多跑道混合运行模式进场航班动态鲁棒调度

doi:10.7527/S1000-6893.2024.30956

Abstract

Abstract:

To address the impact of uncertainties in the terminal area on flight arrival times， a two-stage stochastic programming method for arrival aircraft based on chance constraints is proposed to achieve robustness in the scheduling scheme. Firstly， based on historical flight data， the uncertainty distribution of arrival times from the entry fix to the Initial Approach Fix （IAF） is identified. Secondly， considering the uncertainty distribution， chance constraints are introduced to limit the probability of violating separation constraints， and a two-stage stochastic programming model is then established. The first stage pertains to approach control， flights are pre-sequenced and scheduled before reaching the IAF， so as to minimize landing sequence length and flight time； the second stage pertains to final approach control， safety intervals are established to reduce landing delays on the runway. Subsequently， the Rolling Horizon Control （RHC） algorithm for stochastic programming is introduced to satisfy the real-time requirements of approach operations. Then， the model is reconstructed and solved based on the Sample Average Approximation （SAA） algorithm. Finally， the proposed method is validated using actual operational data from Guangzhou Baiyun International Airport. The results demonstrate that the proposed RHC algorithm not only ensures solution quality but also significantly enhances model-solving efficiency. Moreover， the robustness of the approach scheduling scheme is improved under the “one landing， one takeoff” and “two landings， one takeoff” operational modes. For the landing delay index， the First-Come， First-Served （FCFS） strategy results in delays 6.1 times and 9.6 times higher than those achieved by the proposed method， respectively； for the violation of separation proportion index， the results of FCFS strategy rates are 20% and 18.9%， whereas the proposed method maintains a rate of 3.5% in both modes. Regarding the sequence exchange number， the results of FCFS strategy incurs 5.2 and 5.6 exchanges， respectively， while the proposed method incurs zero exchanges in both modes.

Key words: arrival management, mixed runway operation mode, stochastic programming, chance constraint, Rolling Horizon Control (RHC) algorithm

CLC Number:

V355

Junfeng ZHANG, Zhao MA, Zhuoming DU, Rong HU. Dynamic robust scheduling of aircraft arrival in multi-runway mixed operation mode[J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(7): 330956.

Figures/Tables 12

Fig.1

Table 1

Parameter symbol definition

符号	含义
$A$	进场航班集合
$R$	降落跑道集合
$S$	场景集合
$E ω$	有关不确定性 $ω$ 的期望
$M$	大 $M$ 约束变量
$P$	概率大小
Q	与航班到达IAF时间不确定性相关的表达式
$c 1$	延误到达成本系数
$c 2$	提前到达成本系数
$α$	间隔约束满足要求的概率值
$s i j$	航班 $i 和 j$ 间的尾流间隔要求
$x F I X i$	航班 $i$ 进入终端区进港点时间
$U T F I X I A F, i$	航班 $i$ 从进港点到IAF的无阻碍飞行时间
$U T I A F R W Y, i$	航班 $i$ 从IAF到跑道的无阻碍飞行时间
$E i I A F$	航班 $i$ 从进港点到IAF的最早到达时间
$L i I A F$	航班 $i$ 从进港点到IAF的最晚到达时间
$γ i j$	航班 $i 和 j$ 是否在同一跑道，若是为1，否则为0
$ω i s$	航班 $i$ 在场景 $s$ 下的到达时间不确定性
$E i s, R W Y$	不确定性揭示，航班 $i$ /场景 $s$ 最早着陆时间
$L i s, R W Y$	不确定性揭示，航班 $i$ /场景 $s$ 最晚着陆时间
$z i, s 1$	航班 $i$ 在场景 $s$ 下的延误到达时间
$z i, s 2$	航班 $i$ 在场景 $s$ 下的提前到达时间
$t i s$	航班 $i$ 在场景 $s$ 下的实际到达IAF时间
$n A$	进场航班集合 $A$ 所含航班数量
$n S$	场景集合 $S$ 所含场景数量
$n R$	降落跑道集合 $R$ 所含跑道数量
$x i$	航班 $i$ 到达IAF的预计时间
$y i s$	航班 $i$ 在场景 $s$ 下的预计到达跑道时间
$δ i j$	航班 $i 和 j$ 是否相邻且 $i$ 在前，若是为1，否则为0
$ξ i r$	航班 $i$ 是否分配跑道 $r$ ，若是为1，否则为0

Table 1

Fig.2

Fig.3

Table 2

Data before and after scenario clustering

进港点	跑道	航班架次		$μ$ /s		$σ$ /s
进港点	跑道	聚类前	聚类后	聚类前	聚类后	聚类前	聚类后
GYA	01	5 987	904	7.04	16.44	84.71	60.49
IDUMA	02R	2 940	312	44.04	41.38	76.68	69.22
IGONO	01	3 579	530	26.60	19.20	69.04	56.93
IGONO	02R	5 235	665	35.95	37.41	76.68	67.86
ATAGA	01	3 531	623	15.04	11.11	69.04	50.86
ATAGA	02R	3 147	538	29.67	23.19	58.59	42.63

Table 2

Fig.4

Table 3

Optimization results under different parameters

参数设置

（ $c 1, c 2$ ）

跑道固定

分配跑道

序列长度/s

平均飞行时间/s

平均提前时间/s

平均延误时间/s

目标函数值

序列长度

平均飞行时间/s

平均提前时间/s

平均延误时间/s

目标函数值

（1， 0.8）

3 541

2 613.8

73.42

21.17

6 249.39

3 499

2 521.8

115.51

55.73

6 192.04

（1， 5）

3 541

2 619.16

107.91

6 268.07

3 475

2 645.85

113.81

6 234.08

Table 3

Table 4

Efficiency of different solution methods

$n S$	整体求解效率		滚动时域局部优化效率
$n S$	目标值	求解时间/s	目标值	求解时间/s
10	6 205.05	1 358	6 227.55	36
20	6 234.88	3 564	6 238.68	58
50	6 257.83	7 982	6 259.83	156
100	6 261.17	19 956	6 268.07	435

Table 4

Fig.5

Fig.6

Fig.7

Table 5

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方案	“一落一起”模式扰动实验次数					“两落一起”模式扰动实验次数
方案	1	2	3	4	5	1	2	3	4	5
FCFS	4	6	10	0	6	6	4	10	2	6
SP	0	0	0	0	0	0	0	0	0	0

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Dynamic robust scheduling of aircraft arrival in multi-runway mixed operation mode

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