Although evolutionary algorithms coupled with building simulation codes are often applied in academic research, this approach has a limited use for actual applications of building design due to the high number of expensive simulation runs. The use of a surrogate model can overcome this issue. In the literature there are several functional approximation models that can emulate the building simulation during the optimization, thus increasing the process efficiency. However, there are no evidence-based studies comparing the performances of these methods for the building design optimization. This study compares the efficiency, the efficacy and the quality of the Pareto solutions obtained by Polynomial, Kriging (GRFM), Radial-basis function networks (RBFN), Multivariate Adaptive Regression Splines (MARS) and support vector machines (SVM) functional approximations. The test bed of the comparison is the evaluation of the optimal refurbishment of three reference buildings for which the actual Pareto front is also obtained through a brute-force approach. The results show that the MARS method outperforms the other surrogate models both in terms of efficiency and effectiveness, and also by assessing the quality of the Pareto front.