Aircraft Sequencing Modeling and Algorithm for Shared Waypoints in Airport Group
-
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.
-
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
下载: 导出CSV
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
下载: 导出CSV
-
[1] FAYE A. Solving the aircraft landing problem with time dis-cretization approach[J]. European Journal of Operational Research, 2015, 242(3): 1028-1038. doi: 10.1016/j.ejor.2014.10.064 [2] SALEHIPOUR A. An algorithm for single and multiple-runway aircraft landing problem[J]. Mathematics and Computers in Simulation(MATCOM), 2020(175): 179-191. http://www.sciencedirect.com/science/article/pii/S037847541930309X [3] 崔昳昕, 康道驰. 单跑道进离场航班强化学习排序模型研究[J]. 航空计算技术, 2019, 49(2): 50-53. doi: 10.3969/j.issn.1671-654X.2019.02.013CUI Yixin, KANG Daochi. Reinforcement learning model of aircraft sequencing problem on a single runway[J]. Aeronautical Computing Technique, 2019, 49(2): 50-53. (in Chinese) doi: 10.3969/j.issn.1671-654X.2019.02.013 [4] 张兆宁, 刘珂璇. 基于跑道运行类别的航班优化排序方法[J]. 重庆交通大学学报(自然科学版), 2020, 39(5): 32-37. doi: 10.3969/j.issn.1674-0696.2020.05.06ZHANG Zhaoning, LIU Kexuan. Aircraft sequencing optimization method based on runway operation category[J]. Journal of Chongqing Jiaotong University(Natural Science), 2020, 39(5): 32-37. (in Chinese) doi: 10.3969/j.issn.1674-0696.2020.05.06 [5] 刘继新, 江灏, 董欣放, 等. 基于空中交通密度的进场航班动态协同排序方法[J]. 航空学报, 2020, 41(7): 285-300. https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB202007025.htmLIU Jixin, JIANG Hao, DONG Xinfang, et al. Dynamic collaborative sequencing method for arrival flights based on air traffic density[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(7): 285-300. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB202007025.htm [6] 邱梦雅, 乐美龙, 胡钰明. 机场终端区进场航班优化排序研究[J]. 航空计算技术, 2021, 51(3): 45-49. doi: 10.3969/j.issn.1671-654X.2021.03.011QIU Mengya, LE Meilong, HU Yuming. Research on optimal sequencing of incoming flights in airport terminal area[J]. Aeronautical Computing Technique, 2021, 51(3): 45-49(in Chinese) doi: 10.3969/j.issn.1671-654X.2021.03.011 [7] SARAF A, CLARKE J P, MCLAIN E. Discussion and comparison of metroplex-wide arrival scheduling algorithms[C]. 10th AIAA Aviation Technology, Integration and Operations (ATIO)Conference, Fort Worth, Texas: AIAA, 2010. [8] WIELAND F, TYAGI A, KUMAR V. Metrosim: A metroplex-wide route planning and airport scheduling tool[C]. 14th AIAA Aviation Technology, Integration and Operations (ATIO)Conference, Atlanta: AIAA, 2014. [9] CAPPS A, KISTLER M, ENGELLAND S. Design characteristics of a terminal departure scheduler[C]. 14th AIAA Aviation Technology, Integration and Operations (ATIO)Conference, Atlanta: AIAA, 2014. [10] 黄吉波. 珠三角终端区进离场航班协同排序方法研究[D]. 南京: 南京航空航天大学, 2015.HUANG Jibo. Research on coordinated sequencing for arrival and departure in the Pearl River Delta metropolitan areas[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2015. (in Chinese) [11] 王莉莉, 张潇潇. 多机场协同决策进离场航班排序模型及算法研究[J]. 飞行力学, 2016, 34(1): 90-94. https://www.cnki.com.cn/Article/CJFDTOTAL-FHLX201601021.htmWANG Lili, ZHANG Xiaoxiao. Modeling and algorithm of arrival and departing aircraft sequencing in multi-airport terminal area collaborative decision[J]. Flight Dynamics, 2016, 34(1): 90-94. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-FHLX201601021.htm [12] 陆嘉旻. 多机场终端区进场航班排序方法研究[J]. 科技创新导报, 2016, 13(9): 21-22. https://www.cnki.com.cn/Article/CJFDTOTAL-ZXDB201609013.htmLU Jiamin. Research on arrival aircraft sequencing method in multi-airport terminal area[J]. Science and Technology Innovation Herald, 2016, 13(9): 21-22. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZXDB201609013.htm [13] 张军峰, 葛腾腾, 郑志祥. 多机场终端区进离场航班协同排序研究[J]. 交通运输系统工程与信息, 2017, 17(2): 197-204. https://www.cnki.com.cn/Article/CJFDTOTAL-YSXT201702029.htmZHANG Junfeng, GE Tengteng, ZHENG Zhixiang. Collaborative arrival and departure sequencing for multi-airport terminal area[J]. Journal of Transportation Systems Engineering and Information Technology, 2017, 17(2): 197-204. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSXT201702029.htm [14] 王湛, 吴艺. 基于FS-MOPSO的多机场终端区协同航班调度策略[J]. 西南交通大学学报, 2017, 52(1): 179-185. doi: 10.3969/j.issn.0258-2724.2017.01.025WANG Zhan, WU Yi. Collaborative aircrafts scheduling strategy in metroplex terminal area based on FS-MOPSO[J]. Journal of Southwest Jiaotong University, 2017, 52(1): 179-185. (in Chinese) doi: 10.3969/j.issn.0258-2724.2017.01.025 [15] 胡京. 多机场动态地面等待策略的研究[D]. 南京: 南京航空航天大学, 2018.HU Jing. The research on dynamic multi-airport ground holding policies[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2018. (in Chinese) [16] 黄吉波. 基于延误分配的多机场终端区航班排序模型[J]. 指挥信息系统与技术, 2019, 10(1): 37-42. https://www.cnki.com.cn/Article/CJFDTOTAL-ZHXT201901007.htmHUANG Jibo. Flight sequencing model for multi-airport terminal area based on delay allocation[J]. Command Information System and Technology, 2019, 10 (1): 37-42. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZHXT201901007.htm [17] 张建学. 基于多机场终端区进场航班排序研究[J]. 电子测试, 2019, (14) : 124-125+94. doi: 10.3969/j.issn.1000-8519.2019.14.049ZHANG Jianxue. Research on the arrival flight sorting based on multi-airport terminal area[J]. Electronic Test, 2019, (14): 124-125+94. (in Chinese) doi: 10.3969/j.issn.1000-8519.2019.14.049 [18] 张颖, 胡明华, 谢华. 航路流量间隔限制及排序策略一体化决策模型及算法[J]. 系统工程理论与实践, 2013, 33(9): 2430-2436. https://www.cnki.com.cn/Article/CJFDTOTAL-XTLL201309030.htmZHANG Ying, HU Minghua, XIE Hua. Integrative decision making model and solution algorithm for enroute flow spacing restriction and sequencing strategy[J]. Systems Engineering Theory & Practice, 2013, 33 (9): 2430-2436. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-XTLL201309030.htm [19] 赵嶷飞, 王惠斌. 汇聚航路航班排序的遗传算法研究[J]. 中国科技纵横, 2015, (8): 42-43+45. doi: 10.3969/j.issn.1671-2064.2015.08.032ZHAO Yifei, WANG Huibin. Study on genetic algorithm of convergent route flight sequencing[J]. China Science & Technology Overview, 2015, (8): 42-43+45. (in Chinese) doi: 10.3969/j.issn.1671-2064.2015.08.032 [20] 杜实, 李希璐. 基于交通波模型的交叉点航班排序研究[J]. 航空计算术, 2017, 47 (3): 66-69. https://www.cnki.com.cn/Article/CJFDTOTAL-HKJJ201703016.htmDU Shi, LI Xilu. Research on air traffic sequence of intersection flight based on traffic wave model[J]. Aeronautical Computing Technique, 2017, 47 (3): 66-69. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HKJJ201703016.htm -
点击查看大图
计量
- 文章访问数: 421
- HTML全文浏览量: 266
- PDF下载量: 32
- 被引次数: 0