## 6 Discussion  
In architectural performance optimization research, objective functions are commonly based on economic aspects such as life cycle cost, total investment cost, or building operation cost; energy aspects like electrical load; and environmental aspects such as carbon emissions [94]. In this paper, the optimization objective functions are per unit area heating carbon emissions and the global cost increment of retrofitting. This study has validated that retrofitting strategies, which enhance the insulation performance of the building envelope and add photovoltaic systems to roofs in rural residences in the Wusu area, can significantly reduce heating energy and carbon emissions. [PERSON] and others have proposed that the form factor of rural residences, the window-to-wall area ratio, and the thermal transmittance coefficient of the envelope are positively correlated with heating energy consumption in the severely cold regions of Northeast China [95], collectively indicating that establishing a heating energy consumption prediction model in severely cold regions can provide a basis for energy-saving retrofits for rural dwellings. The entropy weight TOPSIS method is used in this study to evaluate retrofitting schemes obtained through the NSGA-II algorithm. The results indicate that adding additional insulation to the exterior walls has the greatest impact on heating energy consumption, followed by the control of the south-facing window-to-wall ratio and the addition of insulation to the roof. [PERSON] and others, taking residential design in a severely cold village as an example, used the NSGA-II algorithm to filter design parameter combinations related to energy consumption and cost, obtaining a set of Pareto non-dominated solutions and a global balance solution, and selecting different technical templates for various needs [96]. [PERSON] and others took a new rural residential building in a cold region as the research object to simulate and analyze the impact of the thermal performance of various envelopes on building heating energy consumption, noting that the exterior walls have the greatest potential for energy savings, with a potential of 18.35%, windows at 15.64%, and the roof at 4.53% [97]. In addressing multi-objective research problems, the selection of the NSGA-II algorithm is feasible, and the conclusions drawn from the study of the impact of envelope structures on heating energy consumption in cold regions are in line with the trends observed in this study, indicating that in both severely cold and cold regions, greater attention should be paid to the insulation of exterior walls, windows, and roofs. Analysis of the Pareto frontier solutions indicates that the per unit area heating carbon emissions can be reduced to 78.76 kg CO\({}_{2}\)/KW-h, of which the solutions meeting the 75% energy-saving design standard of the autonomous region account for 42.2%, demonstrating the potential for sustainable development in rural housing. The best retrofitting scheme selected through the entropy weight TOPSIS method combines the retrofit of the building envelope and the application of photovoltaic systems, achieving an energy-saving rate of 79.5%. Compared with [PERSON]'s research on the thermal performance of vertical building envelopes in rural housing in the Hohhot-Baotou-Ordos region, the optimized scheme reached an energy-saving rate of up to 76.69% [98]. This proves the energy-saving effect of envelope structure optimization and shows that adding photovoltaic systems to rural housing can further enhance energy savings, validating the correctness of envelope structure optimization and the significant role of photovoltaic systems in promoting energy savings in rural dwellings. Furthermore, this study indicates that in the transitional heating season of October and April, the solar contribution rate of the photovoltaic system exceeds 100%, where the surplus energy can be utilized by metering transmission to the grid or battery storage.