# Study on Multi-Objective Optimization-Based Climate Responsive Design of Residential Building
## 4 Discussion of Optimization Results
### Optimization Results of Residential Buildings in Typical American Cities
It can also be seen from the nZEB optimal solution that the block thickness of the external walls, roofs and ground floors gradually increases from the warmer climate zone to the colder climate zone. For example, the block thickness of the external wall and roof of residential buildings in Houston is 0.3 m and 0.25 m. In Los Angeles, the block thickness of that are 0.25 m, and ground floor is 0.4 m. The remaining cities are 0.4 m, while the block thickness of ground floor in Houston, Chicago, and Helena is 0.25 m, and that in Duluth and Fairbanks is 0.3 m. In addition, except Houston, Los Angeles, and Helena, the block thermal conductivity and density of the external wall and roof of residential buildings in various cities are always maintained between 0.25-0.3 W/mK and 600-800 kg/m\({}^{3}\). For example, the block thermal conductivity and density for the roof of residential buildings in Houston and Helena are 0.72 W/mK, 1800 kg/m\({}^{3}\), and 0.36 W/mK, 1000 kg/m\({}^{3}\) respectively. In Los Angeles, the block thermal conductivity and density for the roof are 0.72 W/mK, 1800 kg/m\({}^{3}\), and for external wall and ground floor are 0.9 W/mK, 2000 kg/m\({}^{3}\). It is clear to see that the block thermal conductivity and density are gradually decreasing from south to north. For example, the thermal conductivity and density of ground floor in Houston and Chicago residential buildings are both 0.9 W/mK and 2000 kg/m\({}^{3}\), while the corresponding values of Helena and Fairbanks residential buildings are 0.43 W/mK, 1200 kg/m\({}^{3}\) and 0.25 W/mK, 600 kg/m\({}^{3}\) respectively. It can be seen from the C-O optimal solution that the envelope block thermal conductivity and density in most typical cities' residential buildings remained between 0.25 \(\sim\) 0.3 W/mK and 600 \(\sim\) 800 kg/m\({}^{3}\). For the transparent component of the envelope (i.e., windows), the triple-glazed with argon-filling, low-e coating, PVC frame window types are more common (i.e., type 7), for example, Chicago, Helena, Duluth, and Fairbanks nZEB optimal solution, Duluth C-O optimal solution, and Fairbanks nZEB' optimal solution, although the price of this type of window is slightly high, but it has the best insulation performance. Houston's nZEB optimal solution recommends the use of tinted double-glazedwith argon-filling, low-e coating, PVC frame window (i.e., type 5), and the C-O optimal solution recommends the use of tinted double-glazed with air-filling, low-e coating, PVC frame window (i.e., type 2), this type of window has a low SHGC value of 0.38, which can effectively reduce excessive solar radiation entering the room. In Los Angeles, double-glazed with air-filling, low-e coating, aluminum frame window (type 1) is recommended in both nZEB optimal solution and C-O optimal solution, probably because it has the lowest price and will not increase the energy demand too much. Chicago, Helena, and Fairbanks C-O optimal solutions recommend double-glazed with argon-filling, low-e coating, PVC frame window (i.e., type 4). This type of window is cheaper and has a higher U value than other alternatives, which is 1.90 W/m\({}^{2}\)K, and the window SHGC is also high, which is 0.69, thus it can make better use of solar radiation, thereby greatly reducing the space heating energy.