The air-conditioning energy consumption, for cooling or heating, has currently a growing trend. The purpose of this work is to develop a method suitable to design optimal threedimensional building forms to reduce air-conditioning needs in a chosen location by using weather data. The method exploits in particular both diuse and direct solar radiation; not independently but rather in relation with the external temperature. For this reason this method could be applied in any climatic region. In fact the warmer the region is the more negative the contribution of the solar radiation is in terms of building energy balance. Hence in this case the problem tends to be equivalent to the one of the annual solar irradiation minimization. On the contrary, in the case of cold regions, the problem tends to be equivalent to the one of the annual solar irradiation maximization. The final aim is to guide designers to reduce energy consumptions in buildings, since the first stages of the design process of future buildings. To achieve that aim, an algebraic cumulative sky is introduced for the computation of the annual useful incident solar irradiation on the building envelope. The methodology consists in using weather data to define in which case the solar irradiation on the envelope gives a positive or negative contribution depending on the external temperature in order to maintain internal comfort of the occupants. The contribution is further associated to the data of the solar irradiation for each hour of a typical year. The algebraic cumulative sky constructed on that basis has the advantage to present particular zones where the solar radiation is useful all year long. Finally we use an hybrid evolutionary algorithm (CMA-ES/HDE algorithm) already applied to maximize solar energy utilization to explore the optimal building forms maximizing the annual useful solar irradiation on the envelope.