## 3 Results and Discussion  
According to the Turkish Standards Institution (TS 825) [55], Turkishye is divided into four different climatic zones, as shown in Figure 3. Among these regions, the first zone corresponds to the hottest climate region, while the fourth zone corresponds to the coldest climate region. In the present study, the cities of Osmaniye, Bursa, Isparta, and Erzurum, located in the first, second, third, and fourth zones, respectively, have been chosen to observe the influence of different climatic zones. As mentioned earlier in the manuscript, the effect of solar radiation has been considered when calculating annual average heating (\(HDD\)) and cooling (\(CDD\)) degree days values to achieve more realistic results. Figure 4 presents the \(HDD\) and \(CDD\) values calculated for each province. Figure 4 illustrates that the cities with the highest \(HDD\) values, which correlate directly with heating energy requirements, are ranked in descending order: fourth zone, third zone, second zone, and first zone. Conversely, the cities with the highest \(CDD\) values, indicating cooling energy demands, are arranged as first zone, second zone, third zone, and fourth zone. The graph clearly demonstrates that the total (heating and cooling) annual energy needs, from greatest to least, are as follows: fourth zone > third zone > second zone > first zone. Figure 3: Different climatic zones of Turkishye and selected cities for the study. As shown in Table 3, in the base case scenario, the wall structure consists of 2 cm thick extruded polystyrene (XPS) as the insulation material, and brick as the wall material. The heating source used is fuel oil. In the following section, multi-objective optimizations for zones are examined. When the Pareto fronts obtained for each zone are examined, it is seen that the four optimization methods overlap. Since the optimum points given in the tables are the same or very close to each other and, therefore, insignificantly low in terms of insulation cases, the examinations are made using the NSGA-II method. In the optimization methods, the population size is selected as 100, while the maximum iteration number is determined as 10,000. Other parameters are taken as the default values of the optimization methods without performing parameter optimization since the same results and the same values or very small differences occurred in all optimization methods. In order to examine the effects of design variables on the objective functions' Cost and CO\({}_{2}\), a stepwise analysis is performed. Here, the initial situation is kept constant, and each parameter is changed to examine its effects on the objective functions. When Figure 5 is examined, it is seen that the most negligible impact in terms of cost is in the change of heating source. The most significant effect is seen in insulation thickness and insulation material. When the CO\({}_{2}\) values in Figure 6 are examined, it is seen that the other parameters, except the insulation material, have a similar effect. As in cost, a sharp increase is observed in CO\({}_{2}\) at small values of the insulation material. \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 & 0.0470 & EPS & Brick & Natural Gas \\ Optimum CO\({}_{2}\) & 0.1961 & EPS & Light concrete & Natural Gas \\ Cost-Oriented Knee Point & 0.1312 & EPS & Brick & Natural Gas \\ CO\({}_{2}\)-Oriented Knee Point & 0.0790 & EPS & Light concrete & Natural Gas \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Optimum insulation thickness, insulation material, wall material, and heating source for different objective functions (Zone I). Figure 4: Annual Average Heating and Cooling Degree Days for Different Zones. thickness of 7.9 cm, EPS insulation material, light concrete wall material, and natural gas as the heating source.