# Slot Optimization Based on Coupled Airspace Capacity of Multi-Airport System
## 4 Algorithm
(3) Analysis of capacity-flow relationships at corridors

Corridors from the 16 th simulation are taken for airport flow-capacity ratio analysis, as shown in Figure 10. In Scenario 1, the AVBOX corridor is overcapacity at 1300, 1400, 2000, and 2100 h; the PEGSO corridor is overcapacity at 0800 h; and the BELAX corridor is overcapacity at 2200 h. In Scenario 2, the AVBOX corridor is overcapacity at 1300, 1400, 2000, and 2100 h; the ELKUR corridor is overcapacity at 0800 and 1700 h; and the PEGSO corridor is overcapacity at 0800 h. Both scenarios show multiple corridor overcapacacities \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Algor-ithm**} & \multicolumn{6}{c}{**Delay Value/Second (Mean \(\pm\) Standard Deviation)**} \\ \cline{2-10}  & \multicolumn{3}{c}{**Average Delay**} & \multicolumn{3}{c}{**Average Approach Delays**} & \multicolumn{3}{c}{**Average Departure Delays**} \\ \cline{2-10}  & **ZBAA** & **ZBAD** & **ZBTJ** & **ZBAA** & **ZBAD** & **ZBTJ** & **ZBAA** & **ZBAD** & **ZBTJ** \\ \hline Scenario & 283.1 \(\pm\) 19.4 & 216.4 \(\pm\) 15.4 & 403.1 \(\pm\) 29.1 & 306.2 \(\pm\) 19.1 & 172.3 \(\pm\) 10.8 & 300.4 \(\pm\) 18.9 & 446.2 \(\pm\) 19.7 & 286.3 \(\pm\) 14.8 & 551.4 \(\pm\) 24.6 \\ Scenario & 211.9 \(\pm\) 21.1 & 201.4 \(\pm\) 20.8 & 331.0 \(\pm\) 36.2 & 174.6 \(\pm\) 17.3 & 209.2 \(\pm\) 18.1 & 379.1 \(\pm\) 30.2 & 244.7 \(\pm\) 22.6 & 200.8 \(\pm\) 21.9 & 300.4 \(\pm\) 41.4 \\ Scenario & 191.3 \(\pm\) 10.2 & 157.6 \(\pm\) 11.2 & 218.4 \(\pm\) 9.6 & 174.1 \(\pm\) 7.9 & 111.0 \(\pm\) 7.8 & 210.4 \(\pm\) 8.9 & 210.1 \(\pm\) 6.3 & 199.6 \(\pm\) 11.2 & 221.8 \(\pm\) 13.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Simulation delay results. Figure 9: **(a) Airport flow–capacity ratio diagram for Scenario 1 sector; (b) airport flow–capacity ratio diagram for Scenario 2 sector; (c) airport flow–capacity ratio diagram for Scenario 3 sector. (The vertical axis represents the sector name. The horizontal axis represents the time period of the day, from 0 to 23. The color blocks in the figure represent the flow–capacity ratio, and the values corresponding to the depth are indicated by the color blocks on the right side of the figure. The black block indicates that the flow–capacity ratio exceeds 100%. )**at peak hour segments, while Scenario 3 does not show corridor overcapacity periods, indicating better corridor constraint effects and optimization for multi-airport flights. ## 6 Conclusions

This study established a multi-objective decision-making model for optimizing flight schedules in a multi-airport system on the basis of the comprehensive consideration of the fairness of flight schedules in the multi-airport system, which was achieved through the introduction of probabilistic competitiveness of the shared resources and ensuring flexible compatibility with China's 24 h schedule coordination parameter and its schedule slot firebreak. Combined with historical data for airport slots in the Beijing multi-airport system, the following conclusions were drawn through computation and analysis using the NSGA-II algorithm:

(1) The multi-airport system, based on the fairness of the flight schedules of the multi-airport system and the single-objective optimization of the single-airport system, demonstrates superior capability in balancing flight schedule slot deviations, the fairness of each airport in the multi-airport system, and the airlines concerned, when compared with the single-objective optimization of the single-airport project. (2) Through the introduction of shared resource probabilistic competitiveness, this study more fully considers the factors influencing multi-airport system airport slot deviations to solve airport slot uncertainty and corridor constraints, thus developing a more realistic and comprehensive model with full consideration of the multi-airport system in terms of corridor capacity constraints, transit time, parking constraints, and so on.