## 7 Conclusions  
Improving the building's structural performance and reducing the economic costs of heating are key to promoting carbon reduction in rural house heating systems. Installing photovoltaic power systems on building roofs offers good economic benefits and significant energy-saving and emission-reduction effects. Effectively utilizing measures such as external wall and roof insulation, the performance of transparent envelope structures, and clean energy can achieve optimal energy-saving and cost-effectiveness. The differentiated performance of various retrofitting plans for rural houses in terms of each target performance is as follows:  
The carbon emission per unit area of heating has been reduced from a high of 109.76 kg CO\({}_{2}\)/KW\(\cdot\)h to 78.76 kg CO\({}_{2}\)/KW\(\cdot\)h. Among the Pareto front solutions, 42.2% meet the autonomous region's current energy-saving residential design standard of a 75% energy-saving rate; the lowest building thermal consumption index can reach 12.427 w/m\({}^{2}\), at which point the energy-saving rate has reached 79.5%. In all retrofitting plans, 64% have \(dC_{g}<0\); within the Pareto front solutions, 80% of the plans with \(dC_{g}<0\) indicate that improving the envelope structure and adding photovoltaic components are economically feasible in reducing heating energy consumption. Balancing the carbon emissions from heating and the overall cost increase from retrofitting, the balanced solution for the retrofit of the rural house is identified: the net height of the house is 2.80 m, the external wall is insulated with 280 mm thick EPS polystyrene board, the insulation thickness of the roof is 240 mm, and the type of external window chosen is type 5 (6 mm translucent low-E, 12 mm argon gas, and 6 mm transparent), with a south-facing window-to-wall ratio controlled at 0.3 and a north-facing window-to-wall ratio of 0.09, without adding external shading. At this point, the corresponding carbon emission per unit building area is 82.11 kg CO\({}_{2}\)/m\({}^{2}\), and the global cost increase is \(-\)31,818.74 CNY. The addition of photovoltaic system components yields an annual electricity output of 8187 kWh, with a total output of 191,661 kWh over 25 years. The photovoltaic system reduces standard coal emissions by 19.28 kgce/(m\({}^{2}\cdot\)a) and carbon emissions by 0.834 kg/(m\({}^{2}\cdot\)a) over its operational cycle. At this point, the payback period for the investment in the heating retrofit of the rural house is 12.51 years, demonstrating good economic and environmental benefits. This study employs the NSGA-II genetic algorithm-based multi-objective optimization plugin, Wallacei, to balance per unit area carbon emissions and the global cost increment of retrofitting, constructing a multi-objective optimization approach suitable for winter heating in rural dwellings in the Wusu area. By analyzing the Pareto frontier solutions, the study evaluates the impact of each optimization scheme on winter heating energy consumption and economic costs, proposing energy-saving and emission-reduction solutions under the premise of economic viability. It also highlights some limitations. Firstly, due to geographical location and manpower constraints, the sample size is limited, with the research perspective focused on the Wusu area. Despite being in the same cold region, there are differences in climate characteristics, cultural backgrounds, and residents' living habits across regions. There is a need for targeted energy-saving retrofit designs for rural dwellings that maintain the characteristics and continuity of regional architecture while meeting energy-saving and emission-reduction requirements. Further analysis of their socio-economic benefits should be conducted to ensure the economic feasibility of the retrofitting schemes. Moreover, this study is limited to analyzing the current typical climate conditions without predicting or assessing the potential impacts of future climate changes.