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We present a novel derivative-free interpolation based optimizationalgorithm. A trust-region method is used where a surrogate model is realizedvia an interpolation framework. The framework for interpolation is provided byUniversal Kriging. A first contribution focuses on the development of anoriginal sampling strategy. A valid model is guaranteed by maintaining awell-poised subset that exhibits the regular simplex geometry approximately. Itfollows that this strategy improves the scattering of points with respect tothe state-of-the-art and, even importantly, assures that the surrogate modelexhibits curvature. A second contribution focuses on the generalization of thespherical trust-region geometry to an ellipsoidal geometry, that to account forlocal anisotropy of the objective function and to improve the interpolationconditions as seen from the output space. The ensemble method is validatedagainst its direct competitors on a set of multidimensional problems.

A Radial Basis Function based Optimization Algorithm with Regular Simplex set geometry in Ellipsoidal Trust-Regions