Synergy design is a novel concept in designing energy-saving buildings. Its main objective is to optimize building material combinations, energy-saving technologies and other relevant properties, ensuring that the energy consumption of the building meets the energy-saving demand. This constitutes an inverse problem, which cannot be solved by conventional methods. Therefore, using a new model that combines numerical calculations with an improved genetic algorithm, we elucidate the synergic relationships between thermophysical properties of wall materials. The investigation is conducted on a south-facing wall under the extreme climatic conditions of Chengdu, China. The results confirmed the existence of these synergic relationships. In particular, the thermal conductivity is a linearly increasing function of insulation thickness; however, if the thermal conductivities of two materials of fixed thickness are simultaneously optimized, increasing one conductivity nonlinearly reduces the other conductivity. These two cases confirm the efficiency and reliability of the proposed model in solving inverse problems related to insulation technology. The identified synergic relationships are also very useful in engineering applications, because the designer can select the combination of thermophysical properties most suited to the energy-saving requirements and local market conditions. (C) 2015 Elsevier Ltd. All rights reserved.