With the recent trend of moving towards a more sustainable economy, the interest on designing buildings with lower cost and environmental impact has grown significantly. In this context, multi-objective optimization has attracted much attention in building design as a tool to study trade-off solutions (“cost” vs “environmental impact”) resulting from the optimization of conflicting objectives. One major limitation of this approach (as applied to building design) is that it is computationally demanding due to the need to optimize several objectives using complex models based on differential equations (which are used to estimate the energy consumed by a building). In this work, we propose a systematic framework for the design of buildings that combines a rigorous objective reduction method (which removes redundant objectives from the analysis) with a surrogate model (which simplifies the calculation of the energy requirements of the building), both of which expedite the identification of alternative designs leading to environmental improvements. The capabilities of our methodology are illustrated through a case study based on a thermal modelling of a house-like cubicle, in which we optimize the insulation thicknesses of the building envelope. Results show that significant economic and environmental improvements can be achieved compared to the base case (cubicle without insulation). Furthermore, it is clearly illustrated how the minimization of an aggregated environmental metric, like the Eco-Indicator 99, as unique environmental objective may overlook some Pareto solutions that may be appealing for decision-makers. The authors would like to acknowledge financial support from the Spanish Government (ENE2015-64117-C5-3-R (MINECO/FEDER, UE)). Joan Carreras would also like to acknowledge financial support from the Pump-Priming Research Programs of The University of Manchester.