# Study on Multi-Objective Optimization-Based Climate Responsive Design of Residential Building
## 3 Multi-Objective Optimization Platform Set-Up
### Definition of Objective Functions
#### Building energy demand  
The climate responsive design optimization in this paper only focuses on passive design strategies. Passive design strategies can be controlled by the architect during the design phase, or adjusted by the user during the operational phase. Other mechanical system parameter setting are beyond the scope of this research. Therefore, the annual building energy demand is defined as the sum of the cooling and heating loads of all apartments, [25; 26; 27; 28] domestic hot water, electrical equipment and other energy needs are not included in the calculation. The cooling period in summer and the heating period in winter are set according to the requirements of different climate zones. In this study, in order to avoid the influence of HVAC system parameters, its performance coefficient is assumed to be 1, so the energy demand can be directly extracted from the EnergyPlus simulation results. It is assumed that no heat recovery device is implemented in the HVAC system. Therefore, the objective function of the annual building energy demand can be calculated as Equation (8):  
\[\text{BED}=\frac{1}{\text{A}}*\sum_{\text{i}=1}^{\text{n}}\left(\text{E}_{ \text{G}}+\text{E}_{\text{hi}}\right) \tag{8}\]  
where BED represents the annual building energy demand per unit building area (kWh/m\({}^{2}\)), the calculation of building energy demand only considers heating and cooling demand, and does not consider other aspects, such as lighting, domestic hot water, etc. E\({}_{\text{ci}}\) is the cooling demand of the i-th floor, E\({}_{\text{hi}}\) is the heating demand of the i-th floor, n is the total number of floors in the building, and A is the total area of each floor in the air-conditioning area of the building. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Month**} & **Outdoor** & \multirow{2}{*}{**Indoor Air Speed**} & **Clothing Thermal** & \multirow{2}{*}{**Metabolic Rate**} \\  & **Temperature** & & & **Resistance** & \\ \hline  & (\({}^{\circ}\)C) & (m/s) & (CLO) & (met) \\ \hline \(1\) & 2.15 & 0.05 & 1.1 & 1.2 \\ \(2\) & 1.66 & 0.05 & 1.1 & 1.2 \\ \(3\) & 6.51 & 0.05 & 0.9 & 1.2 \\ \(4\) & 13.21 & 0.05 & 0.8 & 1.2 \\ \(5\) & 16.32 & 0.05 & 0.6 & 1.2 \\ \(6\) & 20.87 & 0.05 & 0.5 & 1.2 \\ \(7\) & 24.81 & 0.05 & 0.4 & 1.2 \\ \(8\) & 23.26 & 0.05 & 0.5 & 1.2 \\ \(9\) & 19.02 & 0.05 & 0.6 & 1.2 \\ \(10\) & 14.72 & 0.05 & 0.7 & 1.2 \\ \(11\) & 8.49 & 0.05 & 0.9 & 1.2 \\ \(12\) & 3.09 & 0.05 & 1.1 & 1.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Input parameters for thermal comfort calculation. In order to assess the total cost associated with a given building, a life cycle cost analysis (LCCA) was performed using a 30-year time scale [29; 30]. The full life cycle cost of a building includes initial construction costs, annual energy use costs, and ongoing maintenance costs. However, according to the concept of global cost, in the current research for the schematic design stage, only building materials and annual energy costs are considered because they have the greatest impact on life cycle costs. Equations (9)-(11) shows the method used to calculate the life cycle cost in this study. \[\text{GC}=\frac{\text{C}_{\text{I}}+\sum\limits_{\text{i=1}}^{30}\left[\text {C}_{\text{e,i}}*\text{R}_{\text{d}}(\text{i})\right]}{\text{A}} \tag{9}\]  
\[\text{R}_{\text{d}}(\text{i})=[1-(1+\text{R}\text{r})-\text{i}]/\text{R}\text {r} \tag{10}\]  
\[\text{R}\text{r}=(\text{Ri}-\text{Re})/(1+\text{Re}) \tag{11}\]  
where GC represents building life cycle global cost, in $\$. \(\text{C}_{\text{I}}\) represents initial investment cost, in $\$. \(\text{C}_{\text{e,i}}\) is the energy cost of the ith year, in $\$. \(\text{R}_{\text{d}}(\text{i})\) is the discount rate of the ith year. A is the total area of each floor, in \(\text{m}^{2}\). \(\text{R}_{\text{r}}\) is the effective interest rate, \(\text{R}_{\text{e}}\) is the rate of increase in energy prices, which is assumed as 1.2%. \(\text{R}_{\text{i}}\) is the market interest rate, which is 4.25% [31].