Accuracy vs. robustness: Bi-criteria optimized ensemble of metamodels

Simulation has been widely used in modeling engineering systems. A metamodel is a surrogate model used to approximate a computationally expensive simulation model. Extensive research has investigated the performance of different metamodeling techniques in terms of accuracy and/or robustness and concluded no model outperforms others across diverse problem structures. Motivated by this finding, this research proposes a bi-criteria (accuracy and robustness) optimized ensemble framework to optimally identify the contributions from each metamodel (Kriging, Support Vector Regression and Radial Basis Function), where uncertainties are modeled for evaluating robustness. Twenty-eight functions from the literature are tested. It is observed for most problems, a Pareto Frontier is obtained, while for some problems only a single point is obtained. Seven geometrical and statistical metrics are introduced to explore the relationships between the function properties and the ensemble models. It is concluded that the bi-criteria optimized ensembles render not only accurate but also robust metamodels.