A cognitive system for conceptual building design is presented. It is based on an adaptive multi-objective evolutionary algorithm. The adaptive approach is novel and, in contrast with conventional multi-objective evolutionary algorithms, it explores the solution space effectively, while maintaining diversity among the solutions. The suitability of the approach for conceptual design of a multi-purpose building complex is demonstrated in an application. In the application, the goal of maximizing sustainability is treated by means of a model, which is established using neural computations. The approach is found to be suitable for treating the soft nature of the sustainability concept. Also, the capability of the approach to compare the performance of alternative solutions from an unbiased viewpoint, i.e. without committing a-priori to a relative importance among the performance aspects, is demonstrated.