Global Rd optimization when probes are expensive: the GROPE algorithm

A global optimization algorithm is introduced which generalizes H.J. Kushner´s (1964) univariate search. It aims to minimize the number of probes required for a given confidence in the results. All known probes contribute to a stochastic model of the underlying score surface, and this model is interrogated for the location most likely to exceed the current result goal. The surface is assumed to be fractal, leading to a piecewise Gaussian model, where the local regions are defined by the Delaunay triangulation of the probes. The algorithm balances the competing aims of (1) sampling in the vicinity of known peaks, and (2) exploring new regions. Preliminary tests on a standard 2-D search problem were very encouraging