Residential and commercial buildings are responsible for about 40% of primary energy consumption in the US. The design of a building has tremendous effect on its energy profile, and recently there has been an increased interest in developing optimization methods that support the design of high performance buildings. Previous approaches are either based on simulation optimization or on training an accurate predictive model to replace expensive energy simulations during the optimization. We propose a method, suitable for expensive multiobjective optimization in very large search spaces. In particular, we use a Gaussian Process (GP) model for the prediction and devise an active learning scheme in a multi-objective genetic algorithm to preferentially simulate only solutions that are very informative to the model's predictions for the current generation. We develop a comprehensive and publicly available benchmark for building design optimization. We show that the GP model is highly competitive as a surrogate for building energy simulations, in addition to being well-suited for the active learning setting. Our results show that our approach clearly outperforms surrogate-based optimization, and produces solutions close in hypervolume to simulation optimization, while using only a fraction of the simulations and time.