## 3 Model Development
### Baseline Rural House Measure Variable Settings  
Based on the constructed model, optimizing the variables of the building envelope involves focusing on the thickness and type of insulation material, which are key to the optimization of the building's envelope structure. Therefore, the thickness of the insulation layer for external walls and roofs, as well as the type of insulation material, are considered as measure variables. The performance of exterior windows, which is primarily affected by their thermal transmittance (U-value) and size, directly influences indoor heating energy consumption. Hence, the window-to-wall ratio is included as a design parameter to seek optimization that reduces heat transfer losses, effectively decreasing heating energy consumption and improving the building's heating energy efficiency. The names of the optimization variables, their value ranges, and initial investment costs are shown in Table 3. The upper limit of the change interval for the insulation layer thickness and the thermal transmittance of external windows encompasses the limits prescribed by the autonomous region's standards in the \"Energy Efficiency Design Standards for Residential Buildings in Severe Cold and Cold Regions\". The prices for insulation materials and doors/windows are set based on data from the Xinjiang government procurement website and market research to ensure the model's realism and feasibility. The price of EPS insulation board is 260 CNY/m\({}^{3}\), XPS extruded board is 600 CNY/m\({}^{3}\), and rock wool board is 310 CNY/m\({}^{3}\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Retrofit Area** & **Parameter Variable** & **Value Range** & **Simulation Step Size** & **Initial Investment** \\ \hline \multirow{3}{*}{External Wall} & EPS Board & 10–300 mm & 10 mm & 260 CNY/m\({}^{3}\) \\  & XPS Board & 10–300 mm & 10 mm & 600 CNY/m\({}^{3}\) \\  & Rock Wool Board & 10–300 mm & 10 mm & 310 CNY/m\({}^{3}\) \\ \hline \multirow{3}{*}{Roof} & EPS Board & 10–300 mm & 10 mm & 260 CNY/m\({}^{3}\) \\  & XPS Board & 10–300 mm & 10 mm & 600 CNY/m\({}^{3}\) \\  & Rock Wool Board & 10–300 mm & 10 mm & 310 CNY/m\({}^{3}\) \\ \hline \multirow{3}{*}{Farmhouse Story Height} & \multirow{3}{*}{Story Height} & \multirow{3}{*}{2700–3600 mm} & \multirow{3}{*}{100 mm} & \multirow{3}{*}{/} \\  & South-facing window/wall ratio & 0.20–0.45 & 0.01 & / \\  & North-facing window/wall ratio & 0–0.25 & 0.01 & / \\  & East/west-facing & 0–0.30 & 0.01 & / \\  & window/wall ratio & & & \\ \hline \multirow{9}{*}{Window-Wall Ratio} & \multirow{3}{*}{6 mm clear, 12 mm air,} & \multirow{3}{*}{2.8 W/(m\({}^{2}\)-K)} & \multirow{3}{*}{780 CNY/m\({}^{2}\)} \\  & and 6 mm clear & & & \\ \cline{1-1}  & 6 mm high-transmittance low-E, & 1.9 W/(m\({}^{2}\)-K) & & 800 CNY/m\({}^{2}\) \\ \cline{1-1}  & 6 mm medium-transmittance low-E, & & & \\ \cline{1-1}  & 12 mm air, and 6 mm clear & 1.8 W/(m\({}^{2}\)-K) & & 800 CNY/m\({}^{2}\) \\ \cline{1-1}  & 6 mm high-transmittance low-E, & & & \\ \cline{1-1}  & 12 mm argon, and 6 mm clear & 1.5 W/(m\({}^{2}\)-K) & & 820 CNY/m\({}^{2}\) \\ \cline{1-1} Window Type & 6 mm medium-transmittance low-E, & 1.4 W/(m\({}^{2}\)-K) & & Select by type & 820 CNY/m\({}^{2}\) \\ \cline{1-1}  & 12 mm argon, and 6 mm clear & & & \\ \cline{1-1}  & Triple glazing (5 mm clear, & 12 mm air, 5 mm clear, 12 mm air, & 1.7 W/(m\({}^{2}\)-K) & & 880 CNY/m\({}^{2}\) \\ \cline{1-1}  & and 5 mm clear) & & & \\ \cline{1-1}  & Triple glazing (5 mm medium-transmittance low-E, & & & \\ \cline{1-1}  & 12 mm air, 5 mm low-E, 12 mm air, & 1.2 W/(m\({}^{2}\)-K) & & 920 CNY/m\({}^{2}\) \\ \cline{1-1}  & and 5 mm clear) & & & \\ \hline \multirow{3}{*}{Photovoltaic Modules} & Angle & 35\({}^{\circ}\) & 1\({}^{\circ}\) & \\ \cline{1-1}  & Area & 36.43 m\({}^{2}\) & Number of & 875 CNY/m\({}^{2}\) \\ \cline{1-1} \cline{2-5}  & & & & \\ \cline{1-1} \cline{2-5}  & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Retrofit measure variables.