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In many real-world optimization problems, the objective function may come from a simulation evaluation so that it is (a) subject to various levels of noise, (b) not necessarily differentiable, and (c) computationally hard to evaluate.

We propose a two-phase approach for optimization of such functions. Phase I uses classification tools to facilitate the global search process. By learning a surrogate from existing data the approach identifies promising regions for optimization. Additional features of the method are: (a) more reliable predictions obtained using a voting scheme combining the options of multiple classifiers, (b) a data pre-processing step that copes with imbalanced training data and (c) a nonparametric statistical method to determine regions for multistart optimizations.

Phase II is a collection of local trust region derivative free optimizations. Our methods apply Bayesian techniques to guide appropriate sampling strategies, while simultaneously enhancing algorithmic efficiency to obtain solutions of a desired accuracy. The statistically accurate scheme determines the number of simulation runs, and guarantees the global convergence of the algorithm.