Aircraft Sequencing Modeling and Algorithm for Shared Waypoints in Airport Group
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摘要:
机场群上空空域资源共享、运行耦合复杂，拥堵往往发生在共用航路点。为缓解空域拥堵和航班延误问题，开展了机场群共用航路点的优化排序研究。针对共用航路点的运行特征，引入惩罚因子并以总延误时间成本最小为优化目标，建立了机场群共用航路点的航班优化排序模型，基于滑动时间窗算法和粒子群优化算法的原理提出了TW-PSO组合优化算法对模型进行求解。选取京津冀机场群过共用航路点的航班进行算例仿真，结果表明：TW-PSO组合优化算法与FCFS算法、滑动时间窗算法、粒子群优化算法相比在高峰时段的总延误时间成本分别减少了216，212，161 min；在算法性能方面，具有比经典算法迭代次数少、优化效果更佳的优点，能有效缓解航班延误问题，改善机场群的协同运行效率。
Abstract:Congestion often occurs on shared waypoints due to shared airspace resources in airport group and compli⁃ cated operation coupling. The work studies sequencing optimization of the shared waypoint in the airport group to alle⁃ viate the problems of airspace congestion and flight delays. Aiming at the operating characteristics of a shared way⁃ point, penalty factors are adopted to minimize the total delay time cost as the optimization goal, and a model is devel⁃ oped to optimize aircraft sequencing on the shared waypoints in the airport group. Based on the principles of sliding time window algorithm and particle swarm optimization algorithm, a TW-PSO combined optimization algorithm is pro⁃ posed to solve the model. The aircrafts of the Beijing-Tianjin-Hebei airport group passing the shared waypoints are se⁃ lected for a simulation. The results show that the total delay time cost of the TW-PSO combined optimization algorithm in peak hours compared with the FCFS algorithm, sliding time window algorithm, and particle swarm optimization algo⁃ rithm, reduced by 216, 212, and 161 min, respectively. Therefore, in terms of algorithm performance, it has the advan⁃ tages of fewer iterations and better optimization outcomes than classic algorithms, which can alleviate flight delays and improve the coordinated operation of the airport group.
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表 1 变量定义
Table 1. Variable definitions
变量 含义 A 机场群系统中的机场集合 a 机场群系统中的机场，a ∈ A n 从各机场起飞过共用航路点的航班总数 T 航班过共用航路点的时间段 t 航班过共用航路点的时刻 FaT T时间段内从机场a起飞过共用航路点的航班集合，FaT = {fa1, fa2,…,fan} fai T时间段内从机场a起飞过共用航路点的第i个航班(i = 1, 2,…,n) ETfai 过共用航路点的计划时刻 STfai 过共用航路点的实际时刻 PTfai 最早过共用航路点的时刻 DTfai 最晚过共用航路点的时刻 Cp 时间段内共用航路点的最大容量 Ca 时间段内共用航路点所在扇区的最大容量 Si,i+1 前后2个航班在共用航路点的安全间隔
xfai (t) = {0, 1}xfai (t) xfai (t) = 1，即t时刻航班fai过共用航路点
xfai (t) = 0，即t时刻航班fai不过共用航路点
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表 2 算法优化结果对比
Table 2. Comparison of the results of optimized algorithms
航班号 起飞机场 计划过点时刻 FCFS算法优化结果 滑动时间窗算法优化结果 粒子群优化算法优化结果 TW-PSO组合优化算法优化结果 实际过点时刻 延误时间成本/min 实际过点时刻 延误时间成本/min 排序结果 实际过点时刻 延误时间成本/min 排序结果 实际过点时刻 延误时间成本/min 排序结果 F1 B 09：02 09：02 0 09：02 0 1 08：57 -10 1 08：57 -10 1 F2 T 09：05 09：05 0 09：05 0 2 09：00 -5 2 09：00 -5 2 F3 B 09：06 09：07 3 09：07 3 3 09：26 60 13 09：02 -8 3 F4 B 09：07 09：09 6 09：17 30 8 09：02 -10 3 09：12 15 8 F5 D 09：09 09：11 6 09：09 0 4 09：04 -10 4 09：04 -10 4 F6 S 09：10 09：13 9 09：11 3 5 09：30 60 15 09：06 -8 5 F7 T 09：12 09：15 6 09：15 6 7 09：07 -5 5 09：10 -2 7 F8 D 09：13 09：17 12 09：13 0 6 09：33 60 16 09：08 -10 6 F9 B 09：14 09：19 15 09：27 39 13 09：09 -10 6 09：22 24 13 F10 B 09：15 09：21 18 09：29 42 14 09：23 24 12 09：24 27 14 F11 T 09：17 09：23 12 09：31 28 15 09：12 -5 7 09：26 18 15 F12 S 09：18 09：25 14 09：33 30 16 09：38 40 18 09：28 20 16 F13 B 09：19 09：27 24 09：19 0 9 09：14 -10 8 09：14 -10 9 F14 B 09：21 09：29 24 09：21 0 10 09：16 -10 9 09：16 -10 10 F15 S 09：23 09：31 16 09：23 0 11 09：43 40 20 09：18 -5 11 F16 B 09：24 09：33 27 09：25 3 12 09：19 -10 10 09：20 -8 12 F17 D 09：26 09：35 27 09：37 33 18 09：21 -10 11 09：32 18 18 F18 B 09：30 09：37 21 09：39 27 19 09：35 15 17 09：34 12 19 F19 S 09：33 09：39 12 09：41 16 20 09：28 -5 14 09：36 6 20 F20 T 09：34 09：41 14 09：35 2 17 09：40 12 19 09：30 -4 17 总延误时间成本/min 266 262 211 50
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