Multi-fidelity global optimization using a data-mining strategy for computationally intensive black-box problems

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.