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

Abstract: We present a novel derivative-free interpolation based optimization algorithm. A trust-region method is used where a surrogate model is realized via an interpolation framework. The framework for interpolation is provided by Universal Kriging. A first contribution focuses on the development of an original sampling strategy. A valid model is guaranteed by maintaining a well-poised subset that exhibits the regular simplex geometry approximately. It follows that this strategy improves the scattering of points with respect to the state-of-the-art and, even importantly, assures that the surrogate model exhibits curvature. A second contribution focuses on the generalization of the spherical trust-region geometry to an ellipsoidal geometry, that to account for local anisotropy of the objective function and to improve the interpolation conditions as seen from the output space. The ensemble method is validated against its direct competitors on a set of multidimensional problems.