Combined kriging surrogate model for efficient global optimization using the optimal weighting method

When solving design optimization problems using evolutionary algorithms, the optimization process can be computationally expensive. To accelerate the optimization process, ordinary Kriging (OK) surrogate models are often used with the efficient global optimization (EGO) framework. However, in some cases the EGO framework can lead to a globally inaccurate OK surrogate model when many sample points are close to each other. One way to tackle this issue is to use a regression OK model instead of an interpolation OK model. In this paper, we propose an interpolation method which solve the issue by combining a local and a global OK model fitted to different set of the sample points. This paper describes the optimal weighting method used to combine the different Kriging models and compares the performance of the new method to interpolation and regression OK for the modified Branin test function. We find that when many sample points exist close to each other, the combined Kriging method outperform both the interpolation and the regression OK.