基于三支决策和遗传算法的动态武器目标分配

doi:10.12382/bgxb.2024.0281

摘要/Abstract

摘要：

面向动态武器目标分配任务,结合博弈思想开展多阶段问题建模与求解。针对动态多阶段中确定打击目标的问题,引入三支决策理论改进威胁评估模型,通过接受决策、延迟决策和拒绝决策3种分类选取每阶段的优先打击目标用于火力分配;构建基于博弈思想的动态武器目标分配模型,设计构造敌方规避风险值目标函数以充分考虑来袭目标的智能性与不确定性;针对多个打击阶段中不同决策偏好的影响,设计结合拥挤度与参考点的动态选择机制,以应对动态情况下对不同目标函数的偏好并提高求解质量;将改进的遗传算法用于求解所提动态武器目标分配问题,并通过对比仿真实验验证所提算法的有效性。

关键词: 武器目标分配, 三支决策, 多目标优化, 遗传算法, 拥挤度

Abstract:

A multi-stage decision problem of the dynamic weapon-target assignment (DWTA)is modelled and solved based on a game idea.For determining the targets to be attacked in dynamic multi-stage,the three-way decision theory is introduced to improve the threat assessment model,and the priority targets to be attacked in each stage are selected for firepower assignment through the acceptance,delay and reject decisions.A dynamic weapon-target assignment model based on the game idea is constructed,and the objective function of enemy avoidance risk value is designed to take into account the intelligence and uncertainty of the incoming target.For the influence of decision preference in multi-stage solution,a dynamic selection mechanism combining the crowding degree and reference point is designed to cope with the preference of different objective functions in dynamic situations and improve the solution quality.The improved algorithm is used to solve the proposed DWTA problem,and the effectiveness of the proposed algorithm is verified through comparative simulation experiments.

Key words: weapon-target assignment, three-way decision, multi-objective optimization, genetic algorithm, crowding degree

刘富樯, 周伦, 刘中阳, 皮阳军, 蒲华燕, 罗均. 基于三支决策和遗传算法的动态武器目标分配[J]. 兵工学报, 2025, 46(3): 240281-.

LIU Fuqiang, ZHOU Lun, LIU Zhongyang, PI Yangjun, PU Huayan, LUO Jun. Dynamic Weapon-target Assignment Based on Three-way Decisionand Genetic Algorithm[J]. Acta Armamentarii, 2025, 46(3): 240281-.

图/表 7

表1 各情况下的损失函数

Table 1 Loss function in each case

行动	状态
行动	A	$A ¯$
a_P	λ_PP	λ_PN
a_B	λ_BP	λ_BN
a_N	$λ N P$	λ_NN

表1 各情况下的损失函数

Table 1 Loss function in each case

行动	状态
行动	A	$A ¯$
a_P	λ_PP	λ_PN
a_B	λ_BP	λ_BN
a_N	$λ N P$	λ_NN

图1 网格拥挤密度

Fig.1 Grid crowding density

表2 仿真场景规模

Table 2 The scale of the defense scenario

场景规模	防御武器数量	来袭目标数量
1	5	10
2	15	20

表3 5种算法所得解集的超体积指标

Table 3 Hypervolume indexes for the solution sets obtained by the five algorithms

场景		NSGA-Ⅲ	PAGA	IHGA	ANSGA- Ⅲ	DC- NSGA-Ⅲ
规模1	最好值	0.3576	0.4055	0.4055	0.3871	0.4131
	最差值	0.3142	0.3000	0.3504	0.3045	0.3570
	平均值	0.3416	0.3462	0.3750	0.3772	0.3829
	方差值	3.42e-04	1.57e-03	4.79e-04	3.17e-04	5.40e-04
规模2	最好值	0.2355	0.1951	0.2437	0.2552	0.2596
	最差值	0.2002	0.1659	0.1594	0.1883	0.2008
	平均值	0.2148	0.1846	0.1896	0.2214	0.2327
	方差值	1.73e-04	1.46e-04	1.17e-03	1.24e-04	6.31e-04

表4 5种算法所得解集的支配覆盖率

Table 4 Dominant coverages of the solution sets obtained by the five algorithms

场景	X₁	X₂
场景	X₁	S₁	S₂	S₃	S₄	S₅
规模1	S₁	0.0000	0.3711	0.1789	0.1983	0.1515
	S₂	0.1400	0.0000	0.1579	0.2046	0.1010
	S₃	0.2200	0.1577	0.0000	0.1547	0.2323
	S₄	0.2500	0.2154	0.1846	0.0000	0.2472
	S₅	0.2600	0.4433	0.2947	0.3142	0.0000
规模2	S₁	0.0000	0.2232	0.3568	0.1167	0.0534
	S₂	0.3035	0.0000	0.2562	0.1674	0.1336
	S₃	0.1262	0.1321	0.0000	0.2763	0.0486
	S₄	0.1664	0.2157	0.3349	0.0000	0.2075
	S₅	0.3214	0.3472	0.5028	0.3194	0.0000

图2 5种算法在规模1下的各目标函数收敛曲线

Fig.2 Convergence curves of objective functions of the five algorithms under Scale 1

图3 5种算法在规模2下的各目标函数收敛曲线

Fig.3 Convergence curves of each objective function of the five algorithms under Scale 2

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