Optimization of Air Defense and Antimissile Firepower Resource Allocation Based on Adaptive Hybrid Evolution

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

Abstract

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

CLC Number:

TP391.9

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

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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