罗鹏程 , 傅攀峰 , 周经伦 . 武器装备体系作战能力评估框架 [J ] . 系统工程与电子技术 , 2005 , 27 ( 1 ): 72 - 75 .

LUO P C , FU P F , ZHOU J L . Combat capability evaluation framework of weapon system of system [J ] . Systems Engineering and Electronics , 2005 , 27 ( 1 ): 72 - 75 . (in Chinese)

陈启宏 , 赵青松 , 邱薇 , 等 . 基于动态博弈的武器装备体系发展规划论证方法 [J ] . 系统工程与电子技术 , 2022 , 44 ( 10 ): 3124 - 3133 . DOI: 10.12305/j.issn.1001-506X.2022.10.16 http://doi.org/10.12305/j.issn.1001-506X.2022.10.16 武器装备是作战能力生成的重要物质基础, 针对现代战争武器装备成体系对抗的特征, 从对抗博弈的视角分析武器装备体系发展规划问题。首先, 基于作战环构建武器装备体系对抗网络模型, 描述不同功能类型装备之间的影响关系。基于动态博弈的思想, 构建武器装备体系发展规划的博弈脉络, 评估发展规划方案在不同博弈场景下的威胁能力。最后进行了示例分析, 为武器装备体系发展规划论证提供一种新的定量评估方法。

CHEN Q H , ZHAO Q S , QU W , et al. Planning and demonstration method of weapon system of system based on dynamic game [J ] . Systems Engineering and Electronics , 2022 , 44 ( 10 ): 3124 - 3133 . (in Chinese)

SHIH C , KOONG C , HSIUNG P . Billiard combat modeling and simulation based on optimal cue placement control and strategic planning [J ] . Journal of Intelligent & Robotic Systems , 2012 , 67 ( 1 ): 25 - 41 .

SMITH R M . Using kill-chain analysis to develop surface ship CONOPs to defend against anti-ship cruise missiles [D ] . Monterey, CA , US : Naval Postgraduate School , 2010 .

陈登 , 陈楚湘 , 周春华 . 基于“OODA环”的杀伤网节点重要性评估 [J ] . 兵工学报 , 2024 , 45 ( 2 ): 363 - 372 . DOI: 10.12382/bgxb.2022.0623 http://doi.org/10.12382/bgxb.2022.0623 基于网络信息体系的联合作战中,破坏敌杀伤网、降效敌杀伤体系作战效能,要求能够识别敌杀伤网中关键节点。基于OODA环理论及杀伤链概念建模,利用节点删除法,通过网络作战能力及网络循环效率两项指标的下降程度评估杀伤网节点的重要性,克服传统评估方法在指标计算中存在冗余的问题,提高评估精度。采用该方法评估某作战演练中敌方杀伤网节点的重要性,精准识别指挥决策节点的枢纽作用,验证方法的有效性,并对杀伤网节点的重要性进行评估排序,为选择进攻要点提供依据。

CHEN D , CHEN C X , ZHOU C H . Importance evaluation of kill web nodes based on OODA Ring [J ] . Acta Armamentarii , 2024 , 45 ( 2 ): 363 - 372 . (in Chinese) DOI: 10.12382/bgxb.2022.0623 http://doi.org/10.12382/bgxb.2022.0623 In joint operations based on the network information system, paralyzing the enemy kill network and reducingthe operational effectiveness of enemy kill system requires the ability to identify the key nodes in the enemy kill networks. Kill network modeling based on OODA loop theory and kill chain operational concept, this paper uses the node deletion method to evaluate the importance of kill network nodes through the decline degree of network operational capability and network cycle efficiency, so as to overcome the problem of redundancy in the index calculation of traditional evaluation methods and improve the evaluation accuracy. This method is used to evaluate the importance of enemy kill network nodes in the operation drill, which accurately identifies the pivotal role of command and decision nodes to verify the effectiveness of the method, and which evaluates and ranks the importance of kill network nodes to provide a basis for selecting attack nodes.

高保慧 , 胡海 . 天空海一体对海打击动态杀伤网作战概念研究 [J ] . 舰船电子工程 , 2023 , 43 ( 1 ): 28 - 31 .

GAO B H , HU H . Research on the operational concept of sky and sea to sea strike dynamic kill web [J ] . Ship Electronic Engineering , 2023 , 43 ( 1 ): 28 - 31 . (in Chinese)

王玉茜 , 曹亚杰 , 佘晓琼 , 等 . 美军杀伤网概念研究及对我防空作战装备体系的启示 [J ] . 现代防御技术 , 2023 , 51 ( 6 ): 1 - 8 . DOI: 10.3969/j.issn.1009-086x.2023.06.001 http://doi.org/10.3969/j.issn.1009-086x.2023.06.001 DARPA寻求从杀伤链转向杀伤网，意图利用信息网络构建高度分散的杀伤网，形成难以预测的杀伤链。美空军在试验旗体系下开展“橙旗”“翠旗”和“黑旗”试验，探索杀伤网概念的落地应用。首先，围绕杀伤网作战概念，阐述杀伤网与杀伤链的内涵与差异；其次，理清DARPA“自适应跨域杀伤网”项目的发展背景，分析其基于电子商务“供应商—消费者”框架的架构设计，总结其“跨域杀伤网协商与实例化的实时推理分析”软件针对项目关键技术的演示验证情况；再次，从作战管理、体系架构、安全通信、基础设施、标准规范等方面提出构建杀伤网所需的关键技术；最后，瞄准构建未来防御作战弹性杀伤网，从技术角度给出建设我防空作战装备体系的建议。

WANG Y Q , CAO Y J , SHE X Q , et al. Research on the concept of kill-web of American army and its enlightenment to our air defense combat equipment system [J ] . Modern Defence Technology , 2023 , 51 ( 6 ): 1 - 8 . (in Chinese)

王梦 , 杨松 , 李小波 , 等 . 基于可执行架构的杀伤链设计与分析优化方法 [J ] . 系统仿真技术 , 2021 , 17 ( 3 ): 169 - 174 .

WANG M , YANG S , LI X B , et al. Kill chain design and analysis optimization method based on executable architecture [J ] . System Simulation Technology , 2021 , 17 ( 3 ): 169 - 174 . (in Chinese)

刘畅 , 张雪松 . 基于立体网络模型的机群杀伤链架构与规划研究 [J ] . 中国电子科学研究院学报 , 2021 , 16 ( 5 ): 468 - 479 .

LIU C , ZHANG X S . Research on architecture and planning of aircraft group kill chain based on stereoscopic network model [J ] . Journal of China Academy of Electronics and Information Technology , 2021 , 16 ( 5 ): 468 - 479 . (in Chinese)

向南 , 豆亚杰 , 姜江 , 等 . 马赛克战概念下作战模块应急重构自主决策 [J ] . 指挥与控制学报 , 2020 , 6 ( 3 ): 223 - 228 .

XIANG N , DOU Y J , JIANG J , et al. Operational module emergency reconstruction autonomous decision based on mosaic warfare concept [J ] . Journal of Command and Control , 2020 , 6 ( 3 ): 223 - 228 . (in Chinese)

钱丰 , 赵红 . 有无人协同杀伤链引擎设计与实现 [J ] . 信息化研究 , 2023 , 49 ( 2 ): 41 - 47 .

QIAN F , ZHAO H . Design and implementation of man-unmanned coordinated kill chain engine [J ] . Informatization Research , 2023 , 49 ( 2 ): 41 - 47 . (in Chinese)

杨争争 , 白浩 , 侯勇 . 陆战场杀伤网模型与资源优化初探 [J ] . 火炮发射与控制学报 , 2022 , 43 ( 5 ): 49 - 53 .

YANG Z Z , BAI H , HOU Y . Preliminary study on kill net model and resource optimization of land battlefields [J ] . Journal of Gun Launch & Control , 2022 , 43 ( 5 ): 49 - 53 . (in Chinese)

夏博远 , 杨克巍 , 杨志伟 , 等 . 基于杀伤网评估的装备组合多目标优化 [J ] . 系统工程与电子技术 , 2021 , 43 ( 2 ): 399 - 409 . DOI: 10.12305/j.issn.1001-506X.2021.02.15 http://doi.org/10.12305/j.issn.1001-506X.2021.02.15 杀伤网作为众多新型作战理念中均有涉及的概念,将替代杀伤链成为新型作战方式下战斗力生成的主要模式。本文基于杀伤网的评估,对传统的装备组合问题进行多目标优化。首先,基于多层网络模型,构建杀伤网的网络化描述方法。其次,基于杀伤网的特点,构建3个评估指标:冗余性指标、风险性指标、敏捷性指标,并给出了3个评估指标的计算模型。然后,构建了基于杀伤网评估指标的装备组合规划模型,并给出了基于启发式算法的装备组合多目标优化方法。最后，进行示例研究,通过评估两种具有不同装备组成和网络结构的杀伤网,对比其优劣,然后针对第一种包含无人装备的杀伤网进行装备组合优化,分别验证了评估模型的合理性以及优化模型的有效性。

XIA B Y , YANG K W , YANG Z W , et al. Multi-objective optimization of equipment combination based on kill-web evaluation [J ] . Systems Engineering and Electronics , 2021 , 43 ( 2 ): 399 - 409 . (in Chinese)

万斯来 , 王国新 , 明振军 , 等 . 基于知识推理的杀伤网智能设计方法 [J ] . 兵工学报 , 2024 , 45 ( 4 ): 1025 - 1037 . DOI: 10.12382/bgxb.2022.1077 http://doi.org/10.12382/bgxb.2022.1077 针对现有杀伤网设计对人的经验依赖性强、智能化程度低的问题,提出一种基于知识推理的杀伤网智能设计方法。基于OODA循环理论构建作战任务-作战能力-武器装备多层级杀伤网本体,实现杀伤网设计静态知识建模;构建任务-能力-装备映射规则、装备协同规则和杀伤链协同规则3类杀伤网设计规则库,实现杀伤网设计动态知识建模;在静态知识和动态知识的基础上提出一个基于知识推理的杀伤网智能设计流程框架,同时定义了时间链、精度链和成本链3个杀伤链评估指标,以实现动态战场下的杀伤网快速智能设计。在某体系对抗仿真推演平台上,以防空反导作战体系执行典型防空反导任务为案例,验证了所提方法的有效性。

WAN S L , WANG G X , MING Z J , et al. Knowledge reasoning-based intelligent design method of kill-web [J ] . Acta Armamentarii , 2024 , 45 ( 4 ): 1025 - 1037 . (in Chinese) DOI: 10.12382/bgxb.2022.1077 http://doi.org/10.12382/bgxb.2022.1077 A knowledge reasoning-based intelligent design method of kill-web is proposed for the problems of strong dependence on human experience and low intelligence in the design of kill-web. Based on the OODA theory, a multi-level kill-web ontology including combat mission-combat capability-wWeapon equipment is constructed to model the static knowledge related to kill-web design. Three types of kill-web design rule bases, namely mission-capability-equipment mapping rule, equipment coordination rule and kill chain coordination rule, are constructed to model the dynamic knowledge related to kill-web design. Based on static knowledge and dynamic knowledge, a knowledge reasoning-based intelligent design process framework of kill-web is proposed, in which three kill-chain evaluation metrics of time, precision and cost are defined in order to quickly and intelligently design a kill-web in actual combat situations. Taking the air defense and anti-missile system of systems as an example the effectiveness of the proposed method is verified on a simulation platform.

SHI H Q , HE B , LIANG J , et al. Modeling technology of naval formation area antiaircraft kill web based on event graph [C ] //Proceedings of the 2022 9th International Conference on Dependable Systems and Their Applications. Urumqi , China : IEEE , 2022 : 353 - 359 .

WANG L Y , CHEN L B , YANG Z W , et al. A prospect-theory-based operation loop decision-making method for kill web [J ] . Mathematics , 2022 , 10 ( 19 ): 3486.

RICHARDS C . Boyd's OODA loop [J ] . Necesse , 2020 , 5 ( 1 ): 142 - 165 .

智洪欣 , 赵鹏 , 李中 , 等 . 基于可射击概率约束的防空作战火力优化分配 [J ] . 兵工学报 , 2022 , 43 ( 4 ): 952 - 959 . DOI: 10.12382/bgxb.2021.0177 http://doi.org/10.12382/bgxb.2021.0177 针对防空作战火力优化分配中未考虑可射击概率影响防空作战效能的问题，提出一种基于可射击概率约束的火力分配模型。该模型综合考虑可射击概率、空袭强度、火力单元转火时间等多种因素，能够在保证满足可射击概率和联合毁伤概率阈值前提下，优先使用反应快的火力单元拦截飞临时间短的目标，并尽量减少火力资源消耗，为防空系统提供持续作战能力。提出一种基于非线性自适应惯性权重的改进平衡优化器优化算法，对模型进行求解。该算法首先使用Tent混沌映射初始化种群，增强种群多样性；其次引入惯性权重平衡局部搜索和全局搜索能力，有效提高了算法的寻优能力。仿真计算结果验证了所提模型的优点以及优化算法的有效性。

ZHI H X , ZHAO P , LI Z , et al. Optimal fire allocation for air defense operations based on the shot probability constraint [J ] . Acta Armamentarii , 2022 , 43 ( 4 ): 952 - 959 . (in Chinese)

WANG T , FU L Y , WEI Z X , et al. Unmanned ground weapon target assignment based on deep Q-learning network with an improved multi-objective artificial bee colony algorithm [J ] . Engineering Applications of Artificial Intelligence , 2023 , 117 : 105612 .

褚凯轩 , 常天庆 , 张雷 . 基于改进人工蜂群算法的地面作战武器-目标分配 [J ] . 兵工学报 , 2023 , 44 ( 7 ): 2171 - 2183 . DOI: 10.12382/bgxb.2022.0294 http://doi.org/10.12382/bgxb.2022.0294 为了提高地面分队火力分配的科学性,构建基于打击效益的地面作战武器目标分配(WTA)模型,针对战场上打击的收益和代价,制定合理的优化函数。通过对目标的威胁评估,判定打击的迫切性和必要性;通过对目标的战场价值判断,计算毁伤价值收益;通过目标对武器的毁伤概率,预估我方武器的损失;通过分析敌我兵力对比和弹药储备情况,量化弹药的价值;通过分析敌我双方的战术意图,衡量打击的必要性和战术意图暴露的代价。针对WTA模型求解问题,提出一种改进人工蜂群算法,以提高算法的搜索方向性和迭代后期跳出局部最优能力,同时采用基于武器目标组合库的种群初始化策略,提高了算法初期种群质量。仿真算例表明了所提模型的科学性以及新算法在收敛速度、收敛精度和鲁棒性方面的优势。

CHU K X , CHANG T Q , ZHANG L . Ground combat weapon-target allocation based on improved artificial bee colony algorithm [J ] . Acta Armamentarii , 2023 , 44 ( 7 ): 2171 - 2183 . (in Chinese)

ZHI P F , LIANG Z Z , ZHU W L , et al. Weapon target assignment strategy for shipboard power system considering high power pulse loads integration [J ] . Energy Reports , 2023 , 9 ( S8 ): 32 - 40 .

王 , 赵文飞 , 滕克难 , 等 . 不确定因素下海上要地防空动态火力分配模型 [J ] . 兵工学报 , 2022 , 43 ( 11 ): 2885 - 2896 .

WANG Y , ZHAO W F , TENG K N , et al. Dynamic fire distribution model for air defense at key points on sea under uncertain factors [J ] . Acta Armamentarii , 2022 , 43 ( 11 ): 2885 - 2896 . (in Chinese)

KIM J , LEE C , YI M Y . New weapon target assignment algorithms for multiple targets using a rotational strategy and clustering approach [J ] . IEEE Access , 2022 , 10 : 43738 - 43750 .

聂俊峰 , 陈行军 , 苏琦 . 基于NSGA-Ⅲ算法的集群目标来袭火力分配建模与优化 [J ] . 兵工学报 , 2021 , 42 ( 8 ): 1771 - 1779 . DOI: 10.3969/j.issn.1000-1093.2021.08.022 http://doi.org/10.3969/j.issn.1000-1093.2021.08.022 火力分配建模与优化作为集群目标来袭防御任务规划的关键环节，对提高防御效果、保证任务完成质量具有重要意义。针对集群目标来袭防御策略呈现出由传统点对点饱和攻击向合理火力覆盖转变的基本趋势，建立以攻击效益最大、自身剩余价值最大、武器消耗最小为目标函数，以毁伤门限、武器资源总数和0-1整数约束为约束条件的集群目标火力分配模型；提出基于非支配排序遗传算法-Ⅲ（NSGA-Ⅲ）的集群目标来袭火力分配优化框架，给出具体的优化流程；面向想定的作战任务进行仿真实现，并通过收敛性指标和间距指标对NSGA-Ⅲ算法与第2代强度Pareto进化算法、NSGA-Ⅱ算法的性能进行对比分析。结果表明，NSGA-Ⅲ算法各项性能更优，能够更有效地解决集群目标来袭火力分配建模与优化问题。

NIE J F , CHEN X J , SU Q . Clustering target incoming fire distribution modeling and optimization based on NSGA-Ⅲ algorithm [J ] . Acta Armamentarii , 2021 , 42 ( 8 ): 1771 - 1779 . (in Chinese)

PANICHELLA A . An adaptive evolutionary algorithm based on non-euclidean geometry for many-objective optimization [C ] //Proceedings of the Genetic and Evolutionary Computation Conference. New York, NY , US : Association for Computing Machinery , 2019 : 595 - 603 .

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 .

SHARMA S , KUMAR V A . Comprehensive review on multi-objective optimization techniques: past, present and future [J ] . Archives of Computational Methods in Engineering , 2022 , 29 ( 7 ): 5605 - 5633 .

DEB K , JAIN H . An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, Part I: solving problems with box constraints [J ] . IEEE Transactions on Evolutionary Computation , 2013 , 18 ( 4 ): 577 - 601 .

JAIN H , DEB K . An evolutionary many-objective optimization algorithm using reference-point based nondominated sorting approach, Part Ⅱ: handling constraints and extending to an adaptive approach [J ] . IEEE Transactions on Evolutionary Computation . 2013 , 18 ( 4 ): 602 - 622 .

BLANK J , DEB K , ROY P C . Investigating the normalization procedure of NSGA-Ⅲ [C ] //Evolutionary Multi-Criterion Optimization: 10th International Conference. East Lansing, MI , US : Springer , 2019 : 229 - 240 .

THOMPSON A C , THOMPSON A C . Minkowski geometry [M ] . Cambridge , UK : Cambridge University Press , 1996 .

FONSECA C M , PAQUETE L , LÓPEZ-IBÁNEZ M . An improved dimension-sweep algorithm for the hypervolume indicator [C ] //Proceedings of 2006 IEEE international conference on evolutionary computation. Vancouver, BC , Canada : IEEE , 2006 : 1157 - 1163 .

BLANK J , DEB K . Pymoo: multi-objective optimization in python [J ] . IEEE Access , 2020 , 8 : 89497 - 89509 .