# Study on Multi-Objective Optimization-Based Climate Responsive Design of Residential Building
## 4 Discussion of Optimization Results
### Comparison of Optimization Results with Reference Buildings
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Performance Indicator**} & \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** & **C-O** \\  & **(*****)** & **(*****)** & **(*****)** & **(*****)** & **(*****)** & **(*****)** & **(*****)** & **(*****)** & **(*****)** & **(*****)** & **(*****)** & **(*****)** & **(*****)** & **(*****)** \\ \hline BED reduction (kWh/m\({}^{2}\)) (*****) & 20.55 & 3.3 & -5.24 & -2.32 & 20.45 & -521 & 22.32 & 18.8 & 28.32 & 20.43 & 55.23 & 52.37 & 7.22 \\ GC reduction ($m\({}^{2}\)) (***)** & 36.55 & 67.26 & -16.57 & -92.98 & -14.71 & 79.68 & -61.99 & 13.81 & -28.71 & 38.68 & 56.97 & 111.66 & 127.97 \\ DH reduction (*) (***)** & 29.16 & 16.66 & 45.84 & 8.34 & 13.17 & 0 & 12.5 & 8.34 & 8.75 & 6.25 & 8.97 & 14.05 & 06.63 \\ IC reduction ($m\({}^{2}\)) (***)** & 25.22 & 65.4 & 13.7 & -91.71 & -25.94 & 82.54 & -74.64 & 6.27 & -44.24 & 27.47 & 26.65 & 82.91 & 106.12 \\ \hline \hline \end{tabular}  
* (*) nZEB: near zero energy building solution; nZEB: constrained nearly zero energy building solution; C-O: cost optimal solution. (***)** Positive values denote that the proposed solutions induce a reduction (and thus an advantage) of the performance indicator, while negative values denote an increase (and thus a disadvantage).  
\end{table} 
Table 15: Comparison between the proposed optimal solutions and the related reference designs. BED is reduced by 18.8 kWh/m\({}^{2}\), DH is reduced by 8.34%, GC and IC are reduced by 13.81 $/m\({}^{2}\) and 6.27 $/m\({}^{2}\), respectively. Therefore, the design parameters of the C-O optimal solution can be used as reference values for energy-saving design of residential buildings in climate zone 5 cities such as Chicago. In Duluth, compared to the reference building, the BED in the nZEB optimal solution decreased by approximately 28.32 kWh/m\({}^{2}\), and the DH decreased by 8.75%, but the GC and IC increased 28.71 $/m\({}^{2}\) and 44.24 $/m\({}^{2}\) respectively. Compared with the nZEB optimal solution, the GC and IC optimization of the C-O optimal solution did not come at the expense of the degradation of BED and DH. In the C-O optimal solution, BED decreased by approximately 20.43 kWh/m\({}^{2}\), DH decreased by 6.25%, GC and IC decreased by 38.68 $/m\({}^{2}\) and 27.47 $/m\({}^{2}\), respectively. Therefore, from the perspective of comprehensive indicators, the design parameters of the C-O optimal solution can be used as the reference value for energy-saving design of residential buildings in Duluth. In the climate zone 8 represented by Fairbanks, the BED of the nZEB optimal solution decreased by approximately 55.23 kWh/m\({}^{2}\), the GC decreased by 56.97 $/m\({}^{2}\), the IC decreased by 26.65 $/m\({}^{2}\), and the DH decreased by 8.97%. Whereas in the C-O optimal solution, BED only decreased by about 7.22 kWh/m\({}^{2}\), GC decreased by 127.97 $/m\({}^{2}\), IC decreased by 106.12 $/m\({}^{2}\), and DH decreased by 0.63%. From the aspects of building energy demand and global cost, the improvement of these two optimal solutions are not large, so a compromise nZEB' optimal solution is proposed. In the nZEB' optimal solution, BED is reduced by 52.37 kWh/m\({}^{2}\), GC is reduced by 111.66 $/m\({}^{2}\), IC is reduced by 82.91 $/m\({}^{2}\), DH is reduced by 14.05%, the comprehensive indicator is better than nZEB optimal solution and CO optimal solution, thus it can be used as a reference value for residential buildings energy efficiency design in Fairbanks.