考虑随机扰动的动态武器目标分配优化

doi:10.16182/j.issn1004731x.joss.25-0351

摘要/Abstract

摘要：

考虑实际无人系统指挥控制环境中各类随机扰动对武器目标分配问题建模与求解的影响，研究了3类不确定性扰动约束，建立了一个多目标动态传感器武器目标分配模型；针对扰动导致模型性质变化、传统单算子求解算法鲁棒性不足的问题，提出了一种基于DQN的多算子约束多目标进化框架。该算法在目标和决策空间中描述种群的收敛性、多样性和可行性，并建立从状态到再生算子的映射模型，实现动态调整的再生策略。仿真实验验证了算法的优异性能和求解模型时的鲁棒性。

关键词: 动态武器目标分配, 鲁棒性, 深度强化学习, 多算子再生, 元启发式算法

Abstract:

The impact of various random disturbances in the actual command and control environment of unmanned systems on problem modeling and solving of weapon target assignment was considered, and three types of uncertainty disturbance constraints were investigated. A multi-objective dynamic sensor weapontarget assignment model was established. By considering the issues of model property changes caused by disturbances and insufficient robustness of the traditional single-operator solving algorithm, a multi-operator constrained multi-objective evolutionary framework based on the deep Q-network was proposed. The algorithm described the convergence, diversity, and feasibility of the population in both the objective and decision spaces. It established a mapping model from states to reproduction operators, achieving a dynamically adjusted reproduction strategy. Simulation experiments validated the algorithm's excellent performance and robustness when solving models.

Key words: dynamic weapon target assignment, robustness, deep reinforcement learning, multi-operator reproduction, meta-heuristic algorithm

中图分类号:

TN949

白臻祖,侯一帜,何章鸣等 . 考虑随机扰动的动态武器目标分配优化[J]. 系统仿真学报, 2025, 37(12): 2967-2980.

Bai Zhenzu,Hou Yizhi,He Zhangming,et al . Optimization of Dynamic Weapon Target Assignment Considering Random Disturbances[J]. Journal of System Simulation, 2025, 37(12): 2967-2980.

图/表 9

表1

图1

表2

与已有算法对比HV结果

实例	BiCo	MTCMO	C3M	CDEA-DQN
+/–/=	4/17/2	5/13/5	0/21/2
CF1	0.537 (1.84×10^-2) -	0.548 (3.79×10^-3) -	0.547 (3.90×10^-3) -	0.564 (4.72×10^-4)
CF2	0.603 (3.59×10^-2) -	0.615 (2.47×10^-2) -	0.641 (1.83×10^-2) -	0.666 (9.75×10^-3)
CF3	0.1.88 (4.72×10^-2) -	0.157 (4.48×10^-2) -	0.169 (4.01×10^-2) -	0.233 (5.18×10^-2)
CF4	0.411 (3.64×10^-2) -	0.388 (8.39×10^-2) -	0.444 (2.57×10^-2) -	0.466 (9.82×10^-3)
CF5	0.254 (8.13×10^-2) -	0.279 (6.82×10^-2) -	0.197 (6.98×10^-2) -	0.319 (7.17×10^-2)
CF6	0.628 (1.95×10^-2) -	0.642 (1.64×10^-2) -	0.659 (6.92×10^-3) =	0.663 (8.23×10^-3)
CF7	0.424 (8.45×10^-2) -	0.414 (1.34×10^-1) =	0.449 (1.21×10^-1) =	0.478 (6.54×10^-2)
CF8	0.297 (5.70×10^-2) =	0.250 (7.32×10^-2) -	0.195 (5.10×10^-2) -	0.299 (7.59×10^-2)
CF9	0.408 (3.20×10^-2) =	0.422 (1.58×10^-2) +	0.355 (2.91×10^-2) -	0.408 (2.56×10^-2)
MW1	0.438 (4.88×10^-2) -	0.467 (2.52×10^-2) -	0.149 (5.99×10^-2) -	0.487 (7.85×10^-4)
MW2	0.562 (1.23×10^-2) +	0.549 (1.11×10^-2) +	0.415 (6.83×10^-2) -	0.535 (3.15×10^-2)
MW3	0.535 (3.59×10^-3) -	0.540 (1.88×10^-3) =	0.538 (1.47×10^-3) -	0.541 (6.03×10^-4)
MW4	0.831 (4.87×10^-3) +	0.831 (1.91×10^-2) +	0.403 (2.87×10^-1) -	0.824 (3.57×10^-3)
MW5	0.310 (1.05×10^-2) -	0.295 (6.28×10^-2) =	0.086 (5.03×10^-2) -	0.317 (3.28×10^-3)
MW6	0.318 (1.00×10^-2) +	0.304 (2.23×10^-2) +	0.101 (5.96×10^-2) -	0.255 (4.71×10^-2)
MW7	0.405 (2.20×10^-3) -	0.408 (1.24×10^-3) -	0.408 (7.98×10^-4) -	0.411 (3.33×10^-4)
MW8	0.478 (5.22×10^-2) -	0.531 (1.31×10^-2) -	0.314 (1.18×10^-1) -	0.544 (6.85×10^-3)
MW9	0.344 (6.65×10^-2) -	0.348 (1.04×10^-1) -	0.103 (1.61×10^-1) -	0.382 (2.13×10^-2)
MW10	0.290 (1.19×10^-1) -	0.408 (4.03×10^-2) =	0.259 (7.00×10^-2) -	0.415 (2.38×10^-2)
MW11	0.416 (6.62×10^-2) -	0.412 (4.49×10^-2) -	0.443 (9.49×10^-4) -	0.446 (8.12×10^-4)
MW12	0.526 (1.32×10^-1) -	0.533 (1.84×10^-1) -	0.015 (3.68×10^-2) -	0.599 (2.27×10^-2)
MW13	0.445 (2.55×10^-2) +	0.442 (2.04×10^-2) +	0.308 (7.38×10^-2) -	0.417 (3.12×10^-2)
MW14	0.280 (8.11×10^-2) -	0.429 (5.55×10^-2) =	0.198 (6.14×10^-2) -	0.459 (4.44×10^-3)

表2

图2

图3

图4

表3

表4

表5

参考文献 38

[1]	刘大勇, 郭齐胜, 董志明, 等. AI4S驱动的战术博弈对抗仿真体系及应用框架研究[J/OL]. 系统仿真学报. (2025-04-18) [2025-07-21]. .
	Liu Dayong, Guo Qisheng, Dong Zhiming, et al. Research of the System and Application Framework of Tactical Game Simulation Driven by AI 4S[J/OL]. Journal of System Simulation. (2025-04-18) [2025-07-21]. .
[2]	彭雅兰, 段海滨, 张岱峰, 等. 仿灰狼合作捕食行为的无人机集群动态任务分配[J]. 控制理论与应用, 2021, 38(11): 1855-1862.
	Peng Yalan, Duan Haibin, Zhang Daifeng, et al. Unmanned Aerial Vehicle Swarm Dynamic Mission Planning Inspired by Cooperative Predation of Wolf-pack[J]. Control Theory & Applications, 2021, 38(11): 1855-1862.
[3]	Kline A, Ahner D, Hill R. The Weapon-target Assignment Problem[J]. Computers & Operations Research, 2019, 105: 226-236.
[4]	Li Jinrui, Wu Guohua, Wang Ling. A Comprehensive Survey of Weapon Target Assignment Problem: Model, Algorithm, and Application[J]. Engineering Applications of Artificial Intelligence, 2024, 137, Part B: 109212.
[5]	李梦杰, 常雪凝, 石建迈, 等. 武器目标分配问题研究进展:模型、算法与应用[J]. 系统工程与电子技术, 2023, 45(4): 1049-1071.
	Li Mengjie, Chang Xuening, Shi Jianmai, et al. Developments of Weapon Target Assignment: Models, Algorithms, and Applications[J]. Systems Engineering and Electronics, 2023, 45(4): 1049-1071.
[6]	王艺鹏, 辛斌, 陈杰. 多阶段传感器-武器-目标分配问题的建模与优化求解[J]. 控制理论与应用, 2019, 36(11): 1886-1895.
	Wang Yipeng, Xin Bin, Chen Jie. Modeling and Optimization of Multi-stage Sensor-weapon-target Assignment[J]. Control Theory & Applications, 2019, 36(11): 1886-1895.
[7]	Xin Bin, Wang Yipeng, Chen Jie. An Efficient Marginal-return-based Constructive Heuristic to Solve the Sensor-weapon-target Assignment Problem[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, 49(12): 2536-2547.
[8]	Wang Yipeng, Xin Bin, Chen Jie. An Adaptive Memetic Algorithm for the Joint Allocation of Heterogeneous Stochastic Resources[J]. IEEE Transactions on Cybernetics, 2022, 52(11): 11526-11538.
[9]	王晴, 王雨珏, 王浩然, 等. 融合深度强化学习与图神经网络的动态武器目标分配优化[J/OL]. 控制理论与应用. (2025-07-17) [2025-07-29]. .
	Wang Qing, Wang Yujue, Wang Haoran, et al. Dynamic Weapon-target Assignment Optimization Integrating Deep Reinforcement Learning and Graph Neural Networks[J/OL]. Control Theory & Applications. (2025-07-17) [2025-07-29]. .
[10]	Liang Jing, Ban Xuanxuan, Yu Kunjie, et al. A Survey on Evolutionary Constrained Multiobjective Optimization[J]. IEEE Transactions on Evolutionary Computation, 2023, 27(2): 201-221.
[11]	Li Yingwei, Feng Xiang, Yu Huiqun. A Constrained Multiobjective Evolutionary Algorithm with the Two-archive Weak Cooperation[J]. Information Sciences, 2022, 615: 415-430.
[12]	Bai Zhenzu, Zhou Haiyin, Shi Jianmai, et al. A Hybrid Multi-objective Evolutionary Algorithm with High Solving Efficiency for UAV Defense Programming[J]. Swarm and Evolutionary Computation, 2024, 87: 101572.
[13]	Xu Liang, Cao Xianbin, Du Wenbo, et al. Cooperative Path Planning Optimization for Multiple UAVs with Communication Constraints[J]. Knowledge-Based Systems, 2023, 260: 110164.
[14]	Ma Zhongwei, Wang Yong, Song Wu. A New Fitness Function with Two Rankings for Evolutionary Constrained Multiobjective Optimization[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(8): 5005-5016.
[15]	Sri Srinivasa Raju M, Dutta Saykat, Mallipeddi Rammohan, et al. A Dual-population and Multi-stage Based Constrained Multi-objective Evolutionary[J]. Information Sciences, 2022, 615: 557-577.
[16]	Tian Ye, Zhang Tao, Xiao Jianhua, et al. A Coevolutionary Framework for Constrained Multiobjective Optimization Problems[J]. IEEE Transactions on Evolutionary Computation, 2021, 25(1): 102-116.
[17]	Zuo Mingcheng, Gong Dunwei, Wang Yan, et al. Process Knowledge-guided Autonomous Evolutionary Optimization for Constrained Multiobjective Problems[J]. IEEE Transactions on Evolutionary Computation, 2024, 28(1): 193-207.
[18]	Xu Bin, Duan Wei, Zhang Haifeng, et al. Differential Evolution with Infeasible-guiding Mutation Operators for Constrained Multi-objective Optimization[J]. Applied Intelligence, 2020, 50(12): 4459-4481.
[19]	Liu Yijun, Li Xin, Hao Qijia. A New Constrained Multi-objective Optimization Problems Algorithm Based on Group-sorting[C]//Proceedings of the Genetic and Evolutionary Computation Conference Companion. New York: ACM, 2019: 221-222.
[20]	Qian Feng, Xu Bin, Qi Rongbin, et al. Self-adaptive Differential Evolution Algorithm with Α-constrained-domination Principle for Constrained Multi-objective Optimization[J]. Soft Computing, 2012, 16(8): 1353-1372.
[21]	Tian Ye, Li Xiaopeng, Ma Haiping, et al. Deep Reinforcement Learning Based Adaptive Operator Selection for Evolutionary Multi-objective Optimization[J]. IEEE Transactions on Emerging Topics in Computational Intelligence, 2023, 7(4): 1051-1064.
[22]	Deb Kalyanmoy, Sindhya Karthik, Okabe Tatsuya. Self-adaptive Simulated Binary Crossover for Real-parameter Optimization[C]//Proceedings of the 9th annual conference on Genetic and evolutionary computation. New York: ACM, 2007: 1187-1194.
[23]	Storn R, Price K. Differential Evolution—A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces [J] Journal of Global Optimizatio, 1997, 11: 341-359.
[24]	Kukkonen S, Deb K. Improved Pruning of Non-dominated Solutions Based on Crowding Distance for Bi-objective Optimization Problems[C]//2006 IEEE International Conference on Evolutionary Computation. Piscataway: IEEE, 2006: 1179-1186.
[25]	Pan Linqiang, Xu Wenting, Li Lianghao, et al. Adaptive Simulated Binary Crossover for Rotated Multi-objective Optimization[J]. Swarm and Evolutionary Computation, 2021, 60: 100759.
[26]	A Coello Coello Carlos, Nareli Cruz Cortés. Solving Multiobjective Optimization Problems Using an Artificial Immune System[J]. Genetic Programming and Evolvable Machines, 2005, 6(2): 163-190.
[27]	Wang Handing, Jin Yaochu, Yao Xin. Diversity Assessment in Many-objective Optimization[J]. IEEE Transactions on Cybernetics, 2017, 47(6): 1510-1522.
[28]	Sutton R S, Barto A G. Reinforcement Learning: An Introduction[J]. IEEE Transactions on Neural Networks, 1998, 9(5): 1054-1054.
[29]	Deb K, Pratap A, Agarwal S, et al. A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II[J]. IEEE Transactions on Evolutionary Computation, 2002, 6(2): 182-197.
[30]	Zhang Xingyi, Tian Ye, Cheng Ran, et al. An Efficient Approach to Nondominated Sorting for Evolutionary Multiobjective Optimization[J]. IEEE Transactions on Evolutionary Computation, 2015, 19(2): 201-213.
[31]	Tian Ye, Cheng Ran, Zhang Xingyi, et al. PlatEMO: A MATLAB Platform for Evolutionary Multi-objective Optimization [Educational Forum][J]. IEEE Computational Intelligence Magazine, 2017, 12(4): 73-87.
[32]	Zhang Q, Zhou A, Zhao S Z, et al. Multiobjective Optimization Test Instances for the CEC 2009 Special Session and Competition[C]// 2009 IEEE Congress on Evolutionary Computation. Trondheim, Norway: IEEE, 2009: 195-202.
[33]	Ma Zhongwei, Wang Yong. Evolutionary Constrained Multiobjective Optimization: Test Suite Construction and Performance Comparisons[J]. IEEE Transactions on Evolutionary Computation, 2019, 23(6): 972-986.
[34]	Zitzler E, Thiele L. Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach[J]. IEEE Transactions on Evolutionary Computation, 1999, 3(4): 257-271.
[35]	Liu Zhizhong, Wang Bingchuan, Tang Ke. Handling Constrained Multiobjective Optimization Problems via Bidirectional Coevolution[J]. IEEE Transactions on Cybernetics, 2022, 52(10): 10163-10176.
[36]	Qiao Kangjia, Yu Kunjie, Qu Boyang, et al. Dynamic Auxiliary Task-based Evolutionary Multitasking for Constrained Multiobjective Optimization[J]. IEEE Transactions on Evolutionary Computation, 2023, 27(3): 642-656.
[37]	Sun Ruiqing, Zou Juan, Liu Yuan, et al. A Multistage Algorithm for Solving Multiobjective Optimization Problems with Multiconstraints[J]. IEEE Transactions on Evolutionary Computation, 2023, 27(5): 1207-1219.
[38]	Fan Zhun, Li Wenji, Cai Xinye, et al. An Improved Epsilon Constraint-handling Method in MOEA/D for CMOPs with Large Infeasible Regions[J]. Soft Computing, 2019, 23(23): 12491-12510.

实例	CDEA-ARSBX	CDEA-DE	CDEA-GA	CDEA-GAhalf	CDEA-DQN
+/–/=	0/2/7	1/6/2	0/6/3	0/6/3
CF1	0.562 (2.7×10^-4) -	0.564 (3.4×10^-4) +	0.561 (1.1×10^-3) -	0.560 (1.1×10^-3) -	0.563 (8.2×10^-4)
CF2	0.665 (1.2×10^-2) =	0.667 (5.3×10^-3) -	0.618 (2.7×10^-2) -	0.6.16 (2.3×10^-2) -	0.669 (4.7×10^-3)
CF3	0.219 (5.4×10^-2) =	0.106 (4.7×10^-2) -	0.189 (3.8×10^-2) -	0.1.83 (3.7×10^-2) -	0.236 (5.4×10^-2)
CF4	0.458 (1.8×10^-2) / -	0.451 (1.4×10^-2) -	0.417 (3.0×10^-2) -	0.402 (6.1×10^-2) -	0.471 (1.4×10^-2)
CF5	0.314 (6.2×10^-2) =	0.257 (7.6×10^-2) -	0.285 (6.7×10^-2) =	0.269 (6.7×10^-2) =	0.304 (7.3×10^-2)
CF6	0.666 (7.3×10^-3) =	0.662 (8.9×10^-3) =	0.644 (1.5×10^-2) -	0.641 (1.7×10^-2) -	0.663 (9.5×10^-3)
CF7	0.437 (1.0×10^-1) =	0.426 (9.6×10^-2) =	0.4.09 (9.5×10^-2) -	0.423 (6.8×10^-2) -	0.467 (1.1×10^-1)
CF8	0.229 (9.3×10^-2) =	0.053 (3.7×10^-2) -	0.279 (9.7×10^-2) =	0.287 (9.3×10^-2) =	0.276 (8.5×10^-2)
CF9	0.406 (3.6×10^-2) =	0.227 (6.8×10^-2) -	0.388 (5.7×10^-2) =	0.383 (5.9×10^-2) =	0.403 (3.7×10^-2)

不同扰动	S_p/W_p/T
均势	20/10/10	20/50/50	20/100/100
0~10%	2±0	2±0	2±0
10%~20%	2±0	2±0	2±0
20%~30%	2±0	2±0	2±0
30%~40%	2±0	2±0	2±0
40%~50%	1.95±0.22	2±0	2±0
50%~60%	2±0	2±0	2±0
60%~70%	2±0	2±0	2±0
优势	20/20/10	20/75/50	20/150/100
0~10%	1±0	1±0	2±0
10%-~20%	1±0	1±0	2±0
20%~30%	1±0	1±0	2±0
30%~40%	1±0	2±0	2±0
40%~50%	1±0	1±0	2±0
50%~60%	1±0	1.4±0.55	1.8±0.67
60%~70%	1±0	2±0	2±0
劣势	20/10/20	20/50/75	20/100/150
0~10%	5±0	3±0	3±0
10%~20%	4.2±0.91	3±0	3±0
20%~30%	//	3±0	3±0
30%~40%	//	3±0	3±0
40%~50%	//	3±0	3.8±0.57
50%~60%	//	//	//
60%~70%	//	//	//

不同扰动	S_p/W_p/T
均势	20/10/10	20/50/50	20/100/100
0~10%	2±0	2±0	2±0
10%~20%	2±0	2±0	2±0
20%~30%	2±0	2±0	2±0
30%~40%	2±0	2±0	2±0
40%~50%	2±0	2±0	2±0
50%~60%	2±0	2±0	2±0
60%~70%	2±0	2±0	2±0
优势	20/20/10	20/75/50	20/150/100
0%~10%	1±0	1±0	1.67±0.58
10%-~20%	1±0	1.4±0.57	2±0
20%~30%	1±0	1.8±0.45	2±0
30%~40%	1±0	2±0	2±0
40%~50%	1±0	2±0	2±0
50%~60%	1±0	1.8±0.45	2±0
60%~70%	1±0	2±0	2±0
劣势	20/10/20	20/50/75	20/100/150
0~10%	4±0	2.9±0.33	2±0
10%~20%	3.8±0.48	3±0	2±0
20%~30%	4±0	3±0	2±0
30%~40%	3.8±0.45	3±0	3±0
40%~50%	4±0	3±0	3±0
50%~60%	5±0	3±0	3±0
60%~70%	5.8±0.45	3±0	3.67±0.58

不同扰动	S_p/W_p/T
均势	20/10/10	20/50/50	20/100/100
0~5%	1.67±0.58	//	//
5%~10%	6±0	//	//
10%~15%	//	//	//
优势	20/20/10	20/75/50	20/150/100
0~5%	1±0	//	//
5%~10%	1±0	//	//
10%~15%	//	//	//
劣势	20/10/20	20/50/75	20/100/150
0~5%	3±0	//	//
5%~10%	//	//	//
10%~15%	//	//	//