Metamodels (surrogate models, response surfaces) have been incorporated into optimization methods for functions that are expensive to evaluate, so that the number of evaluations must be reduced as much as possible. This Demonstration shows the basic idea of surrogate-based optimization using a Gaussian process (GP) for the metamodel (also known as kriging), and the expected improvement (EI) for an infill criterion. You can click a point at which you think the global minimum exists or consult the infill criterion.