Adaptive infill sampling criterion for multi-fidelity gradient-enhanced kriging model

Multi-fidelity surrogate (MFS) method is very promising for the optimization of complex problems. The optimization capability of MFS can be improved by infilling samples in the optimization process. Furthermore, once the gradient information is provided, the gradient-enhanced kriging (GEK) can be utilized to construct a more accurate MFS model. However, for the existing infill sampling criterions, it is difficult to improve the optimization speed without sacrificing the optimization gains. In this paper, a novel infill sampling criterion named Adaptive Multi-fidelity Expected Improvement (AMEI) is proposed, in which the prediction accuracy and the optimization potential of the surrogate model are both considered. With a set of extra samples calculated, the AMEI determines which fidelity model for the new sample is to be added. Through two numerical examples and two engineering examples, it can be found that the AMEI always provides the best optimization result with the fewest analysis calls, and the robustness is also good. The optimization capability and efficiency of the AMEI have been demonstrated compared with traditional criterions.

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