## 3 Results and Discussion  
### Tradeoffs of Multi-Objective Optimization and Its Value Distribution  
Non-dominated values of objectives in the form of Pareto fronts were returned after 25 generations of calculation. There were 65 and 82 non-dominated solutions for Xi'an and Yulin, respectively. The 4D Pareto front was mapped to a bidimensional (2D) graph, and the relationships between the bi-objective Pareto solutions for Xi'an and Yulin are displayed in Figure 5.  
For the trade-off relationships between the multiple objectives, as shown in Figure 5, in Xi'an, there are incomplete positive correlations between EC and TDHP, EC and LCCO\({}_{2}\), and LCCO\({}_{2}\) and TDHP, while there are nonlinear incomplete negative correlations between EC and LCC, LCC and TDHP, and LCC and LCCO\({}_{2}\). It can be seen that although the correlation is positive, due to the guidance of the four objectives, the pairwise correlation can only reflect the incomplete correlation, and there is a contradictory relationship among the objectives. For Yulin, there is a similar correlation but greater dispersion. The relationship between two objectives consists of multiple parallel curves. For example, when the building energy consumption is the same, there exist several values of TDHP, LCC, and LCCO\({}_{2}\), with large differences. This happens because the objective function considers the offsetting effect of solar power generation, and the solar radiation in the Yulin area is stronger. Under the influence of this factor, the design variables and objective functions form the distribution characteristics of solution sets different from those in the Xi'an area. The details of the relationships between the objectives and variables will be explained in Section 3.2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number** & **Name** & **Material** & **Price** & **CEF** \\ \hline
1 & Insulation layer & XPS board & 850 CNY/m\({}^{3}\) & 175.7 kgCO\({}_{2}\)/m\({}^{3}\) \\ \hline \multirow{8}{*}{2} & \multirow{8}{*}{Exterior window} & A: 6 mm Low-E + 9A + 6 mm clear & K = 1.977 W/m\({}^{2}\)-K & \multirow{8}{*}{870 CNY/m\({}^{2}\)} & \multirow{8}{*}{147 kgCO\({}_{2}\)/m\({}^{2}\)} \\  & & 9A + 6 mm clear & SHGC = 0.568 & & \\  & & Tvis = 0.745 & & \\ \cline{1-1} \cline{3-4}  & & & K = 1.513 W/m\({}^{2}\)-K & \multirow{2}{*}{810 CNY/m\({}^{2}\)} & \multirow{2}{*}{147 kgCO\({}_{2}\)/m\({}^{2}\)} \\  & & 9A + 6 mm Low-E & SHGC = 0.477 & & \\ \cline{1-1} \cline{3-4}  & & & Tvis = 0.709 & & \\ \cline{1-1} \cline{3-4}  & & & C: 6 mm Low-E + & K = 1.182 W/m\({}^{2}\)-K & \multirow{2}{*}{1050 CNY/m\({}^{2}\)} & \multirow{2}{*}{164 kgCO\({}_{2}\)/m\({}^{2}\)} \\  & & 9A + 6 mm clear + & SHGC = 0.436 & & \\ \cline{1-1} \cline{3-4}  & & 9A + 6 mm Low-E & Tvis = 0.631 & & \\ \hline
3 & Sunvisor & 60 mm concrete slab & 120 CNY/m\({}^{2}\) & 17.7 kgCO\({}_{2}\)/m\({}^{2}\) \\ \hline
4 & Photovoltaic panel & Monocrystalline silicon solar panel & 640 CNY/m\({}^{2}\) (4 CNY/W) & 30 kgCO\({}_{2}\)/m\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Price and carbon emission factor (CEF) for different kinds of materials. In terms of the value distribution of objective functions, as can be seen in Figure 5a, the EC of the Pareto solution set is distributed at 15.6\(\sim\)21.7 kW\(\cdot\)h/m\({}^{2}\) in the Xi'an area; that is, when the designer selects the non-dominated solution, the maximum difference is 6.1 KWh/m\({}^{2}\). The variation range of TDHP is 38.5%-41.3%, with a maximum difference value of 2.8%. The LCC ranges from 199.3 to 314. CNY/m\({}^{2}\), with a gap of 115.1 CNY/m\({}^{2}\) between the optimal and the worst solution, while the span for the LCCO\({}_{2}\) is 66.8\(\sim\)120.8 kgCO\({}_{2}\)/m\({}^{2}\), with a maximum difference of 54.0 kgCO\({}_{2}\)/m\({}^{2}\). Regarding the Yulin area, as shown in Figure 5b, the EC ranges from 15.2 kW\(\cdot\)h/m\({}^{2}\) to 20.8 kW\(\cdot\)h/m\({}^{2}\), and there exists a gap of 5.7 kW\(\cdot\)h/m\({}^{2}\) between the maximum and minimum values.