## 3 Results and Discussions  
After an optimization search of 50 generations, the 176 non-dominated solutions in the last generation showed a tendency of convergence, as shown in Figure 12. The three axes of the 3-D scatter plots represent BEC, sDA and UDI values respectively, and the colors of the boxes indicate the EUI values. Non-dominated solutions with higher EUI values are drawn as red boxes and those with lower EUI values are drawn as green, which also indicate a better EUI performance. The closer the boxes are to the origin, the better the sDA, UDI and BEC performance will be. The gray-green boxes represent the feasible solutions in different generations. With the number of iteration rises, the gray-green boxes become darker, and the value distribution range get closer to a surface composed by non-dominated solutions. The non-dominated solutions with higher sDA values suggest a decrease tendency in UDI values and an increase tendency in EUI and BEC values, which demonstrates that sDA has certain contradictory relationships with the other three objectives. To further understand the relationship between four objectives and the distribution characteristics of the non-dominated solutions, a matrix plot was drawn as Figure 13. The upper triangular part of the matrix is composed of the correlation coefficients calculated between different objectives of the non-dominated solutions while the lower triangular part of the matrix is composed of the 2-dimensional scatter plots in objective space. The diagonal part of the matrix shows the distribution of the non-dominated solutions in each objective dimension. The results suggest that the non-dominated solutions tended to be evenly distributed in the EUI range, more non-dominated solutions were distributed in the range where sDA was greater than 90%, UDI was around 60% and BEC was less than \(\forall\)2.5\(\times\)10\({}^{6}\) ($3.6\(\times\)10\({}^{5}\)), which proved that the optimization process could achieve tradeoffs between different objectives. The correlation coefficients in the upper triangular part suggest that there was a significant positive correlation between sDA and EUI, with an R value of 0.680. The scatter plot between sDA and EUI also verifies that with an increase in sDA values, EUI values tended to be higher. That is to say, a better sDA performance may lead to a worse EUI performance, which can be attributed to that both objectives are very sensitive to WWR parameters as well as the window thermal and optical properties. As the reference building is located in severe cold region, the correlation between the WWR value and the energy consumption is very strong. According to the research results obtained by [PERSON] et al. (2013), a lower WWR value can cause less heating and cooling requirement but more lighting requirement in cold region of Frankfurt and Oslo, but in the hot region of Palermo and Torino a lower  
Figure 12: Many-objective optimization results: (**a**) solutions converging by generation and (**b**) non-dominated solutions of the last generation. WWR value can cause less cooling requirement but more heating and lighting requirement. The conflict relationship between building energy consumption and daylighting is obvious in cold regions. On the other hand, it also explains the importance of WWR parameters while designing buildings in cold regions. In addition, windows with lower U values will have a better thermal performance, but in which case the SHGC and VT values of them are often lower, the conflict between window thermal and optical properties can also lead to a contradiction between sDA and EUI. As shown by the correlation coefficient between sDA and UDI, there was a significant negative correlation between the two objectives, with an R value of -0.623. When we focus on the scatter plot of the two objectives, the correlation seems to be more complicated and nonlinear.