Evaluation and optimization of departure flight schedule stability of airport group
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摘要:
随着中国航空运输量的不断增加，机场群航班时刻资源日益稀缺、航班延误严重等问题也逐渐显现，有必要深入研究机场群的航班时刻优化问题。在明确机场群离港航班时刻稳定性概念基础上，提出离港航班延误率、平均延误时间等共6项机场群离港航班时刻稳定性评估指标，并运用改进的逼近理想解排序（TOPSIS）法对稳定性进行质量评估。建立机场群离港航班时刻优化模型，选择改进粒子群算法来实现对该模型的优化，并以稳定性质量为标准对优化前后航班计划进行比较。以京津冀机场群为例进行验证，仿真结果表明：所提优化模型和算法能够降低北京首都国际机场离港航班平均延误时间18.8 s，降低平均延误率9.9%；繁忙航线平均延误时间降低12.7 s，平均延误率降低3.0%；有效降低了京津冀机场群整体延误水平，提高机场群离港航班时刻稳定性。
Abstract:As China’s aviation traffic keeps growing, issues including dwindling flight schedule resources and major flight delays in airport clusters are rapidly becoming more and more prevalent. It is necessary to thoroughly study flight schedule optimization in airport groups. On the basis of defining the concept of departure flight schedule stability of airport groups, this paper puts forward six evaluation indexes of departure flight schedule stability of airport groups, such as departure flight delay rate and average delay time, and evaluates the stability quality by using improved TOPSIS (a technique for order preference by similarity to ideal solution). Following the establishment of the airport group’s departure flight schedule optimization model and the selection of an improved particle swarm optimization algorithm to optimise the model, the flight plans before and after optimization are contrasted using the stability quality as the benchmark. Finally, taking Beijing-Tianjin-Hebei airport group as an example, the simulation results show that the proposed optimization model and algorithm can reduce the average delay time of departure flights at Beijing airport by 18.8 s and the average delay rate by 9.9%; The average delay time of busy routes is reduced by 12.7 s, and the average delay rate is reduced by 3.0%, which effectively reduces the overall delay level of Beijing-Tianjin-Hebei airport group and improves the stability of departure flight schedule of the airport group.
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图 1 机场航班时刻稳定性评估层次递进结构
Figure 1. Hierarchical structure of airport flight schedule stability evaluation
图 2 机场群内多机场间宏观离港运行示意图
Figure 2. Macro departure operation diagram of multiple airports in airport group
图 3 机场群内各航班向各个时刻的指派示意图
Figure 3. Schematic diagram of assignment of flights within airport group to various moments
图 6 优化前后每个航班时刻安排的航班数对比
Figure 6. Comparison of number of flights scheduled for each flight before and after optimization
表 1 模型参数说明
Table 1. Model parameter description
参数 说明 $M$ 机场群内所有机场集合 $ P $ 机场群内所有机场离港航线移交点集合 $ T $ 所考虑时间范围内离港航班时刻集合，其中每个时刻并不是一个具体的时刻，而是指定机场为所有航班预留的一个特定时段，一般以5 min为最小时间单元 $F = \left\{ { {f_m}\left| {m \in M} \right.} \right\}$ 机场群内所有机场起飞离港航班集合，${f_m}$为机场$m$的起飞离港航班集合 $ {\tau _{\max }} $ 可接受的航班延误最大时刻调整量 $ {C_{mf}}\left( * \right) $ 预先设定的机场$m$离场航班$f$关于延误时段数的不减函数 $ {D_m}\left( t \right)\left( {\forall m \in M,\forall t \in T} \right) $ 给定的机场$m$在时刻$t$的离场容量 ${D_p}\left( t \right)\left( {\forall p \in P,\forall t \in T} \right)$ 给定的航线移交点$p$在时刻$t$的离场容量 $ x_{mf}^t\left( {\forall m \in M,\forall f \in {F_m},\forall t \in T} \right) $ 航班时刻优化问题的决策变量 $\alpha _{mf}^{p}\left( {\forall m \in M,\forall f \in {F_m},\forall p \in P} \right)$ 根据已知航班信息确定的、过移交点$p$的0-1型判断系数 
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表 2 京津冀机场群各时刻原始安排航班数（局部）
Table 2. Original scheduled flights of Beijing-Tianjin-Hebei airport group at each time (partial)
序号 航班号 起飞机场 起飞时刻 到达时刻 到达机场 001 3U8896 ZBAA 08:00 11:10 ZUUU 002 CA1431 ZBAA 08:00 10:55 ZUCK 003 MU5636 ZBAA 08:00 10:55 ZSSS 004 3U8838 ZBAA 08:00 11:00 ZGSZ 005 CZ6161 ZBAA 08:00 11:10 ZUUU 006 HU7382 ZBAA 08:00 11:50 ZJHK 007 MU5102 ZBAA 08:00 10:15 ZSSS 008 MU2467 ZBAA 08:00 10:00 ZSSH 009 MU2104 ZBAA 08:00 10:00 ZPPP 010 CA1371 ZBTJ 08:00 11:20 ZGSZ 011 GS7859 ZBTJ 08:00 10:10 ZHHH 012 GS7881 ZBTJ 08:00 10:05 ZSPD 013 NS3219 ZBSJ 08:00 10:00 ZSSS 014 NS3221 ZBSJ 08:00 10:30 ZUCK $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ 699 CA1329 ZBAA 21:00 00:20 ZGGG 700 CA4118 ZBAA 21:00 00:10 ZUUU 701 CF9031 ZBAA 21:00 23:25 ZSPD 702 GS6509 ZBTJ 21:00 00:50 ZJSY
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表 3 时刻序号和航班时刻的对应关系
Table 3. Correspondence between time serial numbers and flight schedule
时刻序号 航班时刻 时刻1 08:00 时刻2 08:05 $\vdots $ $\vdots $ 时刻j XX:XX $\vdots $ $\vdots $ 时刻157 21:00 时刻158 21:05 $\vdots $ $\vdots $ 时刻163 21:30
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表 4 迭代次数及其运行时间
Table 4. Number of iterations and their running time
迭代次数 计算时间/s 总延误成本 400 297 1 707 500 363 1 689 600 425 1 754 700 484 1 718 800 562 1 724 900 625 1 723 1000 737 1 690
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表 5 每个航班优化前后时刻对比
Table 5. Comparison before and after each flight optimization
机场 航班
序号航班号 起飞时刻 延误时段
数/个延误时长/
min优化前 优化后 ZBAA 001 3U8896 08:00 08:05 1 5 002 CA1431 08:00 08:00 0 0 003 MU5636 08:00 08:00 0 0 004 3U8838 08:00 08:00 0 0 005 CZ6161 08:00 08:10 2 10 006 HU7382 08:00 08:05 1 5 007 MU5102 08:00 08:00 0 0 008 MU2467 08:00 08:10 2 10 009 MU2104 08:00 08:00 0 0 ZBTJ 010 CA1371 08:00 08:00 0 0 011 GS7859 08:00 08:00 0 0 012 GS7881 08:00 08:05 1 5 ZBSJ 013 NS3219 08:00 08:00 0 0 014 NS3221 08:00 08:00 0 0 $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ $\vdots $ ZBAA 699 CA1329 21:00 21:00 0 0 700 CA4118 21:00 21:05 1 5 701 CF9031 21:00 21:00 0 0 ZBTJ 702 GS6509 21:00 21:00 0 0
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表 6 优化前后机场群航班时刻稳定性指标数据
Table 6. Flight schedule stability index data of airport group before and after optimization
机场 离港航班平均
延误时间/s离港航班平均
延误率/%航线平均
延误时间/s航线平均
延误率/%机场平均
延误时间/s机场
延误率/%ZBAA 优化前 201.0 35.0 87.0 19.8 174.0 20.2 优化后 182.2 25.1 81.4 17.6 161.3 17.2 偏差 18.8 9.9 5.6 2.2 12.7 3.0 ZBSJ 优化前 56.0 8.2 35.0 4.0 84.0 9.8 优化后 53.1 7.9 32.9 3.9 81.2 9.2 偏差 2.9 0.3 2.1 0.1 2.8 0.6 ZBTJ 优化前 73.0 16.9 50.0 8.3 99.0 11.5 优化后 66.2 15.1 45.3 7.1 93.1 10.1 偏差 6.8 1.8 4.7 1.2 5.9 1.4
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表 7 优化前后航班时刻质量相对贴近度
Table 7. Relative closeness of departure flight schedule quality before and after optimization
机场 优化前 优化后 ZBAA 0.334 0.363 ZBSJ 0.923 0.928 ZBTJ 0.775 0.801
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