基于KnCMPSO算法的异构无人机协同多任务分配

王峰; 黄子路; 韩孟臣; 邢立宁; 王凌

doi:10.16383/j.aas.c210696

基于KnCMPSO算法的异构无人机协同多任务分配

doi: 10.16383/j.aas.c210696

王峰^1,,
黄子路^1,,
韩孟臣^1,,
邢立宁^2,,
王凌^3,

1.
武汉大学计算机学院武汉 430072
2.
国防科技大学系统工程学院长沙 410073
3.
清华大学自动化系北京 100084

基金项目: 国家自然科学基金(62173258, 61773296), 高等学校全国优秀博士学位论文作者专项资金(2014-92)资助

详细信息

作者简介:
王峰：武汉大学计算机学院教授. 主要研究方向为进化计算, 智能信息处理和机器学习. 本文通信作者. E-mail: fengwang@whu.edu.cn

黄子路：武汉大学计算机学院硕士研究生. 主要研究方向为进化计算. E-mail: huangzilu@whu.edu.cn

韩孟臣：武汉大学计算机学院硕士研究生. 主要研究方向为进化计算. E-mail: hanmengchen@whu.edu.cn

邢立宁：国防科技大学系统工程学院研究员. 主要研究方向为智能优化理论, 方法和应用. E-mail: xinglining@gmail.com

王凌：清华大学自动化系教授. 主要研究方向为智能优化, 生产调度. E-mail: wangling@tsinghua.edu.cn

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出版历程
- 收稿日期: 2021-07-22
- 录用日期: 2022-04-12
- 网络出版日期: 2023-02-09
- 刊出日期: 2023-02-20

A Knee Point Based Coevolution Multi-objective Particle Swarm Optimization Algorithm for Heterogeneous UAV Cooperative Multi-task Allocation

1.
School of Computer Science, Wuhan University, Wuhan 430072
2.
College of Systems Engineering, National University of Defense Technology, Changsha 410073
3.
Department of Automation, Tsinghua University, Beijing 100084

Funds: Supported by National Natural Science Foundation of China (62173258, 61773296) and National Excellent Doctoral Dissertation Foundation of China (2014-92)

More Information

Author Bio:
WANG Feng　Professor at the School of Computer Science, Wuhan University. Her research interest covers evolutionary computation, intelligent information processing, and machine learning. Corresponding author of this paper

HUANG Zi-Lu　Master student at the School of Computer Science, Wuhan University. His main rese-arch interest is evolutionary computation

HAN Meng-Chen　Master student at the School of Computer Science, Wuhan University. His main research interest is evolutionary computation

XING Li-Ning　Professor at the College of Systems Engineering, National University of Defense Technology. His research interest covers intelligent optimization theory, method, and application

WANG Ling　Professor in the Department of Automation, Tsinghua University. His research interest covers intelligent optimization and production scheduling

摘要

摘要: 随着无人机(Unmanned aerial vehicle, UAV)技术的广泛应用和执行任务的日益复杂, 无人机多机协同控制面临着新的挑战. 以无人机总飞行距离和任务完成时间为优化目标, 同时考虑异构无人机类型、任务执行时序等多种实际约束, 构建基于多种约束条件的异构无人机协同多任务分配模型. 该模型不仅包含混合变量, 同时还存在多个复杂的约束条件, 因此, 传统的多目标优化算法并不能有效地处理混合变量及对问题空间进行搜索并生成满足多种约束条件的可行解. 为高效求解上述模型, 提出一种基于拐点的协同多目标粒子群优化算法(Knee point based coevolution multi-objective particle swarm optimization, KnCMPSO), 该算法引入基于拐点的学习策略来更新外部档案集, 在保证收敛性的同时增加种群的多样性, 使算法能搜索到更多可行的任务分配结果; 并基于二进制交叉方法, 引入基于学习的粒子更新策略来提升算法的收敛性及基于区间扰动的局部搜索策略以提升算法的多样性. 最后通过在四组实例上的仿真实验验证了所提算法在求解异构无人机协同多任务分配问题上的有效性.
- 无人机多任务分配 /
- 多目标优化 /
- 粒子群算法 /
- 协同进化
Abstract: With the wide application of unmanned aerial vehicle (UAV) technology and the increasing complexity of UAV tasks, the multi-aircraft cooperative control on UAVs faces new challenges. In this paper, a heterogeneous UAV cooperative multi-task allocation model which takes the UAV total flight distance and task completion time as the optimization objectives is set up. The model includes mixed variables and multiple complex constraints, such as UAV type and task execution time. As a result, traditional multi-objective optimization algorithms cannot effectively search the problem space and generate feasible solutions. In this paper, a knee point based cooperative multi-objective particle swarm optimization algorithm, namely knee point based coevolution multi-objective particle swarm optimization (KnCMPSO), is proposed to solve the above model. In KnCMPSO, a knee point based learning strategy is employed to update the external archive set, which can help get more better solutions. The learning-based particle update strategy is proposed to improve the convergence and the interval disturbance based local search strategy is used to enhance the diversity. The experimental results on four sets of examples show that, the proposed KnCMPSO algorithm can solve the heterogeneous UAVs collaborative multi-task allocation problem more effectively than other existing methods.
- Unmanned aerial vehicle multi-task allocation /
- multi-objective optimization /
- particle swarm algorithm /
- coevolution

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图 1 KnCMPSO算法流程图

Fig. 1 Flowchart of KnCMPSO algorithm

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图 2 种群间合作种群内竞争的协同进化策略

Fig. 2 Coevolution strategy of inter-population cooperation and intra-population competition

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图 3 竞争式协同进化策略

Fig. 3 Competitive coevolution strategy

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图 4 粒子向较优个体的学习过程

Fig. 4 The learning process of particles from better individuals

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图 5 基于区间扰动的局部搜索策略

Fig. 5 Local search strategy based on interval disturbance

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图 6 解集分布不均匀图

Fig. 6 Uneven solution set distribution graph

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图 7 拐点图示

Fig. 7 Illustration of knee point

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图 8 4个实例的示意图

Fig. 8 Schematic diagram of four examples

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图 9 算法在各实例上的解集的分布图

Fig. 9 Distribution diagram of the solution set of the algorithm on each example

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表 1 符号说明

Table 1 Symbol description

类别	属性
	侦察无人机总数$S$
	战斗无人机总数$A$
	初始位置$P_i = (x_i, y_i)$
	飞行速度$V_i$
无人机$U$	战斗无人机最大携弹数目$Load_i$
	战斗无人机单次任务最大发射弹药数目$Launch_i$
	侦察无人机单次任务最大侦察时间$T_i$
	无人机最大飞行距离${\rm{Max}}Dis_i$
	无人机$U_i$执行任务$M_k$消耗的资源$C_i^k$
	目标总个数$N_T$
	目标位置坐标$P_j = (x_j, y_j)$
目标$T$	目标$j$的任务个数$N_M^j=3$
	任务总个数$N_M=3 \times N_T$
任务$M$	任务完成所需资源$CR_k$

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表 2 粒子编码方式

Table 2 Particle encoding scheme

目标编号$T$	1		2		2			1		3	1	3	2	3
无人机编号$U$	1	3	2	3	4	5	6	5	6	1	2	4	1	2	3
资源消耗$C$	2.4	2.6	1.1	4.9	2.0	1.0	1.0	2.0	1.0	5.0	3.0	2.0	3.0	0.2	1.1

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表 3 目标队列集合

Table 3 Target formation collection

1	2	3	$\cdots $	$N$
$T_1^O$	$T_2^O$	$T_3^O$	$\cdots $	$T_N^O$
$T_1^A$	$T_2^A$	$T_3^A$	$\cdots $	$T_N^A$
$T_1^E$	$T_2^E$	$T_3^E$	$\cdots $	$T_N^E$

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表 4 无人机集合

Table 4 Drone collection

侦察机$U_S$	$U_1,U_2,\cdots,U_S$
战斗机$U_A$	$U_{S+1},U_{S+2},\cdots,U_{S+A}$

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表 5 实例4中目标属性值

Table 5 The target attribute value in example 4

目标	坐标 (千米, 千米)	观测时间 (秒)	打击所需弹药数 (枚)	评估时间 (秒)
$T1$	(13, 41)	100	2	40
$T2$	(63, 83)	120	1	20
$T3$	(79, 12)	40	3	10
$T4$	(41, 98)	90	4	15
$T5$	(23, 65)	150	2	20
$T6$	(53, 19)	20	2	5
$T7$	(36, 49)	100	2	40
$T8$	(70, 47)	120	1	20
$T9$	(25, 15)	40	3	10
$T10$	(62, 89)	90	4	15
$T11$	(54, 42)	150	2	20
$T12$	(61, 39)	20	2	5
$T13$	(74, 29)	100	2	40
$T14$	(68, 33)	120	1	20
$T15$	(76, 38)	40	3	10
$T16$	(96, 26)	90	4	15
$T17$	(52, 55)	150	2	20
$T18$	(59, 98)	20	2	5
$T19$	(30, 43)	100	2	40
$T20$	(27, 82)	120	1	20
$T21$	(59, 13)	40	3	10
$T22$	(42, 28)	90	4	15
$T23$	(55, 39)	15	2	20
$T24$	(8, 46)	20	2	5

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表 6 实例4中无人机属性值

Table 6 Attribute value of drone in example 4

无人机	坐标 (千米, 千米)	无人机类型	携带弹药数 (枚)	飞行速度 (千米/秒)
$U1$	(57, 5)	侦察机	0	0.10
$U2$	(42, 8)	侦察机	0	0.12
$U3$	(50, 99)	侦察机	0	0.12
$U4$	(62, 25)	侦察机	0	0.11
$U5$	(20, 61)	侦察机	0	0.1
$U6$	(83, 46)	侦察机	0	0.12
$U7$	(56, 90)	侦察机	0	0.11
$U8$	(39, 45)	侦察机	0	0.11
$U9$	(58, 69)	侦察机	0	0.11
$U10$	(13, 86)	侦察机	0	0.1
$U11$	(5, 57)	侦察机	0	0.11
$U12$	(86, 46)	战斗机	11	0.13
$U13$	(89, 34)	战斗机	8	0.09
$U14$	(53, 11)	战斗机	10	0.11
$U15$	(92, 86)	战斗机	9	0.09
$U16$	(96, 18)	战斗机	12	0.11
$U17$	(73, 76)	战斗机	8	0.16
$U18$	(47, 56)	战斗机	7	0.16
$U19$	(56, 80)	战斗机	8	0.12
$U20$	(78, 4)	战斗机	9	0.16

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表 7 算法在各个实例上的HV值

Table 7 The HV value of the algorithm on each example

实例名称	HV	CMPSO	CoMOLS/D	CPSO	C-MOPSO	KnCMPSO
实例 1	Mean	${\underline{1.941 \times 10^{8}}}$	$1.846\times10^8$	$1.934\times10^8$	$1.873\times10^8$	${\bf 1.963}\times10^8$
	Std	${\underline{1.326\times10^6}}$	$2.035\times10^6$	$1.574\times10^6$	$2.483\times10^6$	${\bf{1.053\times10^6}}$
	Worst	${\underline{1.918\times10^8}}$	$1.799\times10^8$	$1.893\times10^8$	$1.836\times10^8$	${\bf{1.942\times10^8}}$
	Best	${\underline{1.969\times10^8}}$	$1.881\times10^8$	$1.958\times10^8$	$1.937\times10^8$	${\bf{1.982\times10^8}}$
实例 2	Mean	${\underline{1.586\times10^8}}$	$1.312\times10^8$	$1.554\times10^8$	$1.371\times10^8$	${\bf{1.629\times10^8}}$
	Std	${\bf{2.916\times10^6}}$	$3.387\times10^6$	$3.158\times10^6$	$3.523\times10^6$	${\underline{3.114\times10^6}}$
	Worst	${\underline{1.525\times10^8}}$	$1.259\times10^8$	$1.494\times10^8$	$1.297\times10^8$	${\bf{1.544\times10^8}}$
	Best	${\underline{1.640\times10^8}}$	$1.371\times10^8$	$1.637\times10^8$	$1.464\times10^8$	${\bf{1.675\times10^8}}$
实例 3	Mean	${\underline{1.326\times10^8}}$	$9.365\times10^7$	$1.284\times10^8$	$1.032\times10^8$	${\bf{1.387\times10^8}}$
	Std	${\bf{3.133\times10^6}}$	$4.722\times10^6$	${\underline{3.174\times10^6}}$	$4.292\times10^6$	$4.271\times10^6$
	Worst	${\underline{1.265\times10^8}}$	$8.571\times10^7$	$1.208\times10^8$	$9.782\times10^7$	${\bf{1.289\times10^8}}$
	Best	${\underline{1.383\times10^8}}$	$1.029\times10^8$	$1.365\times10^8$	$1.130\times10^8$	${\bf{1.487\times10^8}}$
实例 4	Mean	${\underline{1.103\times10^8}}$	$6.209\times10^7$	$1.027\times10^8$	$7.068\times10^7$	${\bf{1.151\times10^8}}$
	Std	$4.482\times10^6$	${\underline{3.658\times10^6}}$	$4.850\times10^6$	${\bf{3.056\times10^6}}$	$6.337\times10^6$
	Worst	${\underline{9.913\times10^7}}$	$5.582\times10^7$	$9.023\times10^7$	$6.601\times10^7$	${\bf{1.033\times10^8}}$
	Best	${\underline{1.192\times10^8}}$	$6.970\times10^7$	$1.116\times10^8$	$7.631\times10^7$	${\bf{1.241\times10^8}}$

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表 8 算法在各个实例上的HV值

Table 8 The HV value of the algorithm on each example

实例名称	HV	KnCMPSO-SLR	KnCMPSO
实例 1	Mean	$1.951\times10^8$	${\bf{1.974\times10^8}}$
	Std	${\bf{7.942\times10^5}}$	$1.046\times10^6$
	Worst	$1.934\times10^8$	${\bf{1.959\times10^8}}$
	Best	$1.961\times10^8 $	${\bf{1.989\times10^8 }}$
实例 2	Mean	${\bf{1.625\times10^8}}$	$1.622\times10^8$
	Std	$3.290\times10^6 $	${\bf{1.632\times10^6}}$
	Worst	$1.569\times10^8 $	${\bf{1.598\times10^8 }}$
	Best	${\bf{1.690\times10^8}}$	$1.645\times10^8$
实例 3	Mean	$1.347\times10^8 $	${\bf{1.395\times10^8}}$
	Std	${\bf{2.031\times10^6}}$	$3.099\times10^6 $
	Worst	$1.318\times10^8 $	${\bf{1.361\times10^8}}$
	Best	$1.385\times10^8 $	${\bf{1.449\times10^8}}$
实例 4	Mean	$1.146\times10^8 $	${\bf{1.184\times10^8}}$
	Std	${\bf{2.251\times10^6}}$	$3.492\times10^6 $
	Worst	$1.087\times10^8$	${\bf{1.124\times10^8}}$
	Best	$1.165\times10^8$	${\bf{1.241\times10^8}}$

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表 9 算法在各个实例上的HV值

Table 9 The HV value of the algorithm on each example

实例名称	HV	KnCMPSO-PF	KnCMPSO-FR	KnCMPSO-SR	KnCMPSO
实例 1	Mean	${\underline{1.800\times10^8}}$	$1.782\times10^8 $	$1.786\times10^8 $	${\bf{1.861\times10^8}}$
	Std	${\underline{3.005\times10^6}}$	$3.881\times10^6 $	$ 3.778\times10^6 $	${\bf{1.948\times10^6 }}$
	Worst	${\underline{1.721\times10^8}}$	$1.703\times10^8$	$1.705\times10^8 $	${\bf{1.800\times10^8}}$
	Best	${\underline{1.860\times10^8}}$	$1.837\times10^8$	$1.839\times10^8 $	${\bf{1.898\times10^8}}$
实例 2	Mean	${\underline{1.362\times10^8}}$	$1.346\times10^8$	$1.356\times10^8 $	${\bf{1.449\times10^8}}$
	Std	${\underline{4.110\times10^6}}$	${\bf{3.981\times10^6}}$	$4.166\times10^6 $	$4.562\times10^6 $
	Worst	$1.275\times10^8 $	$1.257\times10^8$	${\underline{1.296\times10^8}}$	${\bf{1.362\times10^8}}$
	Best	$1.435\times10^8$	$1.426\times10^8$	${\underline{1.453\times10^8}}$	${\bf{1.529\times10^8}}$
实例 3	Mean	${\underline{1.046\times10^8 }}$	$1.036\times10^8$	$1.003\times10^8 $	${\bf{1.175\times10^8}}$
	Std	$4.892\times10^6$	$6.045\times10^6$	${\underline{4.629\times10^6}}$	${\bf{4.027\times10^6}}$
	Worst	${\underline{9.602\times10^7}}$	$8.900\times10^7$	$8.618\times10^7$	${\bf{1.112\times10^8}}$
	Best	${\underline{1.145\times10^8}}$	$1.139\times10^8$	$1.066\times10^8$	${\bf{1.243\times10^8}}$
实例 4	Mean	${\underline{7.920\times10^7}}$	$7.851\times10^7$	$7.833\times10^7$	${\bf{9.603\times10^7}}$
	Std	$6.365\times10^6$	$6.608\times10^6$	${\underline{6.008\times10^6}}$	${\bf{5.376\times10^6}}$
	Worst	${\underline{6.537\times10^7}}$	$6.412\times10^7$	$6.007\times10^7 $	${\bf{8.466\times10^7}}$
	Best	${\underline{9.105\times10^7}}$	$8.916\times10^7$	$8.653\times10^7$	${\bf{1.045\times10^8}}$

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A1 实例3中目标属性值

A1 The target attribute value in example 3

目标	坐标 (千米, 千米)	观测时间 (秒)	打击所需弹药数 (枚)	评估时间 (秒)
$T1$	(13, 41)	100	2	40
$T2$	(63, 83)	120	1	20
$T3$	(79, 12)	40	3	10
$T4$	(41, 98)	90	4	15
$T5$	(23, 65)	150	2	20
$T6$	(53, 19)	20	2	5
$T7$	(36, 49)	100	2	40
$T8$	(70, 47)	120	1	20
$T9$	(25, 15)	40	3	10
$T10$	(62, 89)	90	4	15
$T11$	(54, 42)	150	2	20
$T12$	(61, 39)	20	2	5
$T13$	(74, 29)	100	2	40
$T14$	(68, 33)	120	1	20
$T15$	(76, 38)	40	3	10
$T16$	(96, 26)	90	4	15
$T17$	(52, 55)	150	2	20
$T18$	(59, 98)	20	2	5

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A2 实例3中无人机属性值

A2 Attribute value of drone in example 3

无人机	坐标 (千米, 千米)	无人机类型	携带弹药数 (枚)	飞行速度 (千米/秒)
$U1$	(57, 5)	侦察机	0	0.10
$U2$	(42, 8)	侦察机	0	0.12
$U3$	(50, 99)	侦察机	0	0.12
$U4$	(62, 25)	侦察机	0	0.11
$U5$	(20, 61)	侦察机	0	0.10
$U6$	(83, 46)	侦察机	0	0.12
$U7$	(56, 90)	侦察机	0	0.11
$U8$	(39, 45)	侦察机	0	0.11
$U9$	(58, 69)	侦察机	0	0.11
$U10$	(13, 86)	侦察机	0	0.10
$U11$	(56, 80)	战斗机	8	0.12
$U12$	(86, 46)	战斗机	9	0.13
$U13$	(89, 34)	战斗机	7	0.09
$U14$	(53, 11)	战斗机	9	0.11
$U15$	(92, 86)	战斗机	7	0.09
$U16$	(96, 18)	战斗机	9	0.11
$U17$	(73, 76)	战斗机	7	0.16
$U18$	(47, 56)	战斗机	5	0.16

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A3 实例2中目标属性值

A3 The target attribute value in example 2

目标	坐标 (千米, 千米)	观测时间 (秒)	打击所需弹药数 (枚)	评估时间 (秒)
$T1$	(13, 41)	100	2	40
$T2$	(63, 83)	120	1	20
$T3$	(79, 12)	40	3	10
$T4$	(41, 98)	90	4	15
$T5$	(23, 65)	150	2	20
$T6$	(53, 19)	20	2	5
$T7$	(36, 49)	100	2	40
$T8$	(70, 47)	120	1	20
$T9$	(25, 15)	40	3	10
$T10$	(62, 89)	90	4	15
$T11$	(54, 42)	150	2	20
$T12$	(61, 39)	20	2	5

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A4 实例2中无人机属性值

A4 Attribute value of drone in example 2

无人机	坐标 (千米, 千米)	无人机类型	携带弹药数 (枚)	飞行速度 (千米/秒)
$U1$	(73, 91)	侦察机	0	0.10
$U2$	(65, 64)	侦察机	0	0.12
$U3$	(56, 37)	侦察机	0	0.12
$U4$	(36, 96)	侦察机	0	0.11
$U5$	(20, 0)	侦察机	0	0.10
$U6$	(1, 68)	侦察机	0	0.12
$U7$	(51, 74)	侦察机	0	0.11
$U8$	(58, 69)	侦察机	0	0.11
$U9$	(13, 86)	侦察机	0	0.10
$U10$	(69, 20)	战斗机	10	0.10
$U11$	(52, 46)	战斗机	6	0.12
$U12$	(46, 98)	战斗机	7	0.13
$U13$	(92, 86)	战斗机	5	0.09
$U14$	(96, 18)	战斗机	7	0.11
$U15$	(73, 76)	战斗机	5	0.16
$U16$	(47, 56)	战斗机	5	0.16

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A5 实例1中目标属性值

A5 The target attribute value in example 1

目标	坐标 (千米, 千米)	观测时间 (秒)	打击所需弹药数 (枚)	评估时间 (秒)
$T1$	(36, 49)	100	2	40
$T2$	(70, 47)	120	1	20
$T3$	(25, 15)	40	3	10
$T4$	(62, 89)	90	4	15
$T5$	(54, 42)	150	2	20
$T6$	(61, 39)	20	2	5

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A6 实例1中无人机属性值

A6 Attribute value of drone in example 1

无人机	坐标 (千米, 千米)	无人机类型	携带弹药数 (枚)	飞行速度 (千米/秒)
$U1$	(73, 91)	侦察机	0	0.10
$U2$	(94, 92)	侦察机	0	0.12
$U3$	(56, 37)	侦察机	0	0.12
$U4$	(5, 57)	侦察机	0	0.11
$U5$	(20, 0)	侦察机	0	0.10
$U6$	(1, 68)	侦察机	0	0.12
$U7$	(51, 74)	侦察机	0	0.11
$U8$	(11, 90)	侦察机	0	0.11
$U9$	(73, 76)	战斗机	5	0.16
$U10$	(69, 20)	战斗机	10	0.10
$U11$	(52, 46)	战斗机	6	0.12
$U12$	(46, 98)	战斗机	7	0.13
$U13$	(92, 86)	战斗机	5	0.09
$U14$	(79, 4)	战斗机	7	0.11

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