武器目标分配问题研究进展: 模型、算法与应用

doi:10.12305/j.issn.1001-506X.2023.04.14

Abstract

Abstract:

Weapon target assignment (WTA) is a significant and challenging research topic in the field of command and control and mission planning, and it is also one of the basic research topics in the field of military operations. In recent decades, the weapon target assignment problem has been widely studied in different military operational fields including land, sea, air, space, and electromagnetic, and a large number of models and algorithms have been developed. The typical combat styles, modeling methods, solving algorithms and experiments for WTA are systematically investigated, and a comprehensive review is presented. The new challenges on WTA is analyzed, which are brought by the emerging technologies and operations on intelligent and unmanned systems, and the discussion on future research directions can provide a helpful reference for researchers in this field.

Key words: weapon target assignment (WTA), model, algorithm, review

CLC Number:

E913
C934

Mengjie LI, Xuening CHANG, Jianmai SHI, Chao CHEN, Jincai HUANG, Zhong LIU. Developments of weapon target assignment: models, algorithms, and applications[J]. Systems Engineering and Electronics, 2023, 45(4): 1049-1071.

Figures/Tables 7

Fig.1

Table 1

Problem characteristics of typical combat patterns"

典型作战样式	问题特点
典型作战样式	问题规模	复杂性	时效性
地面防空	不同作战场景时, 问题规模涵盖大、中、小等不同范围。	早期研究一般简化为标准的WTA问题, 近期研究开始考虑与传感器的协同, 问题复杂性增加较大。	拦截目标为弹道导弹时, 时效性要求比较高; 为巡航导弹、飞机等目标时, 时间窗口相对较长, 求解时效性可适当放宽。
舰艇防空	单舰防空时通常为小规模; 舰艇编队防空通常为中、大规模。	单舰防空过程中武器之间以及武器与传感器的协同约束较为复杂, 编队防空时还要增加舰艇间的协同, 一般很难建立标准的数学规划模型。	舰艇防空在作战中, 来袭目标一般速度很快, 对问题求解的时效性要求非常高。
空中拦截	空中拦截以舰载机或战斗机拦截目标为主, 问题规模通常为中、小规模。	通常情况下空中拦截问题的求解复杂性一般。	空中拦截具有高速度移动、时间窗口较短, 时效性通常较高。
协同空战	协同空战通常以编队形式协同作战, 甚至是以大规模无人机等蜂群作战为代表, 问题规模通常较大。	问题求解复杂性通常较高, 需要处理中、大规模的WTA。	协同空战同样具有高速度移动、作战节奏快等特点, 时效性通常较高。
地对地打击	与作战规模相关, 以中、大规模为主, 少量小规模问题。	通常基于标准WTA数学规划模型进行扩展, 大规模问题求解复杂性较大。	通常有较长时间开展战前规划, 时效性要求不高。
空对地打击	与作战规模相关, 以中、小规模为主, 少量大规模问题。	通常基于标准WTA数学规划模型进行扩展, 大规模问题或考虑敌方防空因素时求解复杂性较大。	战前离线规划为主, 时效性要求不高; 动态在线规划时, 时效性要求高。
反舰	反舰通常涉及到几个波次打击的问题, 舰艇编队数量有限, 无论反单舰还是反舰艇编队, 问题规模通常不是太大。	反舰问题的静态规划复杂性不高, 但是考虑敌方拦截对抗时, 复杂性会急剧增大。	反舰作战节奏快, 对战机的把握要求高, 一般需要在极短时间内完成求解。
装甲对战	现代战争, 装甲对战以小规模为主, 特殊场景才会出现大规模集团式的装甲对抗。	小规模的装甲对战, 问题求解复杂性相对较低。	装甲机动性强, 近距离对抗时, 求解时效性要求较高。
联合火力打击	联合火力打击问题规模通常为中、大规模。	考虑武器之间协同或武器与传感器协同时, 问题复杂性通常较大。	战前静态规划, 时间比较宽松; 战中在线规划, 时效性要求较高。

Table 1

Table 2

Fig.2

Table 3

Table 4

Table 5

References 185

1	MANNE A S . A target-assignment problem[J]. Operations Research, 1958, 3 (6): 346- 357.
2	LLOYD S P, WITSENHAUSEN H S. Weapons allocation is NP-complete[C]//Proc. of the Summer Computer Simulation Conference, 1986: 1054-1058.
3	曹奇英, 何张兵. WTA问题的遗传算法研究[J]. 控制理论与应用, 2001, 18 (1): 76- 79. doi: 10.3969/j.issn.1000-8152.2001.01.016
	CAO Q Y , HE Z B . A genetic algorithm of solving WTA problem[J]. Control Theory and Applications, 2001, 18 (1): 76- 79. doi: 10.3969/j.issn.1000-8152.2001.01.016
4	MATLIN S . A review of the literature on the missile-allocation problem[J]. Operations Research, 1970, 18 (2): 334- 373. doi: 10.1287/opre.18.2.334
5	CAI H P , LIU J X , CHEN Y W , et al. Survey of the research on dynamic weapon-target assignment problem[J]. Journal of Systems Engineering and Electronics, 2006, 17 (3): 559- 565. doi: 10.1016/S1004-4132(06)60097-2
6	KLINE A , AHNER D , HILL R . The weapon-target assignment problem[J]. Computers & Operations Research, 2019, 105, 226- 236.
7	SOLAND R M . Optimal defensive missile allocation: a discrete min-max problem[J]. Operations Research, 1973, 21 (2): 590- 596. doi: 10.1287/opre.21.2.590
8	WACHOLDER E . A neural network-based optimization algorithm for the static weapon-target assignment problem[J]. ORSA Journal on Computing, 1989, 1 (4): 232- 246. doi: 10.1287/ijoc.1.4.232
9	BERTSEKAS D P , HOMER M L , LOGAN D A , et al. Missile defense and interceptor allocation by neuro-dynamic programming[J]. IEEE Trans. on Systems, Man, and Cybernetics-Part A: Systems and Humans, 2000, 30 (1): 42- 51. doi: 10.1109/3468.823480
10	刘付显, 王颖龙, 邢清华. 地面防空目标优化分配问题研究[J]. 火力与指挥控制, 2003, (4): 45- 48. doi: 10.3969/j.issn.1002-0640.2003.04.013
	LIU F X , WANG Y L , XING Q H . Study on problems of optimized target assignment in ground to air defense[J]. Fire Control & Command Control, 2003, (4): 45- 48. doi: 10.3969/j.issn.1002-0640.2003.04.013
11	MENQ J Y , TUAN P C , LIU T S . Discrete Markov ballistic missile defense system modeling[J]. European Journal of Operational Research, 2007, 178 (2): 560- 578. doi: 10.1016/j.ejor.2005.12.043
12	WANG J , GAO X G , ZHU Y W . Solving algorithm for TA optimization model based on ACO-SA[J]. Journal of Systems Engineering and Electronics, 2011, 22 (4): 628- 639. doi: 10.3969/j.issn.1004-4132.2011.04.012
13	WANG C H , CHEN C Y , HUNG K N . Toward a new task assignment and path evolution (TAPE) for missile defense system (MDS) using intelligent adaptive som with recurrent neural networks (RNNs)[J]. IEEE Trans. on Cybernetics, 2015, 45 (6): 1134- 1145. doi: 10.1109/TCYB.2014.2345791
14	SEVERSON T A , PALEY D A . Distributed multitarget search and track assignment with consensus-based coordination[J]. IEEE Sensors Journal, 2015, 15 (2): 864- 875. doi: 10.1109/JSEN.2014.2355200
15	LI L Y , LIU F X , LONG G Z , et al. Modified particle swarm optimization for BMDS interceptor resource planning[J]. Applied Intelligence, 2016, 44 (3): 471- 488. doi: 10.1007/s10489-015-0711-9
16	DAVIS M T , ROBBINS M J , LUNDAY B J . Approximate dynamic programming for missile defense interceptor fire control[J]. European Journal of Operational Research, 2017, 259 (3): 873- 886. doi: 10.1016/j.ejor.2016.11.023
17	XU H , XING Q H , TIAN Z H . MOQPSO-D/S for air and missile defense WTA problem under uncertainty[J]. Mathematical Problems in Engineering, 2017, doi: 10.1155/2017/9897153
18	LI X Y , ZHOU D Y , PAN Q , et al. Weapon-target assignment problem by multiobjective evolutionary algorithm based on decomposition[J]. Complexity, 2018, doi: 10.1155/2018/8623051
19	欧阳志宏, 薛磊, 丁锋. 对光电精确制导武器的区域电子防空干扰目标分配方法[J]. 系统工程与电子技术, 2018, 40 (12): 2621- 2628. doi: 10.3969/j.issn.1001-506X.2018.12.01
	OUYANG Z H , XUE L , DING F . Jamming target assignment method of regional electronic air defense against electro-optical precision guided weapon[J]. Systems Engineering and Electronics, 2018, 40 (12): 2621- 2628. doi: 10.3969/j.issn.1001-506X.2018.12.01
20	JANG J , YOON H G , KIM J C , et al. Adaptive weapon-to-target assignment model based on the real-time prediction of hit probability[J]. IEEE Access, 2019, 7, 72210- 72220. doi: 10.1109/ACCESS.2019.2919794
21	GUO D , LIANG Z X , JIANG P , et al. Weapon-target assignment for multi-to-multi interception with grouping constraint[J]. IEEE Access, 2019, 7, 34838- 34849. doi: 10.1109/ACCESS.2019.2898874
22	XU W Q , CHEN C , DING S X , et al. A bi-objective dynamic collaborative task assignment under uncertainty using modified MOEA/D with heuristic initialization[J]. Expert Systems with Applications, 2020, 140, 112844. doi: 10.1016/j.eswa.2019.112844
23	ZHANG K , ZHOU D Y , YANG Z , et al. A novel heterogeneous sensor-weapon-target cooperative assignment for ground-to-air defense by efficient evolutionary approaches[J]. IEEE Access, 2020, 8, 227373- 227398. doi: 10.1109/ACCESS.2020.3043667
24	LEE Y L , LO C . Optimizing an air defense evaluation model using inductive learning[J]. Applied Artificial Intelligence, 1994, 4 (8): 645- 661.
25	VAN DONGEN M P F M , KOS J . The analysis of ship air defense: the simulation model SEAROADS[J]. Naval Research Logistics, 1995, 42 (2): 291- 309. doi: 10.1002/1520-6750(199503)42:2<291::AID-NAV3220420210>3.0.CO;2-K
26	张勇, 张远新. 多通道舰空导弹武器系统目标分配模型[J]. 火力与指挥控制, 2005, (4): 111- 114. doi: 10.3969/j.issn.1002-0640.2005.04.033
	ZHANG Y , ZHANG Y X . Target assignment model for multi-way ship-to-air missile weapon system[J]. Fire Control & Command Control, 2005, (4): 111- 114. doi: 10.3969/j.issn.1002-0640.2005.04.033
27	罗江锋, 朱承, 崔婧, 等. 舰艇防空火力规划与调度方法研究[J]. 国防科技大学学报, 2013, 35 (2): 40- 45. doi: 10.3969/j.issn.1001-2486.2013.02.008
	LUO J F , ZHU C , CUI J , et al. Planning and scheduling for the air defense of warship[J]. Journal of National University of Defense Technology, 2013, 35 (2): 40- 45. doi: 10.3969/j.issn.1001-2486.2013.02.008
28	LI J J , CONG R , XIONG J G . Dynamic WTA optimization model of air defense operation of warships' formation[J]. Journal of Systems Engineering and Electronics, 2006, 17 (1): 126- 131. doi: 10.1016/S1004-4132(06)60023-6
29	KARASAKAL O . Air defense missile-target allocation models for a naval task group[J]. Computers & Operations Research, 2008, 35 (6): 1759- 1770. doi: 10.3969/j.issn.1001-3695.2008.06.046
30	王玮, 康晓予, 张玉芝. 舰艇编队目标武器分配问题的研究方法[J]. 现代防御技术, 2008, 36 (2): 14- 19. doi: 10.3969/j.issn.1009-086X.2008.02.004
	WANG W , KANG X Y , ZHANG Y Z . Research approaches on weapon target assignment (WTA) in surface warship formation[J]. Modern Defense Technology, 2008, 36 (2): 14- 19. doi: 10.3969/j.issn.1009-086X.2008.02.004
31	韩双, 刘以安, 杨新刚, 等. 舰艇编队作战系统的武器目标分配问题[J]. 火力与指挥控制, 2009, (2): 32- 35. doi: 10.3969/j.issn.1002-0640.2009.02.009
	HAN S , LIU Y A , YANG X G , et al. WTA problem in the warship fleet[J]. Fire Control & Command Control, 2009, (2): 32- 35. doi: 10.3969/j.issn.1002-0640.2009.02.009
32	王玮, 董天忠, 张玉芝. CEC条件下舰艇编队目标武器分配研究[J]. 火力与指挥控制, 2009, (10): 51- 55. doi: 10.3969/j.issn.1002-0640.2009.10.013
	WANG W , DONG T Z , ZHANG Y Z . Research on weapon target assignment for surface warship formation with cooperative engagement capability[J]. Fire Control & Command Control, 2009, (10): 51- 55. doi: 10.3969/j.issn.1002-0640.2009.10.013
33	李相民, 张元瀚, 代进进. 异步并行蚂蚁策略在网络化舰艇编队武器目标分配中的应用[J]. 电光与控制, 2010, 17 (9): 14- 19.
	LI X M , ZHANG Y H , DAI J J . Worship fleet's weapon target assignment based on distributed network of parallel ant strategy[J]. Electronics Optics & Control, 2010, 17 (9): 14- 19.
34	陈华东, 王航宇, 王树宗, 等. 网络中心战中基于MAS的分布式辅助决策研究[J]. 火力与指挥控制, 2010, (10): 11- 14. doi: 10.3969/j.issn.1002-0640.2010.10.004
	CHEN H D , WANG H Y , WANG S Z , et al. Research on decision support based on multi-agent systems in network centric warfare[J]. Fire Control & Command Control, 2010, (10): 11- 14. doi: 10.3969/j.issn.1002-0640.2010.10.004
35	李亦伟, 邢昌风, 隋江波. 编队防空火力兼容约束优化问题的COEA方法[J]. 火力与指挥控制, 2010, (11): 69- 71. doi: 10.3969/j.issn.1002-0640.2010.11.020
	LI Y W , XING C F , SUI J B . A COEA for firepower compatibility constrained optimization problem in fleet cooperative air defense[J]. Fire Control & Command Control, 2010, (11): 69- 71. doi: 10.3969/j.issn.1002-0640.2010.11.020
36	陈华东, 刘忠, 李云凡, 等. 黄页服务的合同网在编队武器目标分配中的应用[J]. 火力与指挥控制, 2013, (7): 103- 106. doi: 10.3969/j.issn.1002-0640.2013.07.028
	CHEN H D , LIU Z , LI Y F , et al. Application of contract net protocol based on yellow pages service on weapon target assignment of the fleet[J]. Fire Control & Command Control, 2013, (7): 103- 106. doi: 10.3969/j.issn.1002-0640.2013.07.028
37	KARASAKAL O , ÖZDEMIREL N E , KANDILLER L . Anti-ship missile defense for a naval task group[J]. Naval Research Logistics, 2011, 58 (3): 304- 321. doi: 10.1002/nav.20457
38	KARASAKAL O , KANDILLER L , ÖZDEMIREL N E . A branch and bound algorithm for sector allocation of a naval task group[J]. Naval Research Logistics, 2011, 58 (7): 655- 669.
39	CHEN X L , SHEN S . Weapon-Target assignment problem in the warship fleet based on fast and elitist non-dominated sorting genetic algorithm[J]. Advanced Materials Research, 2012, 605, 2399- 2404.
40	SILAV A , KARASAKAL O , KARASAKAL E . Bi-objective missile rescheduling for a naval task group with dynamic disruptions[J]. Naval Research Logistics, 2019, 66 (7): 596- 615. doi: 10.1002/nav.21867
41	肖冰松, 方洋旺, 许蕴山, 等. 编队内协同超视距空战目标分配模型研究[J]. 系统工程与电子技术, 2010, 32 (7): 1476- 1479. doi: 10.3969/j.issn.1001-506X.2010.07.029
	XIAO B S , FANG Y W , XU Y S , et al. Research on coordinated formation target assignment model for beyond visual range air combat[J]. Systems Engineering and Electronics, 2010, 32 (7): 1476- 1479. doi: 10.3969/j.issn.1001-506X.2010.07.029
42	BAYRAK A E , POLAT F . Employment of an evolutionary heuristic to solve the target allocation problem efficiently[J]. Information Sciences, 2013, 222, 675- 695. doi: 10.1016/j.ins.2012.07.050
43	SHALUMOV V , SHIMA T . Weapon-target-allocation strategies in multiagent target-missile-defender engagement[J]. Journal of Guidance, Control, and Dynamics, 2017, 40 (10): 2452- 2464. doi: 10.2514/1.G002598
44	PENG G , FANG Y Y , CHEN S H , et al. A hybrid multiobjective discrete particle swarm optimization algorithm for cooperative air combat DWTA[J]. Journal of Optimization, 2017, doi: 10.1007/978-981-10-3614-9_15
45	CHANG Y Z , LI Z W , KOU Y X , et al. A new approach to weapon-target assignment in cooperative air combat[J]. Mathematical Problems in Engineering, 2017, doi: 10.1155/2017/2936279
46	LI Z W , CHANG Y Z , KONG Y X , et al. Approach to WTA in air combat using IAFSA-IHS algorithm[J]. Journal of Systems Engineering and Electronics, 2018, 29 (3): 519- 529. doi: 10.21629/JSEE.2018.03.09
47	HU X W , LUO P C , ZHANG X N , et al. Improved ant colony optimization for weapon-target assignment[J]. Mathematical Problems in Engineering, 2018, doi: 10.1155/2018/6481635
48	PAN Q , ZHOU D Y , TANG Y C , et al. A novel antagonistic weapon-target assignment model considering uncertainty and its solution using decomposition co-evolution algorithm[J]. IEEE Access, 2019, 7, 37498- 37517. doi: 10.1109/ACCESS.2019.2905274
49	张涛, 于雷, 魏贤智, 等. 改进遗传算法的超视距协同多目标攻击决策[J]. 火力与指挥控制, 2013, (5): 137- 140. doi: 10.3969/j.issn.1002-0640.2013.05.037
	ZHANG T , YU L , WEI X Z , et al. Decision-making for cooperative multiple target attack based on adaptive pseudo-parallel genetic algorithm[J]. Fire Control & Command Control, 2013, (5): 137- 140. doi: 10.3969/j.issn.1002-0640.2013.05.037
50	王网琴, 姚敏, 赵敏. 多无人机协同攻击目标决策[J]. 指挥控制与仿真, 2014, 36 (2): 9- 13. doi: 10.3969/j.issn.1673-3819.2014.02.003
	WANG W Q , YAO M , ZHAO M . Research on cooperative attack decision of unmanned aerial vehicles for air combat[J]. Command Control & Simulation, 2014, 36 (2): 9- 13. doi: 10.3969/j.issn.1673-3819.2014.02.003
51	马滢滢, 王国强, 胡笑旋, 等. 超视距空战中的多无人机武器目标分配方法[J]. 中国管理科学, 2022, 30 (3): 248- 257.
	MA Y Y , WANG G Q , HU X X , et al. Weapon target assignment method for multiple UAVs in beyond-visual-range air combat[J]. Chinese Journal of Management Science, 2022, 30 (3): 248- 257.
52	顾佼佼, 赵建军, 颜骥, 等. 基于MODPSO-GSA的协同空战武器目标分配[J]. 北京航空航天大学学报, 2015, 41 (2): 252- 258. doi: 10.13700/j.bh.1001-5965.2014.0119
	GU J J , ZHAO J J , YAN J , et al. Cooperative weapon-target assignment based on multi-objective discrete particle swarm optimization-gravitational search algorithm in air combat[J]. Journal of Beijing University of Aeronautics and Astronautics, 2015, 41 (2): 252- 258. doi: 10.13700/j.bh.1001-5965.2014.0119
53	侯满义, 杨永波, 荆献勇, 等. 多无人机协同作战武器目标分配建模[J]. 战术导弹技术, 2017, (5): 68- 73. doi: 10.16358/j.issn.1009-1300.2017.05.13
	HOU M Y , YANG Y B , JING X Y , et al. Weapon target assignment modeling of multi-UAV[J]. Tactical Missile Technology, 2017, (5): 68- 73. doi: 10.16358/j.issn.1009-1300.2017.05.13
54	SAPAZ B , TOROSLUİ H , ÜÇOLUK G . A genetic algorithm approach to the artillery target assignment problem[M]. Dordrecht: Springer, 2011: 39- 42.
55	CHA Y H , KIM Y D . Fire scheduling for planned artillery attack operations under time-dependent destruction probabilities[J]. Omega, 2010, 38 (5): 383- 392. doi: 10.1016/j.omega.2009.10.003
56	CHOI Y B , JIN S H , KIM K S , et al. A robust optimization approach for an artillery fire-scheduling problem under uncertain threat[J]. Computers & Industrial Engineering, 2018, 125, 23- 32.
57	张信启, 黄锐, 范阳涛. 常规导弹火力运用的优化[J]. 四川兵工学报, 2009, 30 (8): 57- 59.
	ZHANG X Q , HUANG R , FAN Y T . Optimizing the use of conventional missile firepower[J]. Journal of Sichuan Armoury, 2009, 30 (8): 57- 59.
58	王然辉, 王超. 面向对地打击武器-目标分配问题的遗传算法变量取值控制技术[J]. 兵工学报, 2016, 37 (10): 1889- 1895. doi: 10.3969/j.issn.1000-1093.2016.10.016
	WANG R H , WANG C . Variable value control technology of genetic algorithm for WTA of ground target attacking[J]. Acta Armamentarii, 2016, 37 (10): 1889- 1895. doi: 10.3969/j.issn.1000-1093.2016.10.016
59	WANG C , FU G Y , ZHANG D Q , et al. Genetic algorithm-based variable value control method for solving the ground target attacking weapon-target allocation problem[J]. Mathematical Problems in Engineering, 2019, doi: 10.1155/2019/6761073
60	FU G Y , WANG C , ZHANG D Q , et al. Research on variable probability assignment technique of genetic algorithm for WTA of ground target attacking[J]. Journal of Physics: Conference Series, 2019, 1324 (1): 012010. doi: 10.1088/1742-6596/1324/1/012010
61	彭星光, 高晓光, 魏小丰. 基于贝叶斯优化算法的UCAV编队对联合目标的协同攻击研究[J]. 系统仿真学报, 2008, 20 (10): 2693- 2696. doi: 10.16182/j.cnki.joss.2008.10.008
	PENG X G , GAO X G , WEI X F . Research on UCAV team coordination attack to associated targets using bayesian optimization algorithm[J]. Journal of System Simulation, 2008, 20 (10): 2693- 2696. doi: 10.16182/j.cnki.joss.2008.10.008
62	彭星光, 高晓光. 基于记忆辅助动态UMDA的UCAV编队动态目标分配[J]. 系统工程与电子技术, 2010, 32 (10): 2166- 2170. doi: 10.3969/j.issn.1001-506X.2010.10.32
	PENG X G , GAO X G . Dynamic target assignment method for UCAV fleet using memory enhanced dynamic UMDA[J]. Systems Engineering and Electronics, 2010, 32 (10): 2166- 2170. doi: 10.3969/j.issn.1001-506X.2010.10.32
63	SHIMA T , SCHUMACHER C . Assigning cooperating UAVs to simultaneous tasks on consecutive targets using genetic algorithms[J]. The Journal of the Operational Research Society, 2009, 60 (7): 973- 982. doi: 10.1057/palgrave.jors.2602617
64	吴文超, 黄长强, 白壬潮, 等. 考虑软杀伤武器应用的多UCAV任务分配[J]. 电光与控制, 2011, 18 (2): 49- 53. doi: 10.3969/j.issn.1671-637X.2011.02.011
	WU W C , HUANG C Q , BAI R C , et al. Task assignment of multi-UCAV considering application of soft kill weapons[J]. Electronics Optics & Control, 2011, 18 (2): 49- 53. doi: 10.3969/j.issn.1671-637X.2011.02.011
65	刘毅, 李为民, 邢清华, 等. 基于双层规划的攻击无人机协同目标分配优化[J]. 系统工程与电子技术, 2010, 32 (3): 579- 583.
	LIU Y , LI W M , XING Q H , et al. Cooperative mission assignment optimization of unmanned combat aerial vehicles based on bilevel programming[J]. Systems Engineering and Electronics, 2010, 32 (3): 579- 583.
66	DENG Q B , YU J Q , WANG N F . Cooperative task assignment of multiple heterogeneous unmanned aerial vehicles using a modified genetic algorithm with multi-type genes[J]. Chinese Journal of Aeronautics, 2013, 26 (5): 1238- 1250. doi: 10.1016/j.cja.2013.07.009
67	DIRIK N , HALL S N , MOORE J T . Maximizing strike aircraft planning efficiency for a given class of ground targets[J]. Optimization Letters, 2015, 9 (8): 1729- 1748. doi: 10.1007/s11590-014-0844-5
68	ZHA W Z , CHEN J , PENG Z H . Dynamic multi-team antagonistic games model with incomplete information and its application to multi-UAV[J]. IEEE/CAA Journal of Automatica Sinica, 2015, 2 (1): 74- 84. doi: 10.1109/JAS.2015.7032908
69	WANG J, LUO P C, ZHOU J L, et al. Optimizing weapon target assignment in air to ground strike based on adaptive immune genetic algorithm[C]//Proc. of the 4th International Conference on Information Science and Control Engineering, 2017: 520-526.
70	LI Y , KOU Y X , LI Z W , et al. A modified Pareto ant colony optimization approach to solve biobjective weapon-target assignment problem[J]. International Journal of Aerospace Engineering, 2017, doi: 10.1155/2017/1746124
71	LI Y , KOU Y X , LI Z W . An improved nondominated sorting genetic algorithm Ⅲ method for solving multiobjective weapon-target assignment part I: the value of fighter combat[J]. International Journal of Aerospace Engineering, 2018, doi: 10.1155/2018/8302324
72	GAO C Q , KOU Y X , LI Y , et al. Multi-objective weapon target assignment based on D-NSGA-Ⅲ-A[J]. IEEE Access, 2019, 7, 50240- 50254. doi: 10.1109/ACCESS.2019.2910241
73	杨飞, 王青, 董朝阳. 实施饱和攻击的导弹多目标火力分配决策[J]. 北京航空航天大学学报, 2010, 36 (8): 996- 999. doi: 10.13700/j.bh.1001-5965.2010.08.020
	YANG F , WANG Q , DONG C Y . Decision-making of saturation attack for missile weapon-target assignment with multi-target[J]. Journal of Beijing University of Aeronautics and Astronautics, 2010, 36 (8): 996- 999. doi: 10.13700/j.bh.1001-5965.2010.08.020
74	王正元, 谭跃进. 坦克会战中动态武器—目标分配问题求解方法[J]. 国防科技大学学报, 2003, 25 (6): 56- 61. doi: 10.3969/j.issn.1001-2486.2003.06.013
	WANG Z Y , TAN Y J . A solution to dynamic weapon-target assignment in the tank warfare[J]. Journal of National University of Defense Technology, 2003, 25 (6): 56- 61. doi: 10.3969/j.issn.1001-2486.2003.06.013
75	白帆, 常天庆, 王钦钊. 基于模糊火力适度原则的坦克分队WTA模型研究[J]. 系统仿真学报, 2012, 24 (6): 1161- 1164.
	BAI F , CHANG T Q , WANG Q Z . Research on fuzzy moderate firing principle-based WTA model for tank unit[J]. Journal of System Simulation, 2012, 24 (6): 1161- 1164.
76	常天庆, 陈军伟, 郝娜, 等. 装甲分队动态武器目标分配中蚁群算法终止控制[J]. 系统工程与电子技术, 2015, 37 (2): 343- 347.
	CHANG T Q , CHEN J W , HAO N , et al. Terminating control of ant colony algorithm for armored unit dynamic weapon-target assignment[J]. Systems Engineering and Electronics, 2015, 37 (2): 343- 347.
77	陈军伟, 常天庆, 张雷, 等. 面向装甲分队战法运用的两阶段WTA模型[J]. 系统工程与电子技术, 2016, 38 (6): 1326- 1331.
	CHEN J W , CHANG T Q , ZHANG L , et al. Two-stage model of WTA oriented armored unit combat method[J]. Systems Engineering and Electronics, 2016, 38 (6): 1326- 1331.
78	孔德鹏, 徐克虎, 陈金玉. 合成分队双层主从决策模型研究[J]. 火力与指挥控制, 2016, (4): 61- 65. doi: 10.3969/j.issn.1002-0640.2016.04.015
	KONG D P , XU K H , CHEN J Y . Research on weapon target assignment method of synthetic unit[J]. Fire Control & Command Control, 2016, (4): 61- 65. doi: 10.3969/j.issn.1002-0640.2016.04.015
79	徐克虎, 孔德鹏, 陈金玉. 合成分队动态武器目标分配协同决策模型[J]. 火力与指挥控制, 2016, (6): 62- 66. doi: 10.3969/j.issn.1002-0640.2016.06.014
	XU K H , KONG D P , CHEN J Y . Synthesis unit dynamic weapon target assignment model of collaborative decision making[J]. Fire Control & Command Control, 2016, (6): 62- 66. doi: 10.3969/j.issn.1002-0640.2016.06.014
80	刘双双, 许瑞明, 潘俊杰. 基于小生境蝙蝠算法的联合远程打击武器目标分配问题建模与求解[J]. 装备学院学报, 2017, 28 (2): 93- 98. doi: 10.3783/j.issn.2095-3828.2017.02.018
	LIU S S , XU R M , PAN J J . Research on the modeling and solving of the joint long-range strike weapon target assignment problem based on the niche bat algorithm[J]. Journal of Equipment Academy, 2017, 28 (2): 93- 98. doi: 10.3783/j.issn.2095-3828.2017.02.018
81	陈曼, 周凤星, 张成尧. 改进MOPSO的联合火力打击目标分配[J]. 火力与指挥控制, 2019, 44 (9): 125- 129. doi: 10.3969/j.issn.1002-0640.2019.09.024
	CHEN M , ZHOU F X , ZHANG C Y . Improved MOPSO joint fire strike target assignment[J]. Fire Control & Command Control, 2019, 44 (9): 125- 129. doi: 10.3969/j.issn.1002-0640.2019.09.024
82	孔德鹏, 常天庆, 郝娜, 等. 基于对抗的突击武器与支援武器协同火力打击决策方法[J]. 兵工学报, 2019, 40 (3): 629- 640. doi: 10.3969/j.issn.1000-1093.2019.03.023
	KONG D P , CHANG T Q , HAO N , et al. Confrontation-based cooperative fire strike decision-making method of assault weapons and support weapons[J]. Acta Armamentarii, 2019, 40 (3): 629- 640. doi: 10.3969/j.issn.1000-1093.2019.03.023
83	田伟, 王志梅, 段威. 基于随机时间影响网络的联合火力打击动态武器目标分配问题研究[J]. 指挥控制与仿真, 2020, 42 (6): 32- 40. doi: 10.3969/j.issn.1673-3819.2020.06.006
	TIAN W , WANG Z M , DAUN W . Research on dynamic weapon target assignment problem in joint fire strike based on stochastic time influence network[J]. Command Control & Simulation, 2020, 42 (6): 32- 40. doi: 10.3969/j.issn.1673-3819.2020.06.006
84	LEE Z J , SU S F , LEE C Y . Efficiently solving general weapon-target assignment problem by genetic algorithms with greedy eugenics[J]. IEEE Trans. on Systems, Man, and Cybernetics, Part B, 2003, 33 (1): 113- 121. doi: 10.1109/TSMCB.2003.808174
85	STIEBER A , FVGENSCHUH A , EPP M , et al. The multiple traveling salesmen problem with moving targets[J]. Optimization Letters, 2015, 9 (8): 1569- 1583. doi: 10.1007/s11590-014-0835-6
86	HU X W, LUO P C, ZHANG X N. IACO algorithm for weapon-target assignment problem in air combat[C]//Proc. of the 2nd International Conference on Intelligent Systems, Metaheuristics & Swarm Intelligence, 2018: 35-40.
87	陆一平, 李慧慧. 静态武器目标分配问题的攻击界整数规划求解方法[J]. 系统工程理论与实践, 2019, 39 (3): 783- 789.
	LU Y P , LI H H . An attack-number bounded integer programming method for the static WTA problem[J]. Systems Engineering-Theory & Practice, 2019, 39 (3): 783- 789.
88	XIN B , WANG Y P , CHEN J . An efficient marginal-return-based constructive heuristic to solve the sensor-weapon-target assignment problem[J]. IEEE Trans. on Systems, Man, and Cybernetics: Systems, 2019, 49 (12): 2536- 2547. doi: 10.1109/TSMC.2017.2784187
89	LI X Y , ZHOU D Y , YANG Z , et al. A novel genetic algorithm for the synthetical sensor-weapon-target assignment problem[J]. Applied Sciences, 2019, 9 (18): 3803. doi: 10.3390/app9183803
90	LU Y P , CHEN D Z . A new exact algorithm for the weapon-target assignment problem[J]. Omega, 2021, 98, 102138. doi: 10.1016/j.omega.2019.102138
91	张毅, 姜青山, 陈国生. 基于模糊-灰色非合作Nash博弈的多组动态武器-目标分配方法[J]. 云南大学学报: 自然科学版, 2012, 34 (1): 26- 32.
	ZHANG Y , JIANG Q S , CHEN G S . An approach of basing-on fuzzy-grey noncooperative Nash games to multi-team dynamic weapon-target assignment[J]. Journal of Yunnan University: Natural Science, 2012, 34 (1): 26- 32.
92	LEBOUCHER C , SHIN H S , LE MÉNEC S , et al. Novel evolutionary game based multi-objective optimisation for dynamic weapon target assignment[J]. IFAC Proceedings Volumes, 2014, 47 (3): 3936- 3941. doi: 10.3182/20140824-6-ZA-1003.02150
93	GOLANY B , GOLDBERG N , ROTHBLUM U G . Allocating multiple defensive resources in a zero-sum game setting[J]. Annals of Operations Research, 2015, 225 (1): 91- 109. doi: 10.1007/s10479-012-1196-0
94	GOLANY B , GOLDBERG N , ROTHBLUM U G . A two-resource allocation algorithm with an application to large-scale zero-sum defensive games[J]. Computers & Operations Research, 2017, 78, 218- 229.
95	王邑, 孙金标, 华玉光, 等. 基于Epsilon-Nash策略的动态武器-目标分配方法[J]. 火力与指挥控制, 2016, 41 (11): 12- 15. doi: 10.3969/j.issn.1002-0640.2016.11.003
	WANG Y , SUN J B , HUA Y G , et al. Research of dynamic weapon-target assignment problem based on epsilon-Nash equlibirum[J]. Fire Control & Command Control, 2016, 41 (11): 12- 15. doi: 10.3969/j.issn.1002-0640.2016.11.003
96	HAN C Y , LUNDAY B J , ROBBINS M J . A game theoretic model for the optimal location of integrated air defense system missile batteries[J]. INFORMS Journal on Computing, 2016, 28 (3): 405- 416. doi: 10.1287/ijoc.2016.0690
97	张先剑. 空陆攻防博弈的动态武器目标分配[J]. 国防科技大学学报, 2019, 41 (2): 185- 190.
	ZHANG X J . Land defense weapon versus target assignment against air attack[J]. Journal of National University of Defense Technology, 2019, 41 (2): 185- 190.
98	黄力伟, 许品刚, 王勤. 基于匈牙利算法求解的火力分配问题[J]. 火力与指挥控制, 2007, (6): 25- 28. doi: 10.3969/j.issn.1002-0640.2007.06.007
	HUANG L W , XU P G , WANG Q . Firepower distribution problems based on Hungarian method[J]. Fire Control & Command Control, 2007, (6): 25- 28. doi: 10.3969/j.issn.1002-0640.2007.06.007
99	LEBOUCHER C , SHIN H S , LE MENEC S , et al. Optimal weapon target assignment based on an geometric approach[J]. IFAC Proceedings Volumes, 2013, 46 (19): 341- 346. doi: 10.3182/20130902-5-DE-2040.00037
100	HAMZEHI S, BOGENBERGER K, FRANECK P, et al. Combinatorial reinforcement learning of linear assignment problems[C]//Proc. of the IEEE Intelligent Transportation Systems Conference, 2019: 3314-3321.
101	AHNER D K , PARSON C R . Optimal multi-stage allocation of weapons to targets using adaptive dynamic programming[J]. Optimization Letters, 2015, 9 (8): 1689- 1701. doi: 10.1007/s11590-014-0823-x
102	XIN B , CHEN J , PENG Z H , et al. An efficient rule-based constructive heuristic to solve dynamic weapon-target assignment problem[J]. IEEE Trans. on Systems, Man, and Cybernetics-Part A: Systems and Humans, 2011, 41 (3): 598- 606. doi: 10.1109/TSMCA.2010.2089511
103	SUMMERS D S , ROBBINS M J , LUNDAY B J . An approximate dynamic programming approach for comparing firing policies in a networked air defense environment[J]. Computers & Operations Research, 2020, 117, 104890.
104	CASTANON D. Advanced weapon-target assignment algorithm quarterly report[R]. Burlington: Alphatech, 1987.
105	AHUJA R K , KUMAR A , JHA K C , et al. Exact and heuristic algorithms for the weapon-target assignment problem[J]. Operations Research, 2007, 55 (6): 1136- 1146. doi: 10.1287/opre.1070.0440
106	CHANG S, JAMES R M, SHAW J J. Assignment algorithm for kinetic energy weapons in boost phase defence[C]//Proc. of the 26th IEEE Conference on Decision and Control, 1987: 1678-1683.
107	BURR S A , FALK J E , KARR A F . Integer prim-read solutions to a class of target defense problems[J]. Operations Research, 1985, 33 (4): 726- 745. doi: 10.1287/opre.33.4.726
108	YANG J S, LI J, WANG Y, et al. Optimization of weapon-target assignment problem by intuitionistic fuzzy genetic algorithm[C]//Proc. of the International Conference on Electronic Information Technology and Computer Engineering, 2017, 128: 02004.
109	ŞAHİN M A , LEBLEBİCİOǦLU K . Approximating the optimal mapping for weapon target assignment by fuzzy reasoning[J]. Information Sciences, 2014, 255, 30- 44. doi: 10.1016/j.ins.2013.08.004
110	CHOI Y B , JIN S H , KIM K S . Deterministic and robust optimization approach for single artillery unit fire scheduling problem[J]. Applied Sciences, 2017, 7 (10): 1038. doi: 10.3390/app7101038
111	DENBROEDER J G G , ELLISON R E , EMERLING L . On optimum target assignments[J]. Operations Research, 1959, 7 (3): 322- 326. doi: 10.1287/opre.7.3.322
112	ROSENBERGER J M, HWANG H S, PALLERLA R P, et al. The generalized weapon target assignment problem[R]. Arlington: Texas University, 2005.
113	KWON O , LEE K , KANG D H , et al. A branch-and-price algorithm for a targeting problem[J]. Naval Research Logistics, 2007, 54 (7): 732- 741. doi: 10.1002/nav.20247
114	KLINE A G , AHNER D K , LUNDAY B J , et al. Real-time heuristic algorithms for the static weapon target assignment problem[J]. Journal of Heuristics, 2019, 25 (3): 377- 397. doi: 10.1007/s10732-018-9401-1
115	BOGDANOWICZ Z R . A new efficient algorithm for optimal assignment of smart weapons to targets[J]. Computers & Mathematics with Applications, 2009, 58 (10): 1965- 1969.
116	LI Z F, LI X M, DAI J J, et al. Sensor-weapon-target assignment based on improved SWT-opt algorithm[C]//Proc. of the IEEE 2nd International Conference on Computing, Control and Industrial Engineering, 2011: 25-28.
117	SIKANEN T. Solving weapon target assignment problem with dynamic programming[EB/OL]. [2021-08-10]. http://salserver.org.aalto.fi/vanhat_sivut/Opinnot/Mat-2.4108/pdf-files/esik08b.pdf.
118	SOLAND R M . Optimal terminal defense tactics when several sequential engagements are possible[J]. Operations Research, 1987, 35 (4): 537- 542. doi: 10.1287/opre.35.4.537
119	SCHULTIS W J . A national-level analytic model for penetration of various combined air defense deployments by cruise missile or bombers[M]. Arlington: Institute for Defense Analyses Science and Technology Division, 1978.
120	ORLIN D . Optimal weapons allocation against layered defenses[J]. Naval Research Logistics, 1987, 34 (5): 605- 617. doi: 10.1002/1520-6750(198710)34:5<605::AID-NAV3220340502>3.0.CO;2-L
121	潘书山, 吴晓云, 马大为, 等. 基于粗集理论的武器目标分配[J]. 弹箭与制导学报, 2005, 25 (1): 56- 59. doi: 10.3969/j.issn.1673-9728.2005.01.019
	PAN S S , WU X Y , MA D W , et al. Weapon-target assignment based on the theory of rough sets[J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2005, 25 (1): 56- 59. doi: 10.3969/j.issn.1673-9728.2005.01.019
122	MEKAWEY H I , ABD EL-WAHAB M S , HASHEM M . Novel goal-based weapon target assignment doctrine[J]. Journal of Aerospace Computing, Information, and Communication, 2009, 6 (1): 2- 29. doi: 10.2514/1.34374
123	彭彰. 空防体系对抗中与规则结合的目标分配过程[J]. 中国电子科学研究院学报, 2013, 8 (3): 286- 291. doi: 10.3969/j.issn.1673-5692.2013.03.013
	PENG Z . Target assignment procedure combined with rules in air defensive system confrontation[J]. Journal of China Aca-demy of Electronics and Information Technology, 2013, 8 (3): 286- 291. doi: 10.3969/j.issn.1673-5692.2013.03.013
124	刘兴林. 基于规则评价的武器目标分配方法[J]. 舰船电子工程, 2015, (2): 29- 32.
	LIU X L . Method of weapon target assignment based on rule-eva-luating[J]. Ship Electronic Engineering, 2015, (2): 29- 32.
125	CHANG T Q , KONG D P , HAO N , et al. Solving the dynamic weapon target assignment problem by an improved artificial bee colony algorithm with heuristic factor initialization[J]. Applied Soft Computing, 2018, 70, 845- 863. doi: 10.1016/j.asoc.2018.06.014
126	JAISWAL N K , SHROTRI P K , NAGABHUSHANA B S . Optimal weapon mix, deployment and allocation problems in multiple layer defense[J]. American Journal of Mathematical and Management Sciences, 1993, 13 (1/2): 53- 82.
127	MADNI A M , ANDRECUT M . Efficient heuristic approach to the weapon-target assignment problem[J]. Journal of Ae-rospace Computing, Information, and Communication, 2009, 6 (6): 405- 414. doi: 10.2514/1.34254
128	SONUC E , SEN B , BAYIR S . A parallel simulated annealing algorithm for weapon-target assignment problem[J]. International Journal of Advanced Computer Science and Applications, 2017, 8 (4): 87- 92.
129	XIN B , CHEN J , ZHANG J , et al. Efficient decision makings for dynamic weapon-target assignment by virtual permutation and tabu search heuristics[J]. IEEE Trans. on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 2010, 40 (6): 649- 662. doi: 10.1109/TSMCC.2010.2049261
130	LEE M Z . Constrained weapon-target assignment: enhanced very large scale neighborhood search algorithm[J]. IEEE Trans. on Systems, Man, and Cybernetics-Part A: Systems and Humans, 2010, 40 (1): 198- 204. doi: 10.1109/TSMCA.2009.2030163
131	TOKGÖZ A , BULKAN S . Weapon target assignment with combinatorial optimization techniques[J]. International Journal of Advanced Research in Artificial Intelligence, 2013, 2 (7): 39- 50.
132	METLER W A, PRESTON F L, HOFMANN J. A suite of weapon assignment algorithms for a SDI mid-course battle manager[R]. Washington DC: Naval Research Lab, 1990.
133	LEE Z J , SU S F , LEE C Y . A genetic algorithm with domain knowledge for weapon-target assignment problems[J]. Journal of the Chinese Institute of Engineers, 2002, 25 (3): 287- 295. doi: 10.1080/02533839.2002.9670703
134	LU H Q, ZHANG H J, ZHANG X J, et al. An improved genetic algorithm for target assignment, optimization of naval fleet air defense[C]//Proc. of the 6th World Congress on Intelligent Control and Automation, 2006: 3401-3405.
135	WU L, WANG H Y, LU F X, et al. An anytime algorithm based on modified GA for dynamic weapon-target allocation problem[C]//Proc. of the IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence), 2008: 2020-2025.
136	SONG Z H, ZHU F S, ZHANG D L. A heuristic genetic algorithm for solving constrained weapon-target assignment problem[C]//Proc. of the IEEE International Conference on Intelligent Computing and Intelligent Systems, 2009: 336-341.
137	LI P, WU L, LU F X. A mutation-based GA for weapon-target allocation problem subject to spatial constraints[C]//Proc. of the International Workshop on Intelligent Systems and Applications, 2009.
138	CHEN J , XIN B , PENG Z H , et al. Evolutionary decision-makings for the dynamic weapon-target assignment problem[J]. Science in China Series F: Information Sciences, 2009, 52 (11): 2006- 2018. doi: 10.1007/s11432-009-0190-x
139	LI J, CHEN J, XIN B, et al. Solving multi-objective multi-stage weapon target assignment problem via adaptive NSGA-Ⅱ and adaptive MOEA/D: a comparison study[C]//Proc. of the IEEE Congress on Evolutionary Computation, 2015: 3132-3139.
140	ZHANG K , ZHOU D Y , YANG Z , et al. Constrained multi-objective weapon target assignment for area targets by efficient evolutionary algorithm[J]. IEEE Access, 2019, 7, 176339- 176360. doi: 10.1109/ACCESS.2019.2955482
141	LI J , XIN B , PARDALOS P M , et al. Solving bi-objective uncertain stochastic resource allocation problems by the CVaR-based risk measure and decomposition-based multi-objective evolutionary algorithms[J]. Annals of Operations Research, 2021, 296 (1/2): 639- 666.
142	ZENG X P, ZHU Y L, NAN L, et al. Solving weapon-target assignment problem using discrete particle swarm optimization[C]//Proc. of the 6th World Congress on Intelligent Control and Automation, 2006: 3562-3565.
143	THANGARAJ R, PANT M, NAGAR A K. Maximization of expected target damage value using quantum particle swarm optimization[C]//Proc. of the 2nd International Conference on Developments in eSystems Engineering, 2009: 329-334.
144	CHEN H D, LIU Z, SUN Y L, et al. Particle swarm optimization based on genetic operators for sensor-weapon-target assignment[C]//Proc. of the 5th International Symposium on Computational Intelligence and Design, 2012: 170-173.
145	ZHOU Y L, LI X B, ZHU Y F, et al. A discrete particle swarm optimization algorithm applied in constrained static weapon-target assignment problem[C]//Proc. of the 12th World Congress on Intelligent Control and Automation, 2016: 3118-3123.
146	WANG Y , LI J , HUANG W L , et al. Dynamic weapon target assignment based on intuitionistic fuzzy entropy of discrete particle swarm[J]. China Communications, 2017, 14 (1): 169- 179. doi: 10.1109/CC.2017.7839767
147	ZHOU D Y, LI X Y, PAN Q, et al. Multiobjective weapon-target assignment problem by two-stage evolutionary multiobjective particle swarm optimization[C]//Proc. of the IEEE International Conference on Information and Automation, 2016: 921-926.
148	FU G Y , WANG C , ZHANG D Q , et al. A multiobjective particle swarm optimization algorithm based on multipopulation coevolution for weapon-target assignment[J]. Mathema-tical Problems in Engineering, 2019, 2019, 1424590.
149	WEI N , LIU M Y , CHENG W B . Decision-making of underwater cooperative confrontation based on MODPSO[J]. Sensors, 2019, 19 (9): 2211. doi: 10.3390/s19092211
150	WANG Y X , QIAN L J , GUO Z , et al. Weapon target assignment problem satisfying expected damage probabilities based on ant colony algorithm[J]. Journal of Systems Engineering and Electronics, 2008, 19 (5): 939- 944. doi: 10.1016/S1004-4132(08)60179-6
151	SHANG G. Solving weapon-target assignment problems by a new ant colony algorithm[C]//Proc. of the International Symposium on Computational Intelligence and Design, 2008: 221-224.
152	CAO M , FANG W G . Distributed MMAS for weapon target assignment based on Spark framework[J]. Journal of Intelligent & Fuzzy Systems, 2018, 35 (3): 3685- 3696.
153	REZENDE M D , DE LIMA B S L P , GUIMARÃES S . A greedy ant colony system for defensive resource assignment problems[J]. Applied Artificial Intelligence, 2018, 32 (2): 138- 152. doi: 10.1080/08839514.2018.1451137
154	PU J, WU X, GUO Y K, et al. Attacking strategy of multiple unmanned surface vehicles based on DAMGWO algorithm[C]//Proc. of the EuroSymposium on Systems Analysis and Design, 2018: 135-145.
155	WANG J , LUO P C , HU X W , et al. A hybrid discrete grey wolf optimizer to solve weapon target assignment problems[J]. Discrete Dynamics in Nature and Society, 2018, doi: 10.1155/2018/4674920
156	KHOSLA D. Hybrid genetic approach for the dynamic weapon-target allocation problem[C]//Proc. of the SPIE-the International Society for Optical Engineering, 2001.
157	BISHT S . Hybrid genetic-simulated annealing algorithm for optimal weapon allocation in multilayer defence scenario[J]. Defense Science Journal, 2004, 54 (3): 395- 405. doi: 10.14429/dsj.54.2054
158	LEE Z J , LEE C Y , SU S F . An immunity-based ant colony optimization algorithm for solving weapon-target assignment problem[J]. Applied Soft Computing, 2002, 2 (1): 39- 47. doi: 10.1016/S1568-4946(02)00027-3
159	ZHANG J Y , WANG X J , XU C Q , et al. ACGA algorithm of solving weapon-target assignment problem[J]. Open Journal of Applied Sciences, 2012, 2 (4): 74- 77. doi: 10.4236/ojapps.2012.24B018
160	YANG S L , YANG M , WANG S , et al. Adaptive immune genetic algorithm for weapon system portfolio optimization in military big data environment[J]. Cluster Computing, 2016, 19 (3): 1359- 1372. doi: 10.1007/s10586-016-0596-3
161	XUE Y , ZHUANG Y , NI T Q , et al. Self-adaptive learning based discrete differential evolution algorithm for solving CJWTA problem[J]. Journal of Systems Engineering and Electronics, 2014, 25 (1): 59- 68. doi: 10.1109/JSEE.2014.00007
162	LIANG H T , KANG F J . Adaptive chaos parallel clonal selection algorithm for objective optimization in WTA application[J]. Optik, 2016, 127 (6): 3459- 3465. doi: 10.1016/j.ijleo.2015.12.122
163	LI N , HUAI W Q , WANG S D . The solution of target assignment problem in command and control decision-making behaviour simulation[J]. Enterprise Information Systems, 2017, 11 (7): 1059- 1077. doi: 10.1080/17517575.2016.1177207
164	ZHANG Y Z, ZHANG L, LI M H. A dynamic decision-maker of anytime algorithm for tasks decision-making problem[C]//Proc. of the 7th International Conference on Intelligent Human-Machine Systems and Cybernetics, 2015: 353-356.
165	WANG Y, ZHANG W G, LI Y. An efficient clonal selection algorithm to solve dynamic weapon-target assignment game model in UAV cooperative aerial combat[C]//Proc. of the 35th Chinese Control Conference, 2016: 9578-9581.
166	LAI C M , WU T H . Simplified swarm optimization with initialization scheme for dynamic weapon-target assignment problem[J]. Applied Soft Computing, 2019, 82, 105542. doi: 10.1016/j.asoc.2019.105542
167	ZHANG K , ZHOU D Y , YANG Z , et al. Efficient decision approaches for asset-based dynamic weapon target assignment by a receding horizon and marginal return heuristic[J]. Electronics, 2020, 9 (9): 1511. doi: 10.3390/electronics9091511
168	AZAK M, BAYRAK A E. A new approach for threat evaluation and weapon assignment problem, hybrid learning with multi-agent coordination[C]//Proc. of the 23rd International Symposium on Computer and Information Sciences, 2008.
169	MOUTON H , LE ROUX H , ROODT J . Applying reinforcement learning to the weapon assignment problem in air defence[J]. Scientia Militaria: South African Journal of Military Studies, 2011, 39 (2): 99- 116.
170	王邑, 孙金标, 肖明清, 等. 基于类型2区间模糊K近邻分类器的动态武器-目标分配方法研究[J]. 系统工程与电子技术, 2016, 38 (6): 1314- 1319.
	WANG Y , SUN J B , XIAO M Q , et al. Research of dynamic weapon-target assignment problem based on type-2 interval fuzzy K-nearest neighbors classifier[J]. Systems Engineering and Electronics, 2016, 38 (6): 1314- 1319.
171	GIBBONS D, LIM C C, SHI P. Deep learning for bipartite assignment problems[C]//Proc. of the IEEE International Conference on Systems, Man and Cybernetics, 2019: 2318-2325.
172	SHOJAEIFARD A , AMROUDI A N , MANSOORI A , et al. Projection recurrent neural network model: a new strategy to solve weapon-target assignment problem[J]. Neural Processing Letters, 2019, 50 (3): 3045- 3057. doi: 10.1007/s11063-019-10068-y
173	NI M F , YU Z K , MA F , et al. A lagrange relaxation method for solving weapon-target assignment problem[J]. Mathema-tical Problems in Engineering, 2011, 873292.
174	KOLITZ S E. Analysis of a maximum marginal return assignment algorithm[C]//Proc. of the 27th IEEE Conference on Decision and Control, 1988: 2431-2436.
175	GELENBE E , TIMOTHEOU S , NICHOLSON D . Fast distributed near-optimum assignment of assets to tasks[J]. The Computer Journal, 2010, 53 (9): 1360- 1369. doi: 10.1093/comjnl/bxq010
176	BOGDANOWICZ Z R , TOLANO A , PATEL K , et al. Optimization of weapon-target pairings based on kill probabilities[J]. IEEE Trans. on Cybernetics, 2013, 43 (6): 1835- 1844. doi: 10.1109/TSMCB.2012.2231673
177	BOGDANOWICZ Z R , PATEL K . Quick collateral damage estimation based on weapons assigned to targets[J]. IEEE Trans. on Systems, Man, and Cybernetics: Systems, 2015, 45 (5): 762- 769. doi: 10.1109/TSMC.2014.2360823
178	NASEEM A , KHAN S A , MALIK A W . A real-time man-in-loop threat evaluation and resource assignment in defense[J]. The Journal of the Operational Research Society, 2017, 68 (6): 725- 738. doi: 10.1057/s41274-016-0139-6
179	ZHAO P , WANG J Z , KONG L R . Decentralized algorithms for weapon-target assignment in swarming combat system[J]. Mathematical Problems in Engineering, 2019, 2019, 8425403.
180	GAO Y , LI D S , ZHONG H . A novel target threat assessment method based on three-way decisions under intuitionistic fuzzy multi-attribute decision making environment[J]. Engineering Applications of Artificial Intelligence, 2020, 87, 103276. doi: 10.1016/j.engappai.2019.103276
181	HU L , YI G X , HUANG C , et al. Research on dynamic weapon target assignment based on cross-entropy[J]. Mathematical Problems in Engineering, 2020, 8618065.
182	LIU X , LIU Z , HOU W S , et al. Improved MOPSO algorithm for multi-objective programming model of weapon-target assignment[J]. Systems Engineering and Electronics, 2013, 35 (2): 326- 330. doi: 10.3969/j.issn.1001-506X.2013.02.15
183	ZHOU D Y, LI X Y, PAN Q, et al. Multiobjective weapon-target assignment problem by two-stage evolutionary multiobjective particle swarm optimization[C]//Proc. of the IEEE International Conference on Information and Automation, 2016: 921-926.
184	GU J J , ZHAO J J , YAN J , et al. Cooperative weapon-target assignment based on multi-objective discrete particle swarm optimization-gravitational search algorithm in air combat[J]. Journal of Beijing University of Aeronautics and Astronautics, 2015, 41 (2): 252- 258.
185	ZHAO Y , CHEN Y F , ZHEN Z Y , et al. Multi-weapon multi-target assignment based on hybrid genetic algorithm in uncertain environment[J]. International Journal of Advanced Robotic Systems, 2020, 17 (2) doi: 10.1177/1729881420905922

建模方法	特点	重点应用领域
数学规划	包括线性整数规划、非线性整数规划、0-1整数规划等, 模型多样, 形式化严谨, 便于数学求解, 应用领域广。	适用于进攻和作战中的所有典型作战样式, 尤其是便于求解大规模问题。
博弈论	便于分析双方对抗策略影响, 数学描述严谨。	包含小规模动态对抗作战场景的作战样式。
图论	一般需要对WTA问题进行转化与简化, 建立在数学规划模型基础上, 不适合求解规模较大的问题。	武器和目标相对简单, 能够建模为基础WTA问题的作战场景。
动态规划	便于分析多阶段分配过程中动态不确定因素的影响, 一般只能求解中小规模问题。	作战过程中存在多个阶段的作战场景。
多智能体建模	强调人工智能的应用, 特别是机器学习和强化学习的应用。	时效性要求高、需要进行分布式协同的作战场景。
网络流	需要对WTA问题进行转化与简化, 建立在数学规划模型基础之上, 便于求解大规模问题。	武器和目标相对简单、不需要考虑协同或额外约束的作战场景。

算法	优点	局限性	适用问题
精确算法	能够求解出精确最优解, 便于理解与实现。	难以求解大规模问题; 一般需要问题的精确数学模型。	时效性要求不高, 约束简单的中、小规模问题。
元启发式算法	算法框架便于实现, 可以对解空间进行大范围搜索, 能够求解大规模问题。	求解时间较长, 算法性能不够稳定。	时效性要求不高的大规模问题。
基于规则的启发式算法	充分利用领域知识, 求解时间短、效率高。	解的质量依赖于规则的设定; 一般只能得到局部最优解。	时效性要求高、约束复杂的中、小规模问题。
机器学习算法	持续学习和进化; 开源工具支持完备; 算法通用性较好; 训练好的模型执行效率高。	训练数据要求高; 可解释性差; 依赖强大算力; 解空间维数灾难。	作战规则明确、时效性要求高的中、小规模问题。

大规模	小规模	中等规模
Lee等^[84] Ahuja等^[105] Gelen等^[175] Sonuc等^[128] Xin等^[88] Lu等^[90]	Manne^[1] Wacholder^[8] Wang等^[150] Cha等^[55] Lebouche等^[99] Li等^[71]	Lee等^[158] Karasakal^[29] Dirik等^[67] Li等^[71]

测试数据	代表文献	获取方式
想定数据	Wacholder^[8]	https://pubsonline.informs.org/doi/abs/10.1287/ijoc.1.4.232
	Li等^[71]	https://www.hindawi.com/journals/ijae/2018/8302324/
	Xin等^[129]	https://ieeexplore.ieee.org/document/5475284
	Wang等^[150]	https://ieeexplore.ieee.org/document/6072411?arnumber=6072411
随机数据	Xin等^[88]	https://pris.bit.edu.cn/home/people/OtherStaff/xinbin.htm
	Lu等^[90]	http://yun.bjtu.edu.cn/public.php?service=files&t=433c75786340cac5c73cc4c5036cd52e&download
	Sonuc^[128]	http://web.karabuk.edu.tr/emrullahsonuc/wta

[1]	Zhongpu CUI, Songhu GE, Yaxing LI, Yu GUO, Jinling XING, Jin MENG. Partially decoupling based nonlinear digital interference cancellation algorithm [J]. Systems Engineering and Electronics, 2023, 45(4): 973-981.
[2]	Xiaofei LU, Shuojing JIN, Ling HONG, Fengzhou DAI. Target micro-Doppler analysis of TVAR model based on clustering [J]. Systems Engineering and Electronics, 2023, 45(3): 660-668.
[3]	Yingjun LI, Yongxiang LIU, Biao TIAN, Wenpeng ZHANG. GTD scattering parameter extraction and RCS reconstruction in frequency hopping mode based on IRLS [J]. Systems Engineering and Electronics, 2023, 45(3): 678-689.
[4]	Xiaoxiu ZHU, Limin LIU, Wenhua HU, Baofeng GUO, Lin SHI, Hanshen ZHU. Multi-angle and multi-band ISAR fusion imaging based on GTD model [J]. Systems Engineering and Electronics, 2023, 45(3): 726-735.
[5]	Wenfei ZHAO, Xiaolei LIU, Cuiling MA, Kenan TENG. DWTA of air defense for strategic location on the sea based on multi-objective fuzzy programming [J]. Systems Engineering and Electronics, 2023, 45(3): 777-784.
[6]	Yan MA, Jianjun WANG, Zebiao FENG. Bayesian modeling and optimization of robust parametric design with non-normal response [J]. Systems Engineering and Electronics, 2023, 45(3): 921-930.
[7]	Xiaojia YAN, Weige LIANG, Gang ZHANG, Bo SHE, Fuqing TIAN. Prediction method for mechanical equipment based on RCNN-ABiLSTM [J]. Systems Engineering and Electronics, 2023, 45(3): 931-940.
[8]	Jiancheng ZHENG, Zhiguo QU, Xiansi TAN, Jingyang WANG, Lujun LI. Comparison of early warning detection characteristics between anti-near-space and anti-missile [J]. Systems Engineering and Electronics, 2023, 45(2): 379-385.
[9]	Zhixing LIU, Yinghui QUAN, Minghui SHA, Wen FANG, Xia GAO, Mengdao XING. Target parameter estimation method for frequency agility and pulse repetition frequency agility radar [J]. Systems Engineering and Electronics, 2023, 45(2): 401-406.
[10]	Ziyi CHEN, Yajie DOU, Xiangqian XU, Yuejin TAN, Kewei YANG, Jiang JIANG. Combinatorial optimization solution of complex equipment driven by contribution and sharing two-tier strategy [J]. Systems Engineering and Electronics, 2023, 45(2): 431-443.
[11]	Xiaofeng LYU, Dongze YANG, Ling MA. Optimal design of modular ammunition scheduling scheme for carrier-based aircraft [J]. Systems Engineering and Electronics, 2023, 45(2): 465-471.
[12]	Qiuping XU, Jiejing ZHOU, Hai JI, Ming GENG, Yuanyuan LE. Automatic analysis and mining algorithm of air target formation [J]. Systems Engineering and Electronics, 2023, 45(2): 481-489.
[13]	Haojie ZHANG, Yudong ZHANG, Rongmin LIANG, Tiantian YANG. Energy-efficient path planning method for robots based on improved A^* algorithm [J]. Systems Engineering and Electronics, 2023, 45(2): 513-520.
[14]	Youran XIA, Jun GUAN, Wenjun YI. Projectile parameter identification: extreme learning machine optimized by improved particle swarm [J]. Systems Engineering and Electronics, 2023, 45(2): 521-529.
[15]	Shengyang HE, Jiepeng DU, Yaqin ZHAO, Baoying WANG, Liang ZHAO, Longwen WU. TDOA-based cooperative single target location using UAV cluster [J]. Systems Engineering and Electronics, 2023, 45(1): 1-8.

Developments of weapon target assignment: models, algorithms, and applications

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 7

References 185

Related Articles 15

Recommended Articles

Metrics

Comments