## 3 Results and Discussion
### Comparison of Findings with Existing Studies, Applications, and Limitations  
In the previous literature review, a broader scope was discussed, including research on multi-objective optimization of high-rise, multi-story, and low-rise residential buildings. This section focuses on the detailed comparison of related studies on high-rise buildings, taking [14; 15; 21; 22] for example, as shown in Table 5.  
In comparison with the existing studies shown in Table 5, the contributions of our work are mainly twofold: firstly, the synchronous effects of four objectives are weighed by using the proposed method, as well as obtaining the Pareto solution set and optimal design solutions; secondly, the utilization of solar photovoltaic energy is considered in the objective function calculation, enabling a more comprehensive assessment of energy efficiency design, and the influence of differences in solar radiation is analyzed. For the different climate zones, such as in [14; 22], the findings obtained are obviously different. Our findings are mainly comparable to those in [15; 21], with the same climate region as our study. In [15], the heating energy consumption and summer uncomfortable hours were taken as optimization objectives in the preliminary screening, without considering the cost and carbon emissions. According to the tradeoff optimal solution obtained, compared with case-1 (Xi'an), the roof insulation layer is thicker and the window performance is better. In [21], the LCC and primary energy consumption were set as the optimization objectives, without considering thermal comfort and carbon emissions. Similarly, in the obtained equilibrium solution, the thermal performance of the exterior wall, roof, and exterior window was better than that of case-1 (Xi'an). This indicates that when the constraints are less, the values of design variables may have adverse effects on other objectives. In addition, the photovoltaic system in the present study was adopted to supplement the energy consumption; thus, our building energy-saving rate was higher than that in [17; 23]. The utilization of renewable energy is indispensable. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Literature** & **Climatic Zone** & **Objectives** & **Design Variables** & **Consider PV?** \\ \hline \multirow{4}{*}{[14]} & \multirow{4}{*}{Hot summer and cold winter zone} & & Layout plans, orientation, shape coefficient, floor area, stories, north/south/west/east window–wall ratio, wall/roof/window heat transfer coefficient, and wall/roof heat inertia index & No \\  & & Heating energy consumption and discomfort hours in summer & Wall/roof insulation thickness, window type, gas tightness, horizontal sunvisor, and equipment system type & No \\ \hline \multirow{4}{*}{[21]} & Severe cold, cold, hot summer and voltd winter, hot summer and warm winter, mild zone & LCC and primary energy consumption & Wall/roof/window heat transfer coefficient, and total heat recovery efficiency & No \\  & & & Wall/roof insulation thickness, window type, south/north/west/east window–wall ratio, and overhang depth, orientation & No \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison with the existing studies on high-rise residential buildings. It should be noted that only typical cases were selected above for contrastive analysis, and in practical applications the optimal scheme can be selected from the Pareto solution set according to the specific weight value of each objective. However, in the actual project design, the challenge is that some objectives or variables will be limited, so not all of the schemes in the Pareto solution set are applicable, and alternative schemes need to be screened out first. For optimization objectives, if the energy-saving rate is limited to a range, the schemes meeting the energy-saving requirements can be screened from the Pareto solution set first, and then the TOPSIS method can be used to determine the optimal scheme.