A robust optimization approach using Kriging metamodels for robustness approximation in the CMA-ES

This paper presents a study for using Kriging metamodeling in combination with Covariance Matrix Adaptation Evolution Strategies (CMA-ES) to find robust solutions. A general, archive based, framework is proposed for integrating Kriging within CMA-ES, including a method to utilize the covariance matrix of the CMA-ES in a straightforward way to improve the accuracy of the Kriging predictions without introducing much additional computational cost. Moreover, it adopts an elegant way to select appropriate archive points for building a local metamodel. The study shows that this Kriging metamodeling scheme for finding robust solutions outperforms common, straightforward approaches and is very useful when there is a limited budget of function evaluations. Though using the covariance matrix can improve the prediction quality, it has no significant effect on the overall quality of the optimization results.