## 4 Conclusions  
In this study, multi-objective optimization, whose objectives are minimum cost and minimum CO\({}_{2}\) emission, has been carried out with the NSGA-II method. The analysis results indicate that for Zone I, the optimal insulation thickness for minimizing cost is 4.7 cm, while the optimal thickness for minimizing CO\({}_{2}\) emissions is 19.61 cm. In Zone II, the optimal cost is achieved with an insulation thickness of 4.99 cm, and the optimal CO\({}_{2}\) emissions occur at a thickness of 20.55 cm. For Zone III, the lowest  
Figure 13: Emission components variation for different insulation thicknesses in the hottest and coldest climate. cost is found with an insulation thickness of 5.6 cm, whereas the lowest CO2 emissions are achieved at 22.45 cm. Lastly, in Zone IV, the optimal cost corresponds to an insulation thickness of 7.97 cm, and the optimal CO2 emissions are attained at 29.71 cm. In the multi-objective optimization analysis, the knee point method is used to determine the optimal insulation thicknesses for cost-oriented and CO2-oriented approaches. For Zone I, the optimal thicknesses are 13.12 cm for the cost-oriented approach and 7.90 cm for the CO2-oriented approach. In Zone II, the optimal thicknesses are 13.68 cm and 8.29 cm for the cost-oriented and CO2-oriented approaches, respectively. For Zone III, the optimal insulation thicknesses are found to be 14.93 cm for the cost-oriented approach and 9.06 cm for the CO2-oriented approach. Finally, in Zone IV, the optimal thicknesses are 19.92 cm for the cost-oriented approach and 12.98 cm for the CO2-oriented approach. When the primary objective is to reduce costs, EPS insulation material should be selected, with brick as the wall material and natural gas as the heating source. Conversely, when the main goal is to minimize CO2 emissions, EPS insulation material should still be used but paired with light concrete for the wall material and natural gas for heating. Across all optimization objectives, Zone IV consistently shows the highest percentage improvements in both cost and CO2 emissions. However, when the analyses are conducted based on the optimum CO2 scenario, a deterioration in costs is observed in all Zones except Zone IV. While a deterioration in costs of up to 23% has been observed in certain Zones and conditions, improvements of up to 49% have been seen in other cases. Besides, improvement in emissions ranges from 23% to 71%. These insights emphasize the importance of climate-specific insulation strategies to maximize environmental and economic benefits. When examining the components that make up the total cost and total emissions individually, it is found that increasing insulation thickness can lead to significant heating cost savings in colder climates. It is also observed that in Zone I, cooling cost savings are more pronounced, while in Zone IV, heating cost savings are more significant. Since emissions released into the atmosphere are related to the amount of energy used, it is understood that increasing insulation thickness can substantially reduce heating emissions in colder climates, making it both an economically and environmentally advantageous approach. Finally, four different multi-objective optimization methods (NSGA-II, CCGDE3, MOEA/D-UR, and DEA-GNG) are examined to determine the optimum points and compare different optimization methods. All four methods give very similar or the same results. It has been determined that all algorithms are highly effective for achieving optimal results in insulation applications that require the simultaneous optimization of two different objective functions. Conceptualization, A.S.C. and E.I.A. ; methodology, A.S.C. ; software, E.I.A. ; validation, A.S.C. and E.I.A. ; formal analysis, A.S.C. and E.I.A. ; investigation, A.S.C. ; resources, E.I.A. ; data curation, A.S.C. and E.I.A. ; writing--original draft preparation, A.S.C. ; writing--review and editing, A.S.C. and E.I.A. ; visualization, A.S.C. and E.I.A. ; supervision, A.S.C. ; project administration, A.S.C. and E.I.A.