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Surrogate model assisted evolutionary algorithms (SAEAs) have recently attracted much attention due to the growing need for computationally expensive optimization in many real-world applications. Most current SAEAs, however, focus on small-scale problems. SAEAs for medium-scale problems (i.e., 20-50 decision variables) have not yet been well studied. In this paper, a Gaussian process surrogate model assisted evolutionary algorithm for medium-scale computationally expensive optimization problems (GPEME) is proposed and investigated. Its major components are a surrogate model-aware search mechanism for expensive optimization problems when a high-quality surrogate model is difficult to build and dimension reduction techniques for tackling the “curse of dimensionality.” A new framework is developed and used in GPEME, which carefully coordinates the surrogate modeling and the evolutionary search, so that the search can focus on a small promising area and is supported by the constructed surrogate model. Sammon mapping is introduced to transform the decision variables from tens of dimensions to a few dimensions, in order to take advantage of Gaussian process surrogate modeling in a low-dimensional space. Empirical studies on benchmark problems with 20, 30, and 50 variables and a real-world power amplifier design automation problem with 17 variables show the high efficiency and effectiveness of GPEME. Compared to three state-of-the-art SAEAs, better or similar solutions can be obtained with 12% to 50% exact function evaluations.