基于图神经网络的导弹时序规划方法

doi:10.12305/j.issn.1001-506X.2025.03.18

Abstract

Abstract:

Multi-missile collaborative formation operation becomes an important means to strike key targets in modern war. In order to cope with the ever-changing battlefield situation, it is required to quickly calculate the missile launch temporal sequence, so that all missiles can accurately complete the strike task within the predetermined time. In order to solve the problem of temporal planning for multiple missile coordinated launch, an integer linear programming model with the goal of minimizing missile launch completion time is established. The missile launch sequence planning algorithm based on graph neural network model is designed, and the missile launch sequence is optimized locally based on node sampling and greedy insertion strategy, which can help battlefield commanders to quickly generate the missile launch sequence plan. Verification and analysis are carried out for the coordinated launch of 20-200 missiles. The experimental results show that the model and method can effectively solve the problem of temporal planning for coordinated launch of multiple missiles.

Key words: cruise missile, launch temporal planning, graph neural network, local optimization

CLC Number:

TP391

Kai CHEN, Deping ZHANG. Missile temporal planning method based on graph neural network[J]. Systems Engineering and Electronics, 2025, 47(3): 862-870.

Figures/Tables 13

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参数	参数意义
M	导弹集合, 且i∈{1, 2, …, M}
U	一个足够大的正整数
L_i	第i枚导弹最早允许飞抵初航点的时刻
R_i	第i枚导弹最晚必须飞抵初航点的时刻
C_i	第i枚导弹到达初航点的飞行耗时
S_ij	第j枚导弹后于第i枚导弹发射的最小安全时间间隔
zL	第1枚导弹飞抵初航点后，后续所有导弹必须全部飞抵各自初航点的总耗时
T_i	第i枚导弹的发射时刻
b_ij	值为1时, 表示第i枚导弹在第j枚导弹之前发射, 否则值为0
$\widetilde{u}$	所有导弹最早发射时刻
$\widetilde{\mathcal{V}}$	所有导弹最晚发射时刻
u	所有导弹最早飞抵初航点的时刻
v	所有导弹最晚飞抵初航点的时刻

模型	导弹数量
模型	20	40	60	80	100
CPLEX	310.39	345.88	360.75	369.50	374.45
GAPN-G	313.51	350.40	366.98	388.93	472.40
GAPN-SI5	313.57	353.84	370.32	384.30	394.12
GAPN-SI20	311.29	349.94	366.04	376.79	383.91

模型	导弹数量
模型	20	40	60	80	100
CPLEX	0.17	0.53	1.52	4.46	14.38
GAPN-G	0.18	0.38	0.62	0.97	1.39
GAPN-SI5	2.32	6.12	14.29	25.55	37.43
GAPN-SI20	4.85	12.46	27.15	47.48	74.45

导弹数量	评价指标	模型
导弹数量	评价指标	CPLEX	GAPN-SI5
160	$\overline{{\rm{QF}}}$	415.13	412.23
	Time	329.62	62.40
	Acc	100.00	100.00
200	$\overline{{\rm{QF}}}$	528.89	437.00
	Time	417.74	100.52
	Acc	84.00	100.00

节点数量	导弹数量
节点数量	20	40	60	80	100
1	314.80	352.68	370.46	392.66	471.41
2	314.72	353.43	372.29	394.83	470.92
4	314.23	351.57	368.27	390.37	472.22
8	313.64	350.40	366.98	389.01	472.23

Missile temporal planning method based on graph neural network

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Figures/Tables 13

References 32

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导弹数量/枚	评价指标	模型
导弹数量/枚	评价指标	GAPN-SI20	Radom-I20
60	Acc	100.00	99.00
60	$\overline{{\rm{QF}}}$	366.91	367.80
100	Acc	100.00	98.00
100	$\overline{{\rm{QF}}}$	384.55	389.71
160	Acc	100.00	47.00
160	$\overline{{\rm{QF}}}$	405.79	434.17
200	Acc	100.00	0.00
200	$\overline{{\rm{QF}}}$	429.70	-

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