The paper proposes a multi-objective optimization approach to address the energy design of the building envelope. A genetic algorithm (GA) is implemented by means of the coupling between MATLAB® and EnergyPlus to minimize primary energy consumption (PEC), energy-related global cost (GC) and discomfort hours (DH). The design variables concern the set point temperatures, the radiative properties of plasters, the thermo-physical properties of envelope components, the window type, the building orientation. The GA performs a Pareto optimization and finally two optimal solutions are recommended: the nZEB (nearly zero energy building) optimal solution, which minimizes PEC, and the cost-optimal solution, which minimizes GC. These solutions provide the optimal design strategies for the public and private stakeholders, respectively, which represent the main actors involved in building design. The approach is applied for the design of a new typical Italian residential building. Four locations are considered to investigate the typical Italian climates. The outcomes can give precious indications to rebuild the Italian residential stock with a view to energy-efficiency and cost-optimality, given that the optimal solutions provide low values of PEC – between 62.0 and 91.9 kWhp/m2a – and of GC – between 456 and 665 €/m2 – depending on the location. Display omitted •The methodology optimizes envelope energy design by using a genetic algorithm.•Primary energy consumption, global cost and discomfort hours are minimized.•The optimal most sustainable (nZEB) and the cost-optimal designs are achieved.•The methodology is applied to four different Italian climatic zones.•Original indications to rebuild the Italian residential stock are provided.