# Efficient global optimization with ensemble and selection of kernel functions for engineering design

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## Abstract

In this paper, we investigate the use of multiple kernel functions for assisting single-objective Kriging-based efficient global optimization (EGO). The primary objective is to improve the robustness of EGO in terms of the choice of kernel function for solving a variety of black-box optimization problems in engineering design. Specifically, three widely used kernel functions are studied, that is, Gaussian, Matérn-3/2, and Matérn-5/2 function. We investigate both model selection and ensemble techniques based on Akaike information criterion (AIC) and cross-validation error on a set of synthetic (noiseless and noisy) and non-algebraic (aerodynamic and parameter tuning) optimization problems; in addition, the use of cross-validation-based local (i.e., pointwise) ensemble is also studied. Since all the constituent surrogate models in the ensemble scheme are Kriging models, it is possible to perform EGO since the Kriging uncertainty structure is still preserved. Through analyses of empirical experiments, it is revealed that the ensemble techniques improve the robustness and performance of EGO. It is also revealed that the use of Matérn-kernels yields better results than those of the Gaussian kernel when EGO with a single kernel is considered. Furthermore, we observe that model selection methods do not yield any substantial improvement over single kernel EGO. When averaged across all types of problem (i.e., noise level, dimensionality, and synthetic/non-algebraic), the local ensemble technique achieves the best performance.

## Keywords

Efficient global optimization Kernel function Surrogate model Model selection Model ensemble## Notes

### Acknowledgments

Koji Shimoyama was supported in part by the Grant-in-Aid for Scientific Research (B) No. H1503600 administered by the Japan Society for the Promotion of Science (JSPS).

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