This work introduces Evolutionary Architectural Space layout Explorer (EASE), a design tool that facilitates the optimization of 3D space layouts. EASE addresses architectural design exploration and the need to attend to many alternatives simultaneously in layout design. For this, we use evolutionary optimization to find a balance between divergent exploration and convergent exploitation. EASE comprises a novel sub-heuristic that constructs valid spatial layouts, a mathematical framework to quantify the satisfaction of constraints, and evolutionary operators to improve alternative layouts' fitness. We test EASE on the design of a library building. We evaluate EASE's performance for different building forms and different evolutionary algorithm parameters. The results suggest that EASE can generate valid layouts, quantify the constraints' degree of satisfaction and find a number of optimal layout solutions. The layouts that EASE generates are intended not as end results but design artifacts that provide insight into the solution space for further exploration.