## 3 Results and Discussion
Figure 8: CO\({}_{2}\) and total cost values at optimum points obtained for different objective functions (Zone II). \begin{table}
\begin{tabular}{c c c c c} \hline  & **Insulation** & **Insulation** & **Wall Material** & **Heating** \\  & **Thickness (m)** & **Material** & **Surface** & **Source** \\ \hline Base Case Scenario & 0.02 & XPS & Brick & Fuel Oil \\ Optimum Cost & 0.0499 & EPS & Brick & Natural Gas \\ Optimum CO\({}_{2}\) & 0.2055 & EPS & Light concrete & Natural Gas \\ Cost-Oriented Knee Point & 0.1368 & EPS & Brick & Natural Gas \\ CO\({}_{2}\)-Oriented Knee Point & 0.0829 & EPS & Light concrete & Natural Gas \\ \hline \end{tabular}
\end{table} 
Table 5: Optimum insulation thickness, insulation material, wall material, and heating source for different objective functions (Zone II). It is understood that for the same objective functions, only the insulation thickness varies, while the wall material, heating type, and insulation material remain unchanged. In the analyses conducted for Zone III, the optimum conditions determined for Zones I and II remain consistent. For Zone III, the insulation thicknesses for the optimum cost, optimum CO\({}_{2}\), cost-oriented knee point, and CO\({}_{2}\)-oriented knee point scenarios are determined to be 5.6 cm, 22.45 cm, 14.93 cm, and 9.06 cm, respectively (see Table 7 and Figure 9). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Scenario**} & \multirow{2}{*}{\begin{tabular}{c} **C\({}_{\text{T}}\)** \\ **(USD/m\({}^{2}\))** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **M\({}_{\text{CO2}}\)** \\ **(kg/m\({}^{2}\))** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **\% C\({}_{\text{T}}\)** \\ **(kg/m\({}^{2}\))** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **\% M\({}_{\text{CO2}}\)** \\ **(kg/m\({}^{2}\))** \\ \end{tabular} } \\ \hline \multirow{4}{*}{CCGDE3} & Base Case Scenario & 48.45 & 22.40 & - & - \\  & Optimum Cost & 34.84 & 15.79 & 28\% & 30\% \\  & Optimum CO\({}_{2}\) & 53.44 & 9.31 & 28\% & 30\% \\ MOEA/D-UR & Optimum Cost & 34.84 & 15.79 & 28\% & 30\% \\  & Optimum CO\({}_{2}\) & 53.44 & 9.31 & 28\% & 30\% \\ DEA-GNG & Optimum Cost & 34.84 & 15.80 & 28\% & 30\% \\  & Optimum CO\({}_{2}\) & 53.47 & 9.31 & 28\% & 30\% \\ NSGA-II & Optimum Cost & 34.84 & 15.79 & 28\% & 30\% \\  & Optimum CO\({}_{2}\) & 53.47 & 9.31 & \(-\)10\% & 58\% \\  & Cost-Oriented Knee Point & 39.51 & 13.83 & 18\% & 38\% \\  & CO\({}_{2}\)-Oriented Knee Point & 44.16 & 10.36 & 9\% & 54\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Total costs, carbon emissions, and their percentage changes compared to the base case scenario for Zone II. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \begin{tabular}{c} **Insulation** \\ **Thickness (m)** \\ \end{tabular} & \begin{tabular}{c} **Insulation** \\ **Material** \\ \end{tabular} & \
\begin{tabular}{c} **Wall Material** \\ **Wall Material** \\ \end{tabular} &
\begin{tabular}{c} **Heating** \\ **Source** \\ \end{tabular} \\ \hline Base Case Scenario & 0.02 & XPS & Brick & Fuel Oil \\ Optimum Cost & 0.056 & EPS & Brick & Natural Gas \\ Optimum CO\({}_{2}\) & 0.2245 & EPS & Light concrete & Natural Gas \\ Cost-Oriented Knee Point & 0.1493 & EPS & Brick & Natural Gas \\ CO\({}_{2}\)-Oriented Knee Point & 0.0906 & EPS & Light concrete & Natural Gas \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Optimum insulation thickness, insulation material, wall material and heating source for different objective functions (Zone III). Figure 9: CO\({}_{2}\) and total cost values at optimum points obtained for different objective functions (Zone III). According to Table 8, the base case scenario for Zone III yields a total cost of 54.52 USD/m\({}^{2}\) and a CO\({}_{2}\) emission of 25.10 kg/m\({}^{2}\). When optimizing for cost, a significant improvement is seen in the total cost, which drops to 36.07 USD/m\({}^{2}\), and CO\({}_{2}\) emissions are reduced to 16.25 kg/m\({}^{2}\).