## 2 Methodology
### Case Study in Two Cities with Different Solar Radiation
#### 2.2.4 Design Variables  
The principle of design variable selection mainly includes two aspects: one is to reflect the passive design and the other is to be related to the four objectives. From this point, according to the theoretical calculation method of building energy consumption, the influencing factors mainly include the building's shape, orientation, interface, and envelope construction. Building shape mainly reflects the length, width, and height of a building, but the building's performance is optimized under the premise of meeting the reasonable use function in this paper, i.e., a certain plane and layout, so we did not take this as a variable. In relation to the objective function, building orientation has a direct impact on the indoor thermal environment and energy consumption, which, in turn, affect the cost and carbon emissions in the operating phase. The building interface includes the window-wall area ratio, sunshade, etc., while the envelope construction includes the exterior wall, roof, window types, etc. These variables all directly affect the four optimization objectives.  
Some specific instructions are as follows: The east and west exterior walls of high-rise residential buildings usually do not have windows or they have small windows. In the benchmark model established in this paper, the east and west exterior walls are only equipped with external windows that meet the ventilation requirements of the bathroom, so they were taken as fixed values during optimization, and only the south and north window-wall ratios were taken as optimization variables. Correspondingly, the south and north exterior window types were also used as optimization variables, and 3 types of exterior windows were set. As the main structure of the exterior wall and roof was unchanged, their thermal performance was mainly affected by the thickness of the insulation layer, so the insulation layer thickness of the exterior wall and roof was taken as the optimization variable. Considering the differences in solar radiation effect in various orientations, the insulation layer thickness of different oriented external walls was also taken as an optimization variable. Taking into account the demand of summer heat protection for residential buildings, a horizontal sunvisor is set in the south exterior window, and the overhang length was taken as an optimization variable. Finally, eleven design variables were determined for optimization. Referring to the survey results and relevant standards, we considered the value extensibility of the design variables. The value ranges of the design variables, material selection, and price were determined. Table 2 shows the name, symbol, type, range, and step of each variable. The materials, prices, and carbon emission factors of the insulation layer, exterior windows, sunvisor, and photovoltaic panels are displayed in Table 3.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number** & **Design Variable** & **Symbol** & **Type** & **Range** & **Step** \\ \hline
1 & Building orientation (\({}^{\circ}\)) & O & Continuous & \(-45^{\circ}\)\(-45^{\circ}\) & \(5^{\circ}\) \\
2 & South window–wall ratio & Swwr & Continuous & 0.3–0.6 & 0.05 \\
3 & North window–wall ratio & Nwwr & Continuous & 0.15–0.3 & 0.05 \\
4 & South exterior window type & Swin & Discrete & 3 Types & — \\
5 & North exterior window type & Nwin & Discrete & 3 Types & — \\
6 & Insulation layer thickness of the south wall (m) & St & Continuous & 0–0.2 & 0.01 \\
7 & Insulation layer thickness of the north wall (m) & Nt & Continuous & 0–0.2 & 0.01 \\
8 & Insulation layer thickness of the east wall (m) & Et & Continuous & 0–0.2 & 0.01 \\
9 & Insulation layer thickness of the west wall (m) & Wt & Continuous & 0–0.2 & 0.01 \\
10 & Insulation layer thickness of the roof (m) & Rt & Continuous & 0–0.2 & 0.01 \\
11 & South horizontal sunvisor overhang length (m) & L & Continuous & 0–1.0 & 0.1 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Optimized design variables and parameter settings.