基于自适应混合进化的防空反导火力资源分配优化

doi:10.16182/j.issn1004731x.joss.25-1216

摘要/Abstract

摘要：

防空反导火力资源分配是现代防御体系的核心优化问题，在时空约束、火力资源限制等复杂条件下，对有限拦截器进行最优配置，属于NP-hard的多约束组合优化问题。构建了包含射程约束、时间窗口约束、可行性矩阵和拦截概率模型的完整数学模型；针对高维非线性特性，提出了自适应混合进化算法(adaptive hybrid evolutionary algorithm，AHEA)，融合问题感知初始化、自适应参数控制、7种专用邻域搜索算子和策略自适应选择机制，实现了全局探索与局部精化的有机结合。在4个标准测试案例(威胁数5~48、拦截器数13~92)上的实验验证了AHEA的性能优势。

关键词: 防空反导, 资源分配, 约束优化, 进化算法, 邻域搜索, 自适应

Abstract:

Air defense and antimissile firepower resource allocation is a core optimization problem in modern defense systems. Under complex conditions such as spatiotemporal constraints and firepower resource limitations, this problem involves the optimal configuration of limited interceptors and belongs to the class of NP-hard multi-constrained combinatorial optimization problems. This paper established a comprehensive mathematical model encompassing range constraints, time window constraints, feasibility matrices, and interception probability models. To address the high-dimensional nonlinearity of the problem, an adaptive hybrid evolutionary algorithm (AHEA) was proposed. The algorithm integrated problem-aware initialization, adaptive parameter control, seven specialized neighborhood search operators, and an adaptive strategy selection mechanism, achieving an organic combination of global exploration and local refinement. Experimental validation on four standard benchmark cases (number of threats ranging from 5 to 48 and number of interceptors ranging from 13 to 92) demonstrates the performance superiority of AHEA.

Key words: air defense and antimissile, resource allocation, constraint optimization, evolutionary algorithm, neighborhood search, adaptability

中图分类号:

TP391.9

刘威,陈德龙,刘泽等 . 基于自适应混合进化的防空反导火力资源分配优化[J]. 系统仿真学报, 2026, 38(4): 959-973.

Liu Wei,Chen Delong,Liu Ze,et al . Optimization of Air Defense and Antimissile Firepower Resource Allocation Based on Adaptive Hybrid Evolution[J]. Journal of System Simulation, 2026, 38(4): 959-973.

图/表 12

图1

表1

图2

图3

表2

表3

表4

表5

图4

图5

图6

图7

参考文献 24

[1]	Ahner D, Parson C. Weapon Tradeoff Analysis Using Dynamic Programming for a Dynamic Weapon Target Assignment Problem Within a Simulation[C]//2013 Winter Simulations Conference (WSC). Piscataway: IEEE, 2013: 2831-2841.
[2]	Soland R M. Optimal Defensive Missile Allocation: A Discrete Min-max Problem[J]. Operations Research, 1973, 21(2): 590-596.
[3]	Kim Yeonseung, Cho Jaeyoung, Han Sangwoo, et al. Weapon Target Assignment Model for Small Unit Ground Combat Using Mixed Integer Nonlinear Program and Lagrangian Relaxation[J]. Mathematical Problems in Engineering, 2022, 2022(1): 9228993.
[4]	Liles J M IV, Robbins M J, Lunday B J. Improving Defensive Air Battle Management by Solving a Stochastic Dynamic Assignment Problem via Approximate Dynamic Programming[J]. European Journal of Operational Research, 2023, 305(3): 1435-1449.
[5]	刘学, 王俊, 张伟, 等. 基于BPSO的联合火力打击武器目标分配优化[J]. 兵工自动化, 2025, 44(3): 1-3.
	Liu Xue, Wang Jun, Zhang Wei, et al. Joint Fire Strike Weapon Target Assignment Optimization Based on BPSO[J]. Ordnance Industry Automation, 2025, 44(3): 1-3.
[6]	孙昕, 邢立宁, 王锐, 等. 基于多目标进化算法的防空导弹武器目标分配[J]. 系统仿真学报, 2024, 36(6): 1298-1308.
	Sun Xin, Xing Lining, Wang Rui, et al. Air Defense Missile Weapon Target Assignment Based on Multi-objective Evolutionary Algorithm[J]. Journal of System Simulation, 2024, 36(6): 1298-1308.
[7]	Li Wenhua, Wang Rui, Heng Yong, et al. Knowledge-guided Evolutionary Optimization for Large-scale Air Defense Resource Allocation[J]. IEEE Transactions on Artificial Intelligence, 2024, 5(12): 6267-6279.
[8]	陈阳, 李姜, 王烨, 等. 基于改进灰狼算法求解武器目标分配问题[J]. 兵器装备工程学报, 2025, 46(6): 227-233.
	Chen Yang, Li Jiang, Wang Ye, et al. Solving Weapon Target Assignment Problem Based on Modified Gray Wolf Algorithm[J]. Journal of Ordnance Equipment Engineering, 2025, 46(6): 227-233.
[9]	周玉虎, 王桐, 陈立伟, 等. 基于人工蜂群算法的大规模武器目标分配研究[J]. 哈尔滨工程大学学报, 2024, 45(6): 1187-1195.
	Zhou Yuhu, Wang Tong, Chen Liwei, et al. Large-scale Weapon-target Allocation Based on an Artificial Bee Colony Algorithm[J]. Journal of Harbin Engineering University, 2024, 45(6): 1187-1195.
[10]	Yi Xiaojian, Yu Huiyang, Xu Tao. Solving Multi-objective Weapon-target Assignment Considering Reliability by Improved MOEA/D-AM2M[J]. Neurocomputing, 2024, 563: 126906.
[11]	Wang Yang, Wang Junpeng, Hao Jinkao, et al. Efficient Adaptive Large Neighborhood Search for Sensor-weapon-target Assignment[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2024, 54(10): 6397-6409.
[12]	杨玉, 张嘉佳, 马金慧, 等. 局部搜索灰狼优化算法求解武器-目标分配问题[J]. 科学技术与工程, 2023, 23(27): 11722-11729.
	Yang Yu, Zhang Jiajia, Ma Jinhui, et al. Local Search Strategy Based Grey Wolf Optimization for Weapon Target Assignment Problem[J]. Science Technology and Engineering, 2023, 23(27): 11722-11729.
[13]	闫世祥, 刘海军. 基于深度强化学习的传感器-武器-目标分配方法[J]. 现代防御技术, 2025, 53(4): 10-17.
	Yan Shixiang, Liu Haijun. Sensor-weapon-target Assignment Method Based on Deep Reinforcement Learning[J]. Modern Defence Technology, 2025, 53(4): 10-17.
[14]	马超, 赵敏睿, 王刚, 等. 基于元强化学习的防空作战任务分配方法研究[J]. 军事运筹与评估, 2025, 40(1): 53-59.
	Ma Chao, Zhao Minrui, Wang Gang, et al. Air Defence Combat Task Assignment Method Based on Meta-reinforcement Learning[J]. Military Operations Research and Assessments, 2025, 40(1): 53-59.
[15]	刘家义, 王刚, 夏智权, 等. 基于深度强化学习的防空反导智能任务分配[J]. 火力与指挥控制, 2024, 49(1): 43-48, 55.
	Liu Jiayi, Wang Gang, Xia Zhiquan, et al. Intelligent Task Assignment Research for Air Defense and Anti-missiles Based on Deep Reinforcement Learning[J]. Fire Control & Command Control, 2024, 49(1): 43-48, 55.
[16]	费帅迪, 蔡长龙, 刘飞, 等. 舰船防空反导的目标分配方法研究[J]. 系统仿真学报, 2025, 37(2): 508-516.
	Fei Shuaidi, Cai Changlong, Liu Fei, et al. Research on the Target Allocation Method for Air Defense and Anti-missile Defense of Naval Ships[J]. Journal of System Simulation, 2025, 37(2): 508-516.
[17]	肖友刚, 金升成, 毛晓, 等. 基于深度强化学习的舰船导弹目标分配方法[J]. 控制理论与应用, 2024, 41(6): 990-998.
	Xiao Yougang, Jin Shengcheng, Mao Xiao, et al. Missile-target Assignment Method of Naval Ship Based on Deep Reinforcement Learning[J]. Control Theory & Applications, 2024, 41(6): 990-998.
[18]	吕娜, 王茂桓, 钟元芾, 等. 二分图匹配模型下的武器目标分配问题[J]. 系统工程与电子技术, 2024, 46(2): 549-560.
	Na Lü, Wang Maohuan, Zhong Yuanfu, et al. Weapon Target Allocation Problem Based on Matching Model of Bipartite Graphs[J]. Systems Engineering and Electronics, 2024, 46(2): 549-560.
[19]	Sonuc Emrullah, Sen Baha, Bayir Safak. A Parallel Simulated Annealing Algorithm for Weapon-target Assignment Problem[J]. International Journal of Advanced Computer Science and Applications, 2017, 8(4): 87-92.
[20]	Kuhn H W. The Hungarian Method for the Assignment Problem[J]. Naval Research Logistics Quarterly, 1955, 2(1/2): 83-97.
[21]	Li Pengcheng, Chu Shibo, Qin Shuang, et al. Optimisation of Prestressed Stayed Steel Columns Based on Strengthen Elitist Genetic Algorithm[J]. Journal of Constructional Steel Research, 2025, 227: 109324.
[22]	Opara Karol R, Arabas Jarosław. Differential Evolution: A Survey of Theoretical Analyses[J]. Swarm and Evolutionary Computation, 2019, 44: 546-558.
[23]	Emmerich Michael, Shir Ofer M, Wang Hao. Evolution Strategies[M]//Rafael Martí, Pardalos P M, Resende M G C. Handbook of Heuristics. Cham: Springer Nature Switzerland, 2025: 89-123.
[24]	Vidal Thibaut. Hybrid Genetic Search for the CVRP: Open-source Implementation and SWAP* Neighborhood[J]. Computers & Operations Research, 2022, 140: 105643.

算子	操作类型	优化目标
1交换分配	两拦截器威胁互换	结构调整多样性
2威胁重分配	增加低覆盖威胁的拦截器	防御强度
3移除冗余	削减高覆盖威胁的拦截器	成本控制
4局部强化	单拦截器全可行集搜索	精细优化
5跨威胁优化	不同威胁间拦截器交换	资源均衡
6覆盖平衡	重新分配实现覆盖均衡	鲁棒性
7成本降低	用低成本拦截器替换	成本优化

威胁类型	飞行速度/Ma
巡航导弹	0.2~0.26
无人机	0.03~0.05
战斗机	0.28~0.4

类型	飞行速度/Ma	射程/km	单位成本/万元
远程	2.2	5~150	1500
中程	1.5	2~90	800
近程	1.1	0.5~40	300

拦截器类型	巡航导弹	无人机	战斗机
远程	0.85	0.65	0.72
中程	0.80	0.78	0.75
近程	0.70	0.90	0.88

测试案例	算法	适应度	AHEA的适应度提升百分比/%	防御成功率/%	资源消耗	平均响应时间/s
案例Ⅰ	Hungarian	0.459 1	14.62	81.07	3 500	45.90
	SEGA	0.523 4	0.53	90.69	4 876	24.36
	DE	0.523 9	0.44	90.69	4 876	23.91
	ES	0.510 5	3.08	92.17	6 180	24.34
	HGS	0.523 3	0.55	90.69	4 876	24.52
	AHEA	0.526 2		90.8	4 820	25.57
案例Ⅱ	Hungarian	0.474 6	5.06	82.85	10 200	38.73
	SEGA	0.485 8	2.63	86.55	14 000	28.56
	DE	0.496 2	0.48	87.12	12 656	30.87
	ES	0.434 4	14.78	86.03	20 800	31.87
	HGS	0.491 5	1.44	86.88	13 502	28.45
	AHEA	0.498 6		87.38	13 120	27.64
案例Ⅲ	Hungarian	0.450 8	5.21	81.80	18 400	42.21
	SEGA	0.461 2	2.84	87.75	27 110	35.71
	DE	0.469 6	1.00	87.68	25 512	33.74
	ES	0.385 4	23.07	80.19	32 090	37.00
	HGS	0.460 9	2.91	86.79	25 830	34.75
	AHEA	0.474 3		88.63	26 600	31.11
案例Ⅳ	Hungarian	0.429 7	1.23	80.79	33 400	48.45
	SEGA	0.425 0	2.35	84.13	46 460	42.21
	DE	0.432 8	0.51	83.92	42 630	43.06
	ES	0.311 4	39.69	68.26	46 930	43.60
	HGS	0.427 5	1.75	82.94	42 310	42.28
	AHEA	0.435 0		85.93	51 700	40.81