Low-altitude planar air route network planning method based on gradient optimization
Article Text (Baidu Translation)
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摘要: 为解决低空航路网结构不完善、规划方法不成熟的问题，设计低空航路网结构并提出创新规划技术。结构上，构建“三层空域”整体框架（底层物流航路网、中层通行航路网、上层应急/公共航路网），内部采用单层双向航路设计，交叉点参考立交桥模式实现全向无等待通行；规划方法上，创新提出基于梯度优化的两阶段技术，全局规划通过路径规划算法生成航线，采用“扫描体”法识别转弯点与交叉点，经基于密度的带噪声应用空间聚类合并形成初始网络，局部优化将问题转化为航路汇聚点布局问题，设置9个移动方向构建方向矩阵，以航路网络总长度、航线总长度和安全约束为目标函数，通过动态更新转移概率迭代优化交叉点位置；以上海某区域为仿真场景，以150 m为高层建筑界定标准，设置12个起降点与34条航线验证。研究结果表明：规划的无冲突航路网，较现有方法迭代次数减少66%；85.3%的航线长度变化率为-10%~2%，未出现过度延长情况；节点布局规整，空域占用率与冲突风险显著降低。该结构框架与规划技术为城市低空航路网实际建设提供了可行方案，后续可拓展干线航路网规划研究。Abstract: To address the problems of imperfect structure and immature planning method of low-altitude air route networks, the structure of low-altitude air route networks was designed and an innovative planning technology was proposed. In terms of structure, an overall "three-layer airspace" framework was constructed (the bottom layer is the logistics air route network, the middle layer is the commuter air route network, and the upper layer is the emergency/public air route network). A single-layer bidirectional air route design was adopted for the internal structure, with intersections referring to the overpass model to achieve omnidirectional non-waiting traffic. In terms of planning method, an innovative two-stage technology based on gradient optimization was proposed. In the global planning stage, a path planning algorithm was used to generate routes, the "scanning volume" method was adopted to identify turning points and intersection points, and density-based spatial clustering of applications with noise (DBSCAN) was employed to merge them to form an initial network. In the local optimization stage, the problem was transformed into the crossing waypoints location problem (CWLP), 9 movement directions were set to construct a direction matrix, and the total length of the air route network, the total length of routes, and safety constraints were taken as the objective function. The position of intersection points was iteratively optimized by dynamically updating the transition probability. With a certain area in Shanghai as the simulation scenario and 150 m as the standard for defining high-rise buildings, 12 take-off and landing points and 34 routes were set for verification. The results show that a conflict-free low-altitude air route network is successfully planned, with the number of iterations reduced by 66% compared with existing methods. 85.3% of the route length change rates are between -10% and 2%, with no excessive extension. The node layout is regular. The airspace occupancy rate and conflict risk are significantly reduced. The structural framework and planning technology provide a feasible scheme for the practical construction of urban low-altitude air route networks. The planning research of trunk air route networks can be expanded in the future.
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图 29 航路网络加权总长度对比
Figure 29. Comparsion of the weighted total length of air route network
表 1 全局航路网络规划总结
Table 1. Summary of global air route network planning
大类方法 子方法细分 优点 缺点 适用场景 局限性 基于节点需求的方法 考虑冲突约束 1.量化冲突（如交叉点数量），提升安全性；2.兼顾经济性与安全性目标 1.计算复杂，需迭代寻优；2.路径数量过多时，冲突消解效果下降 终端区过渡网络设计、城市低空交通（如无人机物流） 路径数量多时难以完全消解冲突，需依赖“申请- 调度”机制补充 不考虑冲突约束 1.模型简单，易实现；2.适用于大规模初始规划 1.易产生航线冲突（如夹角过小、航段不合理）；2.结果需人工调整 中国/区域航路规划、城市空中交通初始阶段 结果可能不符合实际运行需求，需结合《航路网络规划方法参考材料》进行后期优化 基于多级航路的方法 枢纽/干线航路网络 1.层级清晰，适应不同流量需求；2.便于集中管理与调度 1.层级划分复杂，需协调各级网络关系；2.层级衔接可能存在效率损失 民航中国枢纽/干线网络、城市低空无人机网络 枢纽与干线的流量匹配难度大，易出现局部拥堵 双层规划模型 1.兼顾管理者（上层）与用户（下层）视角；2.结果贴合实际流量需求 1.模型复杂，求解难度大；2.依赖上下层迭代效率，数据需求高 城市空中交通（如物流无人机网络） 迭代过程耗时，对算法性能要求高 多级优化 1.逐步迭代，考虑因素全面（如正/ 负约束要素）；2.可行性强，贴合实际环境 1.规划周期长，需多阶段验证；2.依赖实地测试反馈，推广成本高 低空航路网络 对环境数据（如障碍物、绿化带）依赖性强 基于节点/航段合并的方法 航段合并 1.减少航线数量，简化网络结构；2.降低冲突风险 1.仅适用于特定航线（如大圆航线）；2.通用性差，仅70% 航班适用 民航大圆航线、密集航线区域 难以推广至复杂空域（如城市低空） 航段延长 1.通过延长航线合并节点，减少冲突；2.操作简单 1.研究较少，适用场景有限；2.依赖航线相近性，灵活性不足 低空无人机航路网络（航线密集区域） 仅能处理相近航线，对分散航线无效 航迹挖掘 1.基于历史轨迹，贴合实际运行规律；2.适用于无预设路径的场景 1.依赖高质量航迹数据（如AIS）；2.特征点（转向/速度）提取难度大 有大量历史轨迹的区域 小区域内易出现过多转向，需人工平滑 基于空域剖分的方法 空域剖分 1.节点定位明确，网络结构规整；2.适应复杂障碍物环境 1.剖分方法（如圆半径、聚类参数）对结果影响大；2.需适配不同空域环境 城市低空空域、军事战场空域 剖分参数需反复调试，否则易出现覆盖不均 
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表 2 局部航路规划总结
Table 2. Summary of local air route planning
方法 优点 缺点 适用场景 局限性 航路汇聚点布局问题 1.优化节点位置，提升网络效率；2.减少节点冲突（如合并相近节点） 1.易出现节点过近，需额外约束；2.合并后可能出现容流不匹配 航路交叉节点优化、复杂空域节点调整 需反复进行合并-分解操作，计算成本高 局部航路规划问题 1.方法成熟，适用于局部调整；2.能规避“三区”等约束 1.多依赖单一算法，复杂环境适应性有限；2.动态调整能力弱 规避“三区”（禁区、限制区、危险区）、航路更新（如RNAV/PBN转变） 元胞自动机等方法在动态流量下适应性不足
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表 3 节点在不同方向上的梯度
Table 3. Gradient of nodes in different directions
交叉点 梯度 [0，1] [1，0] [0，-1] [-1，0] [1，1] [1，-1] [-1，-1] [-1，1] [0，0] 1 -0.488 -0.318 0.477 0.312 -0.812 0.164 0.784 -0.170 0 2 0.046 0.114 -0.060 -0.136 0.158 0.056 -0.200 -0.086 0 3 0.069 0.045 -0.092 -0.071 0.113 -0.046 -0.166 0.000 0 4 -0.228 0.235 0.210 -0.249 0.006 0.446 -0.039 -0.477 0 5 0.345 0.827 -0.350 -0.834 1.171 0.478 -1.186 -0.488 0 6 0.546 -0.296 -0.553 0.267 0.242 -0.841 -0.294 0.821 0 7 0.646 0.018 -0.651 -0.053 0.656 -0.624 -0.714 0.601 0 8 -0.695 0.521 0.686 -0.542 -0.171 1.204 0.147 -1.241 0 9 -0.615 -0.414 0.596 0.395 -1.034 0.186 0.988 -0.215 0 10 0.281 -1.116 -0.297 1.098 -0.831 -1.418 0.803 1.375 0 11 -0.293 -0.682 0.265 0.668 -0.972 -0.420 0.937 0.370 0 12 0.798 -0.744 -0.818 0.740 0.054 -1.562 -0.078 1.538 0 13 0.032 -0.038 -0.065 0.024 -0.003 -0.106 -0.038 0.054 0 14 -0.051 0.438 0.018 -0.466 0.379 0.465 -0.456 -0.510 0 15 0.784 0.033 -0.800 -0.048 0.808 -0.757 -0.857 0.745 0 16 0.711 0.901 -0.736 -0.907 1.618 0.160 -1.638 -0.201 0
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表 4 梯度优化结果
Table 4. Gradient optimization results
交叉点 梯度 [0，1] [1，0] [0，-1] [-1，0] [1，1] [1，-1] [-1，-1] [-1，1] [0，0] 1 0 0 1 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 0 5 0 0 0 0 0 0 1 0 0 6 1 0 0 0 0 0 0 0 0 7 1 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 1 9 0 0 0 1 0 0 0 0 0 10 0 0 0 1 0 0 0 0 0 11 0 0 0 0 1 0 0 0 0 12 0 0 0 1 0 0 0 0 0 13 0 0 0 0 0 1 0 0 0 14 0 0 0 0 1 0 0 0 0 15 0 0 0 0 1 0 0 0 0 16 0 0 0 0 1 0 0 0 0
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[1] 百度地图. 2025第1季度中国城市交通报告[R]. 北京: 百度地图, 2025.Map Baidu. China urban traffic report: Q1 2025[R]. Beijing: Baidu Maps, 2025. [2] 国家统计局. 中华人民共和国2024年国民经济和社会发展统计公报[R]. 北京: 国家统计局, 2025.National bureau of statistics of China. Statistical communiqué of the People's Republic of China on the 2024 national economic and social development[R]. Beijing: National Bureau of Statistics, 2025. [3] 刘志硕, 许俊哲, 李艳华, 等. 考虑路网负载均衡的AGV分拣系统动态路径规划方法[J]. 交通运输工程学报, 2026, DOI: 10.19818/j.cnki.1671-1637.2026.120 .LIU Zhi-shuo, XU Jun-zhe, LI Yan-hua, et al. Dynamic path planning method with load balancing of road network for AGV-based sorting system[J/OL]. Journal of Traffic and Transportation Engineering, 2026, DOI:10.19818/j.cnki.1671-1637.2026.120 .[4] 吕迪, 王凯, 曲小波. 城市空中交通: 网络结构与运营规划[J]. 交通建设与管理, 2023(2): 78-81.LYU Di, WANG Kai, QU Xiao-bo. Urban air traffic: Network structure and operation planning[J]. Transport Construction & Management, 2023(2): 78-81. [5] 李嘉宝. 中国"低空经济"如何成为发展"新引擎"[EB/OL]. (2025-02-24). https://m.newsduan.com/static/content/WG/2025-02-24/1343542472428623315.html .LI Jia-bao. How China's "low-altitude economy" becomes a new engine of development[EB/OL]. (2025-02-24).https://m.newsduan.com/static/content/WG/2025-02-24/1343542472428623315.html .[6] 国务院. 国家综合立体交通网规划纲要[R]. 北京: 国务院, 2021.The State Council of the People's Republic of China. Outline of the national comprehensive three-dimensional transportation network plan[R]. Beijing: The State Council of the People's Republic of China, 2021. [7] 国务院. 中共中央关于进一步全面深化改革、推进中国式现代化的决定[R]. 北京: 国务院, 2024.The State Council. Decision of the CPC central committee on further comprehensively deepening reform and advancing Chinese modernization[R]. Beijing: The State Council, 2024. [8] 李诚龙, 屈文秋, 李彦冬, 等. 面向eVTOL航空器的城市空中运输交通管理综述[J]. 交通运输工程学报, 2020, 20(4): 35-54. doi: 10.19818/j.cnki.1671-1637.2020.04.003LI Cheng-long, QU Wen-qiu, LI Yan-dong, et al. Overview of traffic management of urban air mobility (UAM)with eVTOL aircraft[J]. Journal of Traffic and Transportation Engineering, 2020, 20(4): 35-54. doi: 10.19818/j.cnki.1671-1637.2020.04.003 [9] 张洪海, 夷珈, 李姗, 等. 低空空域容量评估研究综述[J]. 交通运输工程学报, 2023, 23(6): 78-93. doi: 10.19818/j.cnki.1671-1637.2023.06.003ZHANG Hong-hai, YI Jia, LI Shan, et al. Review on research of low-altitude airspace capacity evaluation[J]. Journal of Traffic and Transportation Engineering, 2023, 23(6): 78-93. doi: 10.19818/j.cnki.1671-1637.2023.06.003 [10] 廖小罕, 徐晨晨, 岳焕印. 基于地理信息的无人机低空公共航路规划研究[J]. 无人机, 2018, 19(2): 45-49.LIAO Xiao-han, XU Chen-chen, YUE Huan-yin. Research on low-altitude public air route planning for UAVs based on geographic information[J]. Unmanned Vehicles, 2018, 19(2): 45-49. [11] 徐晨晨, 叶虎平, 岳焕印, 等. 城镇化区域无人机低空航路网迭代构建的理论体系与技术路径[J]. 地理学报, 2020, 75(5): 917-930.XU Chen-chen, YE Hu-ping, YUE Huan-yin, et al. Iterative construction of UAV low-altitude air route network in an urbanized region: Theoretical system and technical roadmap[J]. Acta Geographica Sinica, 2020, 75(5): 917-930. [12] ZHANG H H, TIAN T, FENG O G, et al. Research on public air route network planning of urban low-altitude logistics unmanned aerial vehicles[J]. Sustainability, 2023, 15(15): 12021. doi: 10.3390/su151512021 [13] LI J, SHEN D, YU F P, et al. A method for air route network planning of urban air mobility[J]. Aerospace, 2024, 11(7): 584. doi: 10.3390/aerospace11070584 [14] DAI W, PANG B Z, LOW K H. Conflict-free four-dimensional path planning for urban air mobility considering airspace occupancy[J]. Aerospace Science and Technology, 2021, 119: 107154. doi: 10.1016/j.ast.2021.107154 [15] LI J, SHEN D, YU F P, et al. Air channel planning based on improved deep Q-learning and artificial potential fields[J]. Aerospace, 2023, 10(9): 758. doi: 10.3390/aerospace10090758 [16] SRIDHAR B, GRABBE S, SHETH K, et al. Initial study of tube networks for flexible airspace utilization[C]//AIAA. AIAA Guidance, Navigation, and Control Conference and Exhibit. Reston: AIAA, 2006: 1-9. [17] 马令琪. 基于信息熵和AIS数据的沿海水域船舶航路网络构建[D]. 大连: 大连海事大学, 2022.MA Ling-qi. Construction of ship route network in coastal waters based on information entropy and AIS data[D]. Dalian: Dalian Maritime University, 2022. [18] STUIVE L, GZARA F. Airspace network design for urban UAV traffic management with congestion[J]. Transportation Research Part C: Emerging Technologies, 2024, 169: 104882. doi: 10.1016/j.trc.2024.104882 [19] 朱涛, 陈元, 丁轶. 空中航路网规划方法研究[J]. 信息化研究, 2019, 45(1): 13-17.ZHU Tao, CHEN Yuan, DING Yi. Research on planning method of air route network[J]. Informatization Research, 2019, 45(1): 13-17. [20] 李姗, 张洪海, 李卓伦. 城市低空物流无人机立体航路网络规划方法[J/OL]. 交通运输工程学报, 2026, DOI: 10.19818/j.cnki.1671-1637.2026.163 .LI Shan, ZHANG Hong-hai, LI Zhuo-lun. Planning method for three-dimensional air route network of urban low-altitude logistics drones[J/OL]. Journal of Traffic and Transportation Engineering, 2026, DOI:10.19818/j.cnki.1671-1637.2026.163 [21] SIDDIQUEE M W. Mathematical aids in air route network design[C]∥IEEE. 1973 IEEE Conference on Decision and Control Including the 12th Symposium on Adaptive Processes. New York: IEEE, 1973: 651-654. [22] 郦晴云. 基于交通流特征的航路网络节点布局优化[D]. 南京: 南京航空航天大学, 2016.LI Qing-yun. Air route network node optimization based on traffic flow feature[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2016. [23] LI S, ZHANG H H, YI J, et al. A bi-level planning approach of logistics unmanned aerial vehicle route network[J]. Aerospace Science and Technology, 2023, 141: 108572. doi: 10.1016/j.ast.2023.108572 [24] LI S, ZHANG H H, LI Z L, et al. An air route network planning model of logistics UAV terminal distribution in urban low altitude airspace[J]. Sustainability, 2021, 13(23): 13079. doi: 10.3390/su132313079 [25] 彭国栋. 航路网络动态优化研究[D]. 广汉: 中国民用航空飞行学院, 2021.PENG Guo-dong. Research on dynamic optimization of airway network[D]. Guanghan: Civil Aviation Flight University of China, 2021. [26] ZHAO S, ZHANG X J, ZHU Y B, et al. A methodology for designing transition route network between en-route airspace and terminal areas[C]∥IEEE. 2008 IEEE/AIAA 27th Digital Avionics Systems Conference. New York: IEEE, 2008: 1-7. [27] MOHAMED SALLEH M F B, CHI W C, WANG Z K, et al. Preliminary concept of adaptive urban airspace management for unmanned aircraft operations[C]∥AIAA. 2018 AIAA Information Systems-AIAA Infotech @ Aerospace. Reston: AIAA, 2018: 1-22. [28] TAN Q Y, WANG Z K, ONG Y S, et al. Evolutionary optimization-based mission planning for UAS traffic management (UTM)[C]∥IEEE. 2019 International Conference on Unmanned Aircraft Systems (ICUAS). New York: IEEE, 2019: 952-958. [29] 黄启翔, 江志彬, 张虹, 等. 基于NSGA-Ⅱ算法的区级无人驾驶航空器起降点布局规划——以深圳市南山区为例[J/OL]. 交通运输工程学报, 2026, DOI: 10.19818/j.cnki.1671-1637.2026.170 .HUANG Qi-xiang, JIANG Zhi-bin, ZHANG Hong, et al. District-level layout planning of UAV takeoff and landing points based on the NSGA-Ⅱ algorithm: A case study of Nanshan district, Shenzhen[J/OL]. Journal of Traffic and Transportation Engineering, 2026, DOI:10.19818/j.cnki.1671-1637.2026.170 .[30] 戴福青, 万小艳. 主干航路网络规划方法[J]. 科学技术与工程, 2014, 14(3): 271-276.DAI Fu-qing, WAN Xiao-yan. Trunk route network planning method based on improved gravity model[J]. Science Technology and Engineering, 2014, 14(3): 271-276. [31] 石新鹏. 基于流量需求分布的航路网络优化[D]. 天津: 中国民航大学, 2020.SHI Xin-peng. Route network optimization based on traffic demand distribution[D]. Tianjin: Civil Aviation University of China, 2020. [32] IB-TM-2009-009, 航路网络规划方法参考材料[S].IB-TM-2009-009, Reference material for air route network planning methods[S]. [33] 吴越, 王莉莉. 骨干航路网络的规划研究[J]. 中国民用航空, 2013(9): 57-59.WU Yue, WANG Li-li. To research the planning of backbone routes network[J]. China Civil Aviation, 2013(9): 57-59. [34] 王莉莉, 吴越, 吴桐水. 基于几何航路汇聚点设置的骨干航路网络规划[J]. 中国民航大学学报, 2014, 32(2): 23-26.WANG Li-li, WU Yue, WU Tong-shui. Plan of backbone air route network based on route crossing waypoint setting by geometric method[J]. Journal of Civil Aviation University of China, 2014, 32(2): 23-26. [35] RIVIERE T. Redesign of the European route network for sector-less[C]∥IEEE. The 23rd Digital Avionics Systems Conference. New York: IEEE, 2004: 1-11. [36] 王世锦, 曹希, 郦晴云, 等. 航路网络生成及优化[J]. 航空计算技术, 2016, 46(4): 4-8.WANG Shi-jin, CAO Xi, LI Qing-yun, et al. Generation and optimization of air route network based on complex network theory[J]. Aeronautical Computing Technique, 2016, 46(4): 4-8. [37] 张洪海, 于文娟, 周锦伦, 等. 基于需求的城市低空无人机航路网络构建方法[J]. 武汉理工大学学报(交通科学与工程版), 2024, 48(4): 609-615.ZHANG Hong-hai, YU Wen-juan, ZHOU Jin-lun, et al. Demand-based route network construction method for urban low-altitude UAV[J]. Journal of Wuhan University of Technology (Transportation Science & Engineering), 2024, 48(4): 609-615. [38] WANG S J, LIN J J, HAN Y X. Air route network generation based on traffic assignment[J]. Transactions of Nanjing University of Aeronautics and Astronautics, 2020, 37(2): 223-231. [39] 冯棣坤, 张洪海, 华明壮, 等. 面向城市低空物流的多层异质起降场点网络协同规划[J]. 交通运输工程学报, 2026, 26(2): 110-124. doi: 10.19818/j.cnki.1671-1637.2026.086FENG Di-kun, ZHANG Hong-hai, HUA Ming-zhuang, et al. Multi-level heterogeneous landing site network collaborative planning for urban low-altitude logistics[J]. Journal of Traffic and Transportation Engineering, 2026, 26(2): 110-124. doi: 10.19818/j.cnki.1671-1637.2026.086 [40] 黎涛, 王洵, 雷雨. 基于构建城市低空空域的无人机航路网对策研究[J]. 科技创新与生产力, 2025, 46(7): 47-50.LI Tao, WANG Xun, LEI Yu. Research on countermeasures for UAV route network based on constructing urban low altitude airspace[J]. Taiyuan Science and Technology, 2025, 46(7): 47-50. [41] XU C C, LIAO X H, YE H P, et al. Iterative construction of low-altitude UAV air route network in urban areas: Case planning and assessment[J]. Journal of Geographical Sciences, 2020, 30(9): 1534-1552. doi: 10.1007/s11442-020-1798-4 [42] XUE M, KOPARDEKAR P. High-capacity tube network design using the Hough transform[J]. Journal of Guidance, Control, and Dynamics, 2009, 32(3): 788-795. doi: 10.2514/1.40386 [43] 王非, 张洪海, 冯讴歌, 等. 基于改进A*算法的物流无人机航路网络协同规划[J]. 现代交通与冶金材料, 2022, 2(5): 31-38.WANG Fei, ZHANG Hong-hai, FENG Ou-ge, et al. Research on the design method of vertical take-off and landing procedures for logistics drones in urban areas based on the improved A* algorithm[J]. Modern Transportation and Metallurgical Materials, 2022, 2(5): 31-38. [44] 项迪, 黄亮, 周春辉, 等. 基于船舶轨迹挖掘的海上航路网络构建方法[J]. 交通信息与安全, 2023, 41(3): 69-79.XIANG Di, HUANG Liang, ZHOU Chun-hui, et al. A method of constructing maritime route network based on ship trajectory mining[J]. Journal of Transport Information and Safety, 2023, 41(3): 69-79. [45] 牟军敏, 郭绍卿, 张志江, 等. 基于AIS数据的水域航路网络提取方法[J]. 中国航海, 2023, 46(2): 152-160.MOU Jun-min, GUO Shao-qing, ZHANG Zhi-jiang, et al. Extraction of ship track pattern from AIS data[J]. Navigation of China, 2023, 46(2): 152-160. [46] 牛敬华, 马良荔, 覃基伟. 基于网格的航道模式提取算法研究[J]. 舰船电子工程, 2019, 39(4): 94-99.NIU Jing-hua, MA Liang-li, QIN Ji-wei. Research on sea route extraction algorithm based on grid[J]. Ship Electronic Engineering, 2019, 39(4): 94-99. [47] 陈宏昆, 察豪, 刘立国, 等. 基于船舶自动识别系统信息和Hough变换的海上船舶航道提取[J]. 计算机应用, 2018, 38(11): 3332-3335, 3341.CHEN Hong-kun, CHA Hao, LIU Li-guo, et al. Vessel traffic pattern extraction based on automatic identification system data and Hough transformation[J]. Journal of Computer Applications, 2018, 38(11): 3332-3335, 3341. [48] MCFADYEN A, BRUGGEMANN T. Unmanned air traffic network design concepts[C]∥IEEE. 2017 IEEE 20th International Conference on Intelligent Transportation Systems (ITSC). New York: IEEE, 2017: 1-7. [49] CAI K Q, ZHANG J, ZHOU C. Optimization of the crossing Waypoints in air route network[C]∥IEEE. 29th Digital Avionics Systems Conference. New York: IEEE, 2010: 1-8. [50] 严伟, 王瑛, 孟祥飞, 等. 航路网络航路点布局的多目标优化设计[J]. 空军工程大学学报(自然科学版), 2017, 18(6): 20-26.YAN Wei, WANG Ying, MENG Xiang-fei, et al. A multi-objective optimization design for crossing waypoints location in air route network[J]. Journal of Air Force Engineering University (Natural Science Edition), 2017, 18(6): 20-26. [51] 陈才龙. 基于复杂网络的航路汇聚点布局优化方法研究[D]. 合肥: 中国科学技术大学, 2011.CHEN Cai-long. Research on optimization method based on complex network for crossing waypoints location[D]. Hefei: University of Science and Technology of China, 2011. [52] ZHOU C, ZHANG X J, CAI K Q, et al. Comprehensive learning multi-objective particle swarm optimizer for crossing waypoints location in air route network[J]. Chinese Journal of Electronics, 2011, 20(3): 533-538. [53] CAI K Q, ZHANG J, ZHOU C, et al. Using computational intelligence for large scale air route networks design[J]. Applied Soft Computing, 2012, 12(9): 2790-2800. doi: 10.1016/j.asoc.2012.03.063 [54] 许有臣, 朱衍波. 航路网络关键节点优化与"三区"避让设计方法[J]. 中国民航大学学报, 2013, 31(1): 41-45.XU You-chen, ZHU Yan-bo. Methodology of key network nodes optimization and re-stricted airspace avoiding[J]. Journal of Civil Aviation University of China, 2013, 31(1): 41-45. [55] 沐瑶, 贺亚光. 基于交通需求的航路网络优化[J]. 中国科技信息, 2022(3): 19-22.MU Yao, HE Ya-guang. Route network optimization based on traffic demand[J]. China Science and Technology Information, 2022(3): 19-22. [56] 陈振坤, 陈可嘉. 考虑点融合系统的进离场航路分配双目标规划模型[J/OL]. 交通运输工程学报, 2026, DOI: 10.19818/j.cnki.1671-1637.2026.226 .CHEN Zhen-kun, CHEN Ke-jia. Bi-objective programming model for the assignment of arrival anddeparture routes considering the point merge system[J/OL]. Journal of Traffic and Transportation Engineering, 2026, DOI:10.19818/j.cnki.1671-1637.2026.226 .[57] 辛正伟. 航路网络规划技术研究[D]. 南京: 南京航空航天大学, 2013.XIN Zheng-wei. Research on air route network planning technology[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2013. [58] 郑煜坤, 王瑛, 李超, 等. 基于航路点布局的多目标网络结构优化方法[J]. 北京航空航天大学学报, 2019, 45(1): 1-9.ZHENG Yu-kun, WANG Ying, LI Chao, et al. Multi-objective network structure optimization method based on waypoint layout[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(1): 1-9. [59] 魏志强, 安心. 基于值迭代的无人机动态避撞优化方法[J]. 交通运输工程学报, 2026, 26(3): 215-227. doi: 10.19818/j.cnki.1671-1637.2026.153WEI Zhi-qiang, AN Xin. A dynamic collision avoidance method for UAVs using value iteration[J]. Journal of Traffic and Transportation Engineering, 2026, 26(3): 215-227. doi: 10.19818/j.cnki.1671-1637.2026.153 [60] 曹希. 基于复杂网络理论的航路网络生成及优化[D]. 南京: 南京航空航天大学, 2017.CAO Xi. Air route network generation and optimization based on complex network theory[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2017. [61] WANG S J, GONG Y H. Research on air route network nodes optimization with avoiding the three areas[J]. Safety Science, 2014, 66: 9-18. doi: 10.1016/j.ssci.2014.01.008 [62] 公言会. 航路网络规划技术研究[D]. 南京: 南京航空航天大学, 2015.GONG Yan-hui. Research on air route network planning technology[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2015. [63] WANG Shi-jin, LI Qing-yun, CAO Xi, et al. Optimization of air route network nodes to avoid "Three Areas" based on an adaptive ant colony algorithm[J]. Transactions of Nanjing University of Aeronautics and Astronautics, 2016, 33(4): 469-478. [64] 姜雨, 杨玲, 王华伟, 等. UAM起降设施选址与网络规划研究综述[J/OL]. 交通运输工程学报, 2026, DOI: 10.19818/j.cnki.1671-1637.2026.284 .JIANG Yu, YANG Ling, WANG Hua-wei, et al. Research review on the vertiport location and network planning of UAM[J/OL]. Journal of Traffic and Transportation Engineering, 2026, DOI:10.19818/j.cnki.1671-1637.2026.284 .[65] EMANI M E, COULIBALY A, DIAGNE S G, et al. Optimization of a route network in Dakar airspace: Surface navigation[J]. American Journal of Operations Research, 2022, 12(2): 64-81. doi: 10.4236/ajor.2022.122004 -
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