An Advanced and Robust Ensemble Surrogate Model: Extended Adaptive Hybrid Functions

Hybrid or ensemble surrogate models developed in recent years have shown a better accuracy compared to individual surrogate models. However, it is still challenging for hybrid surrogate models to always meet the accuracy, robustness, and efficiency requirements for many specific problems. In this paper, an advanced hybrid surrogate model, namely, extended adaptive hybrid functions (E-AHF), is developed, which consists of two major components. The first part automatically filters out the poorly performing individual models and remains the appropriate ones based on the leave-one-out (LOO) cross-validation (CV) error. The second part calculates the adaptive weight factors for each individual surrogate model based on the baseline model and the estimated mean square error in a Gaussian process prediction. A large set of numerical experiments consisting of up to 40 test problems from one dimension to 16 dimensions are used to verify the accuracy and robustness of the proposed model. The results show that both the accuracy and the robustness of E-AHF have been remarkably improved compared with the individual surrogate models and multiple benchmark hybrid surrogate models. The computational time of E-AHF has also been considerately reduced compared with other hybrid models.