Robust design optimization using surrogate models

The use of surrogate models (response surface models, curve fits) of various types (radial basis functions, Gaussian process models, neural networks, support vector machines, etc.) is now an accepted way for speeding up design search and optimization in many fields of engineering that require the use of expensive computer simulations, including problems with multiple goals and multiple domains. Surrogates are also widely used in dealing with uncertainty quantification of expensive black-box codes where there are strict limits on the number of function evaluations that can be afforded in estimating the statistical properties of derived performance quantities. Here, we tackle the problem of robust design optimization from the direction of Gaussian process models (Kriging). We contrast two previously studied models, co-Kriging and combined Kriging (sometimes called level 1 Kriging), and propose a new combined approach called combined co-Kriging that attempts to make best use of the key ideas present in these methods.