## 2 Methodology
### Case Study in Two Cities with Different Solar Radiation
#### 2.2.3 Objective Functions  
Building energy consumption generally includes heating, cooling, lighting, and equipment energy use. This paper mainly reduces energy consumption from the perspective of passive design, and the design variables do not involve the parameters related to equipment; therefore, the energy consumption for hot water, electrical appliances, and lighting is \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Construction** & **Layers** & **Thickness** & **Conductivity** & **Density** & **Specific Heat** \\
**Component** & **(from Exterior to Interior)** & **(mm)** & **(W/m-K)** & **(kg/m3)** & **(J/kg-K)** \\ \hline \multirow{8}{*}{Roof} & 40 mm fine aggregate concrete & 40 & 1.74 & 2500 & 920 \\  & XPS & — & 0.03 & 35 & 1647 \\  & 3 m SBS waterproof layer & 3 & 0.23 & 900 & 1680 \\  & 20 mm cement mortar & 20 & 0.93 & 1800 & 1050 \\  & 120 mm reinforced concrete & 120 & 1.74 & 2500 & 920 \\  & 20 mm mixed mortar & 20 & 0.87 & 1700 & 1050 \\ \hline \multirow{8}{*}{Exterior wall} & 20 mm cement mortar & 20 & 0.93 & 1800 & 1050 \\  & XPS & — & 0.03 & 35 & 1647 \\ \cline{1-1}  & 20 mm cement mortar & 20 & 0.93 & 1800 & 1050 \\ \cline{1-1}  & 200 mm aerated concrete & 200 & 0.22 & 700 & 1050 \\ \cline{1-1}  & 20 mm mixed mortar & 20 & 0.87 & 1700 & 1050 \\ \hline \multirow{3}{*}{Exterior window} & Clear glass & 6 & 0.76 & 1800 & 1260 \\ \cline{1-1}  & Air cavity & 6 & 0.026 & 1.293 & 1005 \\ \cline{1-1}  & Clear glass & 6 & 0.76 & 1800 & 1260 \\ \hline \hline \end{tabular} Note: The thickness of XPS is an optimization variable in the following text.  
\end{table} 
Table 1: Details of the building envelope. Figure 4: (a) Layout of the benchmark building; (b) location of the research object in the residential area. the same for each scheme and is not affected by design variables, so the heating and cooling energy consumption is mainly calculated during the optimization process. Through the Rhino-Grasshopper platform, we used the Honeybee plugin to invoke the EnergyPlus engine to simulate energy consumption. Chinese Standard Weather Data (CSWD) for Xi'an and Yulin were used for meteorological parameters. The heating period was set as 15 November to 15 March, with the indoor temperature calculated at 18 \({}^{\circ}\)C and the air change rate calculated at 0.5 h\({}^{-1}\). The cooling period was set as 15 June to 31 August, with the indoor temperature calculated at 26 \({}^{\circ}\)C and the air change rate calculated at 1.0 h\({}^{-1}\). There is no heating or cooling equipment in the bathroom or kitchen. For other spaces, in order to increase the simulation speed while reducing the impact of simplification [42], the building was divided into two thermal zones: the bedroom, and the living and dining rooms. The personnel occupancy rate, heating and cooling equipment control mode, and time in each thermal zone were set uniformly according to Appendix C of the \"JGJ/T 449-2018 Standard for green performance calculation of civil buildings\" [43]. Life-cycle cost is an important index to measure the economy of design schemes, including the costs of investment, operation, replacement, and maintenance. A 30-year period was considered for the life-cycle analysis. The lifespans of insulation materials, windows, and shading devices are generally 30 years or longer; therefore, their replacement costs are not taken into account [22]. Life-cycle analysis mainly considers the present value of the investment and operating costs. As for the investment cost, since the main structure and the cost of labor and transportation of different design schemes are essentially the same, the initial investment cost does not need to calculate the absolute value but only the incremental cost generated by the change in the optimization design variable.