This work describes a methodology for the identification of the optimal features for the envelope of a residential building. The optimization process allows minimizing operating energy consumption, investment costs and life cycle energy and environmental embodied impacts. A dynamic model for the estimation of building energy consumption during its use phase has been employed, while literature data were adopted for embodied energy and global warming potential impacts. The considered variables refer to the envelope of the building, i.e. external walls and roof insulation and external walls thermal mass. The model was obtained combining EnergyPlus building energy simulator and MOBO, a versatile freeware that allows running the optimization of building features. The optimization was solved using NSGA II, a widespread adopted multi-objective genetic algorithm available in MOBO. The same building was simulated in two different climatic zones, namely Palermo (Italy) and Copenhagen (Denmark), in order to compare differences attained in the optimal solutions. The case study shows that the adoption of glass wool for the roof insulation and small concrete layers for external walls are to be preferred, providing optimal results in both climates. The present work was developed within the framework of IEA EBC Annex 72.