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

摘要/Abstract

摘要：

武器目标分配问题是指挥控制与任务规划领域的关键难点之一, 也是军事运筹领域的基础研究课题。经过多年研究, 武器目标分配问题在陆海空天电等领域都得到了广泛研究, 涌现出了大量模型和算法。系统梳理武器目标分配问题的典型作战样式、建模方法、求解算法和实验验证, 掌握当前该领域的研究现状, 在此基础上, 结合智能化、无人化战争带来的新挑战, 分析武器目标分配的发展趋势, 为后续研究提供参考。

关键词: 武器目标分配, 模型, 算法, 综述

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

中图分类号:

E913
C934

李梦杰, 常雪凝, 石建迈, 陈超, 黄金才, 刘忠. 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.

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.

图/表 7

图1

表1

典型作战样式的问题特点"

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。

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表2

图2

表3

表4

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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

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