The quantity and positioning of glazing on a building’s facade has a strong influence on the building’s heating, lighting, and cooling performance. Evolutionary algorithms have been effective in finding glazing layouts that optimise the trade-offs between these properties. However, this is time-consuming, needing many calls to a building performance simulation. Surrogate fitness functions have been used previously to speed up optimisation without compromising solution quality; our novelty is in the application of a surrogate to a binary encoded, multi-objective, building optimisation problem. We propose and demonstrate a process to choose a suitable model type for the surrogate: a multilayer perceptron (MLP) is found to work best in this case. The MLP is integrated with the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) algorithm, and experimental results show that the surrogate leads to a significant (400x) speedup. This allows the algorithm to find solutions that are better than the algorithm without a surrogate in the same timeframe. Updating the surrogate at intervals improves the solution quality further with a modest increase in run time.