## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Scenario**} & \multirow{2}{*}{
\begin{tabular}{c} **Cr** \\ **(USD/m\({}^{2}\))** \\ \end{tabular} } & **M\({}_{\text{CO2}}\)** & \multirow{2}{*}{\% **C\({}_{\text{T}}\)**} & \multirow{2}{*}{\% **M\({}_{\text{CO2}}\)**} \\  & & **(USD/m\({}^{2}\))** & & & \\ \hline \multirow{4}{*}{CCGDE3} & Base Case Scenario & 79.66 & 36.58 & - & - \\  & Optimum Cost & 40.80 & 17.97 & 49\% & 51\% \\  & Optimum CO\({}_{2}\) & 63.64 & 10.60 & 20\% & 71\% \\ MOEA/D-UR & Optimum Cost & 40.80 & 17.97 & 49\% & 51\% \\  & Optimum CO\({}_{2}\) & 63.52 & 10.60 & 20\% & 71\% \\ DEA-GNG & Optimum Cost & 40.80 & 17.97 & 49\% & 51\% \\  & Optimum CO\({}_{2}\) & 63.84 & 10.60 & 20\% & 71\% \\ NSGA-II & Optimum Cost & 40.80 & 17.97 & 49\% & 51\% \\  & Optimum CO\({}_{2}\) & 63.60 & 10.60 & 20\% & 71\% \\  & Cost-Oriented Knee Point & 47.21 & 15.20 & 41\% & 58\% \\  & CO\({}_{2}\)-Oriented Knee Point & 50.71 & 11.93 & 36\% & 67\% \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Total costs, carbon emissions, and their percentage changes compared to the base case scenario for Zone IV. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Study** \\ \end{tabular} } & \multicolumn{2}{c}{**Erzurum**} \\  & \multicolumn{2}{c}{**x\({}_{\text{opt}}\) (cm)**} \\ \hline Present Study & & 7.97 \\ [PERSON] et al. [56] & & 8.0 \\ [PERSON] [57] & & 7.39 \\ [PERSON] et al. [58] & & 8.0 \\ [PERSON] [34] & & 7.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Comparative analysis with other studies. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Insulation** & **Insulation** & **Wall Material** & **Heating Source** \\ \hline Base Case Scenario & 0.02 & XPS & Brick & Fuel Oil \\ Optimum Cost & 0.0797 & EPS & Brick & Natural Gas \\ Optimum CO\({}_{2}\) & 0.2971 & EPS & Light concrete & Natural Gas \\ Cost-Oriented Knee Point & 0.1992 & EPS & Brick & Natural Gas \\ CO\({}_{2}\)-Oriented Knee Point & 0.1298 & EPS & Light concrete & Natural Gas \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Optimum insulation thickness, insulation material, wall material, and heating source for different objective functions (Zone IV). Figure 11 shows the percentage improvements in cost (%C\({}_{\text{T}}\)) and emissions (%MCO\({}_{2}\)) when insulation is applied, based on the optimum insulation thicknesses obtained for four different objective functions across four different climate zones. In the optimum cost scenario, the improvements in cost and CO\({}_{2}\) emissions are more balanced across all zones. Zone IV leads with the highest improvements, followed closely by Zone III, Zone II, and Zone I, which have relatively similar performance. This indicates that the optimum cost scenario leads to significant gains in both cost and CO\({}_{2}\) emissions, with consistent results across different climate zones. The optimum CO\({}_{2}\) scenario focuses on minimizing CO\({}_{2}\) emissions. Zone IV demonstrates the highest CO\({}_{2}\) reduction, exceeding 70%, while the cost reduction is around 20%. Zone I shows a deterioration in cost but still achieves a substantial CO\({}_{2}\) reduction of 54%. Figure 11: Percentage improvement in total cost and CO\({}_{2}\) emissions for different insulation thicknesses under various optimization objectives across climate zones. Under the Cost-Oriented Multi Objective scenario there is a noticeable improvement in both cost and CO2 emissions across all zones. Zone IV exhibits the biggest improvement in cost reduction, reaching close to 60%, while its CO2 emission improvement is also significant, nearing 41%. Zone I has the lowest percentage improvements in both cost and CO2 emissions compared to other zones, but the improvements are still meaningful. In the CO2-Oriented Multi-Objective scenario, Zone IV exhibits the highest CO2 improvement at around 67%, with cost improvement slightly lower at around 36%.