Kriging surrogate model with coordinate transformation based on likelihood and gradient

The Kriging surrogate model, which is frequently employed to apply evolutionary computation to real‐world problems, with a coordinate transformation of the design space is proposed to improve the approximation accuracy of objective functions with correlated design variables. The coordinate transformation is conducted to extract significant trends in the objective function and identify the suitable coordinate system based on either one of two criteria: likelihood function or estimated gradients of the objective function to each design variable. Compared with the ordinary Kriging model, the proposed methods show higher accuracy in the approximation of various test functions. The proposed method based on likelihood shows higher accuracy than that based on gradients when the number of design variables is less than six. The latter method achieves higher accuracy than the ordinary Kriging model even for high‐dimensional functions and is applied to an airfoil design problem with spline curves as an example with correlated design variables. This method achieves better performances not only in the approximation accuracy but also in the capability to explore the optimal solution.