Global Rd Optimization when Probes are Expensive: the GROPE Algorithm

A global optimization algorithm i s introduced which generalizes Kushner’s univariate search [1]. It aims to minimize the number o f probes (function evaluations) required for a g i v e n confidence in the results. All known p r o b e s contribute to a stochastic model of the underly ing “score surface”; this model is interrogated for the location most likely to exceed the current result goal. The surface is assumed to be fractal, l e a d i n g to a piecewise Gaussian model, where the local regions are defined by the Delaunay triangulation o f the probes. The algorithm balances the c o m p e t i n g aims of 1) sampling in the vicinity of known p e a k s , and 2) exploring new regions. Preliminary tests o n a standard 2-d search problem are very encouraging.