## 4 Conclusions  
This paper, focused on high-rise residential buildings located in two areas of Northwestern China with different solar radiation, introduces a multi-objective optimization method, which was implemented through the Grasshopper simulation and optimization platform coupled with a TOPSIS method to find the optimal design solution that minimized the EC, TDHP, LCC, and LCCO\({}_{2}\). A series of Pareto non-dominated solutions were identified. The main conclusions are as follows:  
The optimization generated 65 and 82 Pareto-optimal solutions in total that significantly improved the four objectives for Xi'an and Yulin, respectively. From the comparison of the two cities, in terms of the relationship between building energy consumption and the other three objectives, the Pareto solution set in Yulin showed a more dispersed distribution, showing multiple approximately parallel curves. This is mainly because the objective function considers the offset of solar power generation, and the solar radiation in Yulin is stronger, leading to different solution set distribution characteristics from those in Xi'an. This is mainly due to the fact that solar power generation is considered in the objective function calculation, and the solar radiation in Yulin is stronger, thus forming a solution set distribution characteristic different from that in Xi'an. From the perspective of objective value distribution, the LCC and LCCO\({}_{2}\) in Yulin have a wide distribution range, and the LCCO\({}_{2}\) is also negative due to the carbon reduction effect of photovoltaic power generation. However, the distribution of EC and TDHP is similar to that in Xi'an. In the value distribution of the four objectives, LCC has the largest distribution interval, followed by LCCO\({}_{2}\) and EC, while TDHP has the smallest span, indicating that the adjustment of design variables has a significant impact on the first three objectives, while the effect on TDHP is relatively small. According to the value distribution of the design variables, as well as the quantitative relationship between the design variables and each objective, the value distribution characteristics of the design variables are different due to the constraints of the four objectives. Within a given threshold, the values of some variables are centrally distributed, such as the building orientation, which is concentrated in the middle. The value range of Xi'an is 20-30\({}^{\circ}\) south by west, while that of Yulin is 0\({}^{\circ}\)-15\({}^{\circ}\) south by west. The south and north window-wall ratios are concentrated at the lower limit of the threshold. The thickness of the roof insulation layer is mainly concentrated in the upper limit of the threshold. The values of the other variables are discretized, such as the sunvisor overhang length, but Yulin is different from Xi'an in that they are concentrated at the lower limit of threshold. The south and north exterior window types, along with the thickness of the external wall insulation layer, are discretionally distributed. These can also be reflected in the clustering parallel coordinate graph of the optimization objectives and variables. The reason for these conditions is that the design variables have different influence rules on each objective and, affected by the differences in climate conditions and solar radiation, these mechanisms will change. Even for the same region, when other design variables change, it will affect the influence degree of some design variables on the optimization objective. The Pareto non-dominated solution set provides enough schemes for designers. The TOPSIS method was adopted to obtain the optimal scheme, from the perspective of comprehensive performance, with an energy-saving rate of 61.7%, TDHP improvement rate of 20.3%, LCC of 254.8 CNY/m\({}^{2}\), and LCCO\({}_{2}\) of 72.3 kgCO\({}_{2}\)/m\({}^{2}\) in the Xi'an area. The corresponding values in the Yulin area are 69.7%, 19.4%, 230.2 CNY/m\({}^{2}\), and 0 kgCO\({}_{2}\)/m\({}^{2}\).