## 3 Results and Discussion
In the scenario optimized for CO\({}_{2}\), while the cost has slightly increased to 55.57 USD/m\({}^{2}\), CO\({}_{2}\) emissions fall to 9.58 kg/m\({}^{2}\), which is a substantial reduction. For the cost-oriented optimum scenario, the total cost is further reduced to 41.10 USD/m\({}^{2}\), with CO\({}_{2}\) emissions at 14.11 kg/m\({}^{2}\). For the CO\({}_{2}\)-oriented optimum scenario, the total cost is 45.42 USD/m\({}^{2}\), and CO\({}_{2}\) emissions are 10.74 kg/m\({}^{2}\). As mentioned before, for the same objective functions, only the insulation thickness changes, while the other design variables remain unchanged. In the analyses conducted for Zone IV, the optimum conditions determined for other zones remain constant. For Zone IV, 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 7.97 cm, 29.71 cm, 19.92 cm, and 12.98 cm, respectively (see Table 9 and Figure 10). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **Scenario** & \
\begin{tabular}{c} **Cr** \\ **(USD/m\({}^{2}\))** \\ \end{tabular} &
\begin{tabular}{c} **M\({}_{\text{CO2}}\)** \\ **(kg/m\({}^{2}\))** \\ \end{tabular} & \% C\({}_{\text{T}}\) & \% M\({}_{\text{CO2}}\) \\ \hline \multirow{4}{*}{CCGDE3} & Base Case Scenario & 54.52 & 25.10 & - & - \\  & Optimum Cost & 36.07 & 16.26 & 34\% & 35\% \\  & Optimum CO\({}_{2}\) & 55.62 & 9.58 & \(-\)2\% & 62\% \\ MOEA/D-UR & Optimum Cost & 36.07 & 16.24 & 34\% & 35\% \\  & Optimum CO\({}_{2}\) & 55.50 & 9.58 & \(-\)2\% & 62\% \\ DEA-GNG & Optimum Cost & 36.07 & 16.24 & 34\% & 35\% \\  & Optimum CO\({}_{2}\) & 55.57 & 9.58 & \(-\)2\% & 62\% \\ NSGA-II & Optimum Cost & 36.07 & 16.25 & 34\% & 35\% \\  & Optimum CO\({}_{2}\) & 55.57 & 9.58 & \(-\)2\% & 62\% \\  & Cost-Oriented Knee Point & 41.10 & 14.11 & 25\% & 44\% \\  & CO\({}_{2}\)-Oriented Knee Point & 45.42 & 10.74 & 17\% & 57\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Total costs, carbon emissions, and their percentage changes compared to the base case scenario for Zone III. Figure 10: CO\({}_{2}\) and total cost values at optimum points obtained for different objective functions (Zone IV). As shown in Table 10, the base case scenario identified in the study for Zone IV has a total cost of 79.66 USD/m\({}^{2}\) and a total CO\({}_{2}\) emission of 36.58 kg/m\({}^{2}\). In the optimum cost scenario, the total cost has decreased to 40.80 USD/m\({}^{2}\), while the total CO\({}_{2}\) emission is determined to be 17.97 kg/m\({}^{2}\). In the optimum CO\({}_{2}\) scenario, although the cost has slightly decreased to 63.60 USD/m\({}^{2}\), the main improvement is observed in the CO\({}_{2}\) amount, which is 10.60 kg/m\({}^{2}\). In the cost-oriented optimum scenario determined using the knee point approach, the total cost has decreased to 47.21 USD/m\({}^{2}\), and the total CO\({}_{2}\) emission to 15.20 kg/m\({}^{2}\). In the CO\({}_{2}\)-oriented optimum scenario, the total cost has been determined to be 50.71 USD/m\({}^{2}\), and the total CO\({}_{2}\) emission is 11.93 kg/m\({}^{2}\). The degree-day method, mentioned before, is a widely accepted and well-established approach for estimating energy consumption in buildings. Annual energy consumption is analyzed to determine the optimal insulation thickness. In order to validate the energy consumption calculation model, this study compares the insulation thicknesses that minimize costs with those determined in other studies examining the city of Erzurum, which is also analyzed in this research. The comparative results are presented in Table 11. It can be observed that the results are close to each other. The slight differences may be due to the use of different fuel types, different insulation materials, or periodic changes in financial parameters.