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We present an overview of evolutionary algorithms that use empirical models of the fitness function to accelerate convergence, distinguishing between evolution control and the surrogate approach. We describe the Gaussian process model and propose using it as an inexpensive fitness function surrogate. Implementation issues such as efficient and numerically stable computation, exploration versus exploitation, local modeling, multiple objectives and constraints, and failed evaluations are addressed. Our resulting Gaussian process optimization procedure clearly outperforms other evolutionary strategies on standard test functions as well as on a real-world problem: the optimization of stationary gas turbine compressor profiles.