航路时空资源分配的多目标优化方法

田文; 杨帆; 尹嘉男; 宋津津

doi:10.19818/j.cnki.1671-1637.2020.06.019

航路时空资源分配的多目标优化方法

doi: 10.19818/j.cnki.1671-1637.2020.06.019

南京航空航天大学民航学院, 江苏南京 211106

基金项目:

国家自然科学基金项目 71971112

国家自然科学基金项目 61903187

国家自然科学基金项目 52002178

江苏省自然科学基金项目 BK20190416

江苏省自然科学基金项目 BK20190414

中央高校基本科研业务费专项资金项目 kfjj20190717

详细信息

作者简介:
田文(1981-), 女, 山东青岛人, 南京航空航天大学讲师, 工学博士, 从事空中交通流量管理研究

中图分类号: V355
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出版历程
- 收稿日期: 2020-08-06
- 刊出日期: 2020-06-25

Multi-objective optimization method of air route space-time resources allocation

School of Civial Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, Jiangsu, China

Funds:

National Natural Science Foundation of China 71971112

National Natural Science Foundation of China 61903187

National Natural Science Foundation of China 52002178

Natural Science Foundation of Jiangsu Province BK20190416

Natural Science Foundation of Jiangsu Province BK20190414

Fundamental Research Funds for the Central Universities kfjj20190717

More Information

Author Bio:
TIAN Wen(1981-), female, lecturer, PhD, tw1981@nuaa.edu.cn

摘要

摘要: 为了提高航空公司与空管方之间的协同决策程度, 降低航班延误水平, 以航路飞行的航班为研究对象, 研究了航路时空资源的多目标分配; 考虑实际运行条件下航班的唯一性约束、时间顺序约束和可行性约束的影响, 以航班在流量受限区所分配的飞行航迹和进入时隙为决策变量, 以航班总延误成本最小和航空公司延误公平损失偏差系数最小为目标函数, 构建了多目标非线性0-1整数规划模型; 基于模型特点引用了非支配排序遗传算法(NSGA-Ⅱ), 并利用排列编码法设计了一种整数基因编码方式, 以最大限度保证基因产生可行解集; 为了验证模型与算法的有效性, 基于南中国海地区航班运行实例, 对算法搜寻最优解的性能进行了研究, 并将此算法与传统按时刻表分配(RBS)方法进行了对比。研究结果表明: 改进编码方式的NSGA-Ⅱ算法使解集种群在约50代后世代距离从600收敛至30并稳定, 具有良好的收敛性; 针对实例中的多目标优化模型共生成有6组解的帕累托解集, 结果有66.7%的概率完全支配RBS方法, 且优化结果中航班平均延误成本比RBS方法降低了8.5%, 平均公平损失偏差系数降低了70.6%。可见提出的航路时空资源多目标优化方法的执行效果显著, 可在降低总延误成本的基础上兼顾各航空公司的公平性, 是解决航路飞行航班航迹与时隙资源分配问题的一种有效方法。
- 空中交通管理 /
- 航路资源分配 /
- 多目标遗传算法 /
- 协同航迹选择程序 /
- 帕累托解 /
- 基因编码
Abstract: To improve the degree of collaborative decision-making between airlines and air traffic controllers, as well as reduce the level of flight delays, air route flights were used as a research object and the multi-objective allocation of route space-time resources was studied. The effects of uniqueness, time sequence, and feasibility constraints of flights under actual operating conditions were considered and the flight trajectory and entry time slot assigned by the flight in the restricted area were viewed as decision variables. The lowest total flight delay cost and the lowest airline delay fair loss deviation coefficient were regarded as objective functions. A multi-objective nonlinear 0-1 integer programming model was constructed. Based on the characteristics of the model reference, the non-dominated sorting genetic algorithm-Ⅱ(NSGA-Ⅱ) was used and an integer gene encoding scheme was designed by the permutation encoding method. A feasible solution set was generated to maximize genes. To verify the validities of the model and algorithm, based on the South China sea area flight operation example, the performance of searching for the optimal solution was studied and the algorithm was compared with the traditional ration-by-schedule(RBS) method. Research result shows that the improved encoding style of the NSGA-Ⅱ algorithm makes the generation distance of the solution set population converge from 600 to 30 and becomes stable after approximately 50 generations, with suitable convergence. The Pareto solution set with six solutions is generated for the multi-objective optimization model, with a 66.7% probability that the RBS method is completely dominated by the results. The average flight delay cost in the optimization results is 8.5% lower than that of the RBS method, and the average fair loss deviation coefficient is 70.6% lower. The implementation effect of the multi-objective optimization method for the space-time resources of the air route is remarkable. The fairness of each airline can be considered on the basis of reducing the total delay cost, making this an effective method for solving the problem of flight trajectory and slot resource allocation.
- air traffic control /
- air route resources allocation /
- multi-objective genetic algorithm /
- collaborative trajectory options program /
- Pareto solution /
- gene encoding

HTML全文

图 1 航迹选项示例

Figure 1. Example of trajectory options

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图 2 基因编码结构

Figure 2. Gene encoding structure

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图 3 g_i取值规则流程

Figure 3. Flow of g_i value rules

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图 4 染色体G的可行解映射流程

Figure 4. Feasible solution mapping process of chromosome G

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图 5 部分匹配交叉过程示例

Figure 5. Example of partial matching cross procedure

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图 6 帕累托最优前沿

Figure 6. Pareto optimal frontiers

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图 7 世代距离

Figure 7. Generation distances

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图 8 帕累托最优解集

Figure 8. Pareto optimal solution sets

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图 9 各优化方案与RBS对比结果

Figure 9. Comparison results between each optimization scheme and RBS

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表 1 航路相关信息

Table 1. Route information

航迹	容量(个·h^-1)
FCA1	10
FCA2	12

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表 2 可用时隙信息

Table 2. Available time slot informations

基因值	FCA1的时隙	基因值	FCA2的时隙
1	19:10:00	2	19:12:00
3	19:16:00	4	19:15:00
5	19:22:00	6	19:17:00
7	19:28:00	8	19:20:00
9	19:34:00	10	19:24:00
11	19:40:00	12	19:29:00
13	19:46:00	14	19:34:00
15	19:52:00	16	19:39:00
17	19:58:00	18	19:44:00
19	20:04:00	20	19:49:00
21	20:10:00	22	19:54:00
23	20:16:00	24	19:59:00
25	20:22:00	26	20:04:00
27	20:28:00	28	20:09:00

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表 3 航班信息

Table 3. Flight information

航班编号	航空公司	机型	乘客数量/人次	预计进入FCA1的时间	预计进入FCA2的时间	最早进入时间
1	A	M	130	19:10:00	19:13:28	19:10:00
2	A	M	120	19:10:30	19:10:30	19:10:30
3	B	M	150	19:15:47	19:15:47	19:15:47
4	B	M	120	19:17:22	19:18:44	19:17:22
5	C	M	150	19:18:46	19:19:17	19:18:46
6	A	H	270	19:18:52	19:22:29	19:18:52
7	B	H	290	19:21:00	19:21:00	19:21:00
8	C	M	130	19:22:46	19:21:23	19:21:23
9	C	M	150	19:25:49	19:25:10	19:25:10
10	B	H	380	19:26:05	19:25:38	19:25:38
11	A	M	130	19:33:31	19:30:48	19:30:48
12	C	M	130	19:35:39	19:34:40	19:34:40
13	A	M	130	19:35:00	19:39:53	19:35:00
14	C	M	150	19:40:36	19:35:56	19:35:56
15	A	M	120	19:37:30	19:41:28	19:37:30
16	C	M	170	19:40:00	19:43:49	19:40:00
17	C	H	300	19:46:17	19:49:18	19:46:17
18	B	M	120	19:48:45	19:56:50	19:48:45
19	C	M	150	19:49:34	19:53:44	19:49:34
20	C	H	300	19:55:38	19:52:04	19:52:04
21	A	M	120	19:54:47	19:54:47	19:54:47
22	A	M	170	19:55:00	19:55:18	19:55:00
23	B	H	380	19:56:38	19:58:38	19:56:38

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表 4 帕累托解集对应的目标值

Table 4. Target values of Pareto solution sets

航迹时隙选择方案	延误成本/min	公平损失偏差系数
1	251.55	0.076 50
2	257.18	0.012 60
3	275.48	0.011 90
4	281.33	0.011 80
5	295.55	0.005 11
6	305.06	0.001 82
平均值	277.69	0.019 96

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