# 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
The thermal conductivity and density of the external wall and ground floor bricks are 0.9 W/mK and 2000 Kg/m\({}^{3}\), while for roof are 0.72 W/mK and 1800 Kg/m\({}^{3}\) in Los Angeles. This helps the building absorb solar radiation during the day and delay solar energy entering the room, then at night when these heat-capacity materials release the solar energy absorbed during the day, heat is taken out of the room through night ventilation. With the exception of Houston and Los Angeles, the recommended values for the insulation thickness of external walls, roofs, and ground floors of the nZEB optimal for residential buildings in almost all cities are  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**U Value**} & \multicolumn{2}{c}{**Houston**} & \multicolumn{2}{c}{**Los Angeles**} & \multicolumn{2}{c}{**Chicago**} & \multicolumn{2}{c}{**Helena**} & \multicolumn{2}{c}{**Duluth**} & \multicolumn{2}{c}{**Fairbanks**} \\ \cline{2-13}  & **nZEB** & **C-O** & **nZEB** & **C-O** & **nZEB** & **C-O** & **nZEB** & **C-O** & **nZEB** & **C-O** & **nZEB** & **nZEB\({}^{\prime}\) & **C-O** \\  & **(P)** & **(P)** & **(P)** & **(P)** & **(P)** & **(P)** & **(P)** & **(P)** & **(P)** & **(P)** & **(P)** & **(P)** & **(P)** \\ \hline External wall & 0.61 & 0.70 & 1.41 & 0.70 & 0.15 & 0.38 & 0.16 & 0.15 & 0.22 & 0.15 & 0.16 & 0.33 \\ Ro 0.12 m. The C-O optimal is quite different. Specifically, the thickness of the insulation layer on the external wall, roof and ground floor of the residential building in Chicago is 0.03 m, 0.04 m, and 0.03 m, respectively, making the U value of envelope slightly higher than that in the nZEB optimal, and the uncomfortable hours throughout the year is higher. In the Duluth C-O optimal solution, the thickness of the insulation layer of the external wall and roof is slightly lower than that of the nZEB optimal solution, which is 0.08 m and 0.1 m, respectively. But the block thermal conductivity and density of the roof and the ground floor in the C-O optimal solution are lower than the values in the nZEB optimal solution, which compensates for the lower thickness of the external wall and roof insulation layer, making the C-O optimal solution's building energy demand value (BED) and the annual discomfort hours (DH) is not much different from that in the nZEB optimal solution, and reduces the global cost (GC) to some extent. In the Fairbanks C-O optimal solution, the recommended value of the insulation layer thickness of the external wall is 0.04 m, but the block thermal conductivity and density of the roof, external wall, and the ground floor of the C-O optimal solution and the nZEB optimal solution are the same, making the BED and DH values of the C-O optimal solution much higher than that in the nZEB optimal solution. Thus, a compromised nZEB' solution is proposed, which uses the same insulation thickness of the roof, external wall, and ground floor, while only reducing the block thickness of roof and ground floor. The results show that the nZEB' solution is able to achieve lower BED and DH values while reducing the global cost (GC), therefore, from the perspective of comprehensive indicators, it has better benefits. In general, when a thick insulation layer is installed in the envelope, the U value of it generally remains at a low value, between 0.15-0.18 W/m\({}^{2}\)K, when the insulation is not used, the U value of envelope is related to block thickness, thermal conductivity, and density. For example, the nZEB optimal solution and the C-O optimal solution in Houston are not recommended to install insulation on the external walls, roofs, and ground floors, however, the thermal conductivity and density of the roof and ground floor recommended by the C-O optimal solution are much lower than the nZEB optimal solution, leading to the U value of roof and ground floor in C-O optimal solution (0.87 W/m\({}^{2}\)K and 0.71 W/m\({}^{2}\)K) much lower than that in nZEB optimal solution (2.04 W/m\({}^{2}\)K and 1.45 W/m\({}^{2}\)K).