleaning, and Deep-mining ” is developed to capture useful knowledge from the LF surrogate model and improve the optimization efficiency of the HF surrogate model. In the first phase, a multi-start exploration is utilized to find the multiple local optimums of the LF surrogate model. In the second phase, a hierarchical agglomerative method is used to divide the local optimums into several clusters and select elite individual of each cluster. In the last two phases, the points around the unpromising area are deleted according to a distance-based cleaning criterion, and the remaining points are further mined with four screening criteria to identify helpful information and create a self-adaption trust region around the best solution. More importantly, three optimization stages including the data-mining process, global search and local search are executed alternately on the HF surrogate model, which achieves a reasonable balance between exploitation and exploration. Finally, three versions of MFGO were verified by comparing with five well-known methods on eight benchmark cases and one engineering problem, which performed superior computational efficiency and robustness.

在本文中，提出了一种使用名为 MFGO 的数据挖掘策略的新多保真全局优化算法来解决计算密集型黑盒问题，其中克里金法用于构建和更新高保真 (HF) 和低保真 (LF) ) 替代模型。在MFGO中，数据挖掘策略包括四个连续的阶段“数据收集、数据聚类、数据清理和深度挖掘”的开发是为了从 LF 代理模型中获取有用的知识，并提高 HF 代理模型的优化效率。在第一阶段，利用多开始探索来寻找 LF 代理模型的多个局部最优值。在第二阶段，采用层次凝聚法将局部最优划分为若干簇，并选择每个簇中的精英个体。在最后两个阶段，根据基于距离的清理标准删除无希望区域周围的点，并通过四个筛选标准进一步挖掘剩余点，以识别有用信息并围绕最佳解决方案创建自适应信任区域. 更重要的是，包括数据挖掘过程在内的三个优化阶段，在HF代理模型上交替执行全局搜索和局部搜索，实现了开发和探索之间的合理平衡。最后，通过在八个基准案例和一个工程问题上与五种众所周知的方法进行比较，验证了三个版本的MFGO，具有优越的计算效率和鲁棒性。