## 4 Optimizing the Air Supply Parameters of a Dual-Aisle Single-Row Cabin
### Optimization Results  
Figure 11 shows the change in \(F^{\prime}_{min}\), where the abrupt drop in Iteration 4 was due to the fact that the airflow organization with the smallest \(F^{\prime}\) changes from A-shaped to B-shaped. And after Iteration 8, some non-dominated solutions were obtained, but \(F^{\prime}_{min}\) did not decrease. Meanwhile, Figure 12 shows the Pareto Frontier with all non-dominated solutions. For such a five-parameter optimization process, a fully meta-heuristic optimization approach may require thousands of samples to obtain a reliable optimization result. The above results show that the thermal comfort of the occupants in the two zones is antagonistic and cannot be maximized at the same time because of the limitations of the air supply. Case A shows the form of airflow organization that is present when maximizing the thermal comfort of the middle occupants, and it can be seen that the thermal comfort of the occupants on both sides is completely abandoned, while the opposite is true for case C. Case B is probably the best, as the airflow on each side converges from the aisle to the bottom, creating two symmetrical loops, with only the middle occupant near the aisle being slightly affected by the cold air. The other Pareto solutions (Figure 12) correspond to less favorable situations. Furthermore, the concave Pareto Frontier makes the total volume be maximized in case B (located in the middle part of the Pareto Frontier). So, there is no need to completely abandon a region to obtain the maximum total volume, which should be consistent with the optimal solution obtained with single-objective optimization using the total volume. According to additional study of the non-dominated solutions surrounding solution 3 through Table 5, the air supply parameters (solutions 2-8) show small variation. It shows that the requirements for forming the airflow organization depicted in B in the two-aisle cabin are more demanding and that the effect of raising supply air temperature on the _PMV_ cannot be mitigated by raising air velocity [4] as in the single-aisle cabin, where there is no occupant in the middle. Figure 12: Pareto Frontier. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**No.** & \(\mathbf{t}\) (\({}^{\circ}\)**C**) & \(\mathbf{V_{1}}\) (m/s) & \(\mathbf{V_{2}}\) (m/s) & \(\mathbf{\theta_{1}}\) (\({}^{\circ}\)) & \(\mathbf{\theta_{2}}\) (\({}^{\circ}\)) & **Volume 1 (m\({}^{3}\))** & **Volume 2 (m\({}^{3}\))** & **Total (m\({}^{3}\))** \\ \hline
1 & 8 & 0.76 & 0.98 & 19 & 12 & 0.786 & 0.709 (max) & 1.496 \\
2 & 10.8 & 0.83 & 0.29 & \(-\)56 & \(-\)15 & 1.236 & 0.621 & 1.856 \\
3 & 10.8 & 0.87 & 0.28 & \(-\)57 & \(-\)17 & 1.296 & 0.596 & 1.893 (max) \\
4 & 10.6 & 0.9 & 0.27 & \(-\)55 & \(-\)20 & 1.301 & 0.578 & 1.880 \\
5 & 11 & 0.87 & 0.31 & \(-\)60 & \(-\)14 & 1.304 & 0.550 & 1.854 \\
6 & 10.9 & 0.86 & 0.29 & \(-\)58 & \(-\)17 & 1.305 & 0.549 & 1.854 \\
7 & 10.9 & 0.87 & 0.29 & \(-\)59 & \(-\)15 & 1.316 & 0.526 & 1.841 \\
8 & 10.8 & 0.86 & 0.31 & \(-\)59 & \(-\)17 & 1.340 & 0.495 & 1.834 \\
9 & 9.8 & 1.01 & 0.97 & \(-\)72 & \(-\)68 & 1.371 (max) & 0.394 & 1.765 \\ \hline \hline \end{tabular}  
* Notes: Volume 1 (2) refers to the volume in controlled area 1 (2) that satisfies \(|\)PMV1 \(<\) 0.5, and the total volume of controlled area 1 (2) is 1.47 (0.73) m\({}^{3}\).  
\end{table} 
Table 5: Part of Pareto solutions and the corresponding volume values. For example, once the air velocity at the bottom air inlets has been increased, the airflow cannot form a rounded airflow like B at low angles of air supply, and the airflow will be directed towards the occupants next to the aisle, while at high angles of air supply, an airflow organization similar to that shown in C will form, meaning that the thermal comfort of the occupants in the middle is sacrificed. For the case of decreasing the temperature and velocity and increasing the angle, there is a lack of samples, as the surrogate model may again show large errors in the face of such scenarios with rapidly changing response values.