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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 . A weapon-target assignment in air-defense operations based on shooting probability constraint [J ] . Acta Armamentarii , 2022 , 43 ( 4 ): 952 - 959 . (in Chinese) DOI: 10.12382/bgxb.2021.0177 http://doi.org/10.12382/bgxb.2021.0177 A novel weapon-target assignment model based on shooting probability constraint is proposed in which the impact of shooting probability on the effectiveness of air-defense operations is considered. The proposed model takes many factors into account，such as shooting probability，air strikes intensity，and fire transfer time of firepower unit. The proposed can give priority to using firepower units with quick response to intercept the targets with short flying time on the premise of meeting the thresholds of shooting probability and joint damage probability. At the same time，it minimizes the consumption of fire resources to provide continuous combat capability for the air-defense system.On this basis，an improved equilibrium optimizer algorithm based on nonlinear adaptive inertia weight is presented to solve the weapon-target assignment problem. The Tent chaotic map is used to generate the initial population to enhance the diversity of the population. And the inertia weight is introduced to balance local search and global search ability，which effectively improves the optimization ability of the algorithm. Simulated results verify the advantages of the proposed model and the effectiveness of the optimization algorithm.

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 . A ground combat weapon target assignment model based on shooting effectiveness and improved artificial bee colony algorithm [J ] . Acta Armamentarii , 2023 , 44 ( 7 ): 2171 - 2183 . (in Chinese) DOI: 10.12382/bgxb.2022.0294 http://doi.org/10.12382/bgxb.2022.0294 This paper presents a ground combat Weapon Target Assignment (WTA) model that enhances the validity of firepower allocation for ground units. The model incorporates shooting effectiveness as a key factor and formulates an optimization function considering the benefits and costs of attack decisions on the battlefield. By assessing the threat level of targets, the model determines the urgency and necessity of an attack. By evaluating the battlefield value of targets, it calculates the threat reduction value. The model predicts enemy attack plans and estimates weapon losses based on the probability of damage inflicted by targets. It quantifies the value of ammunition by comparing forces with ammunition reserves. By analyzing the tactical intentions of both sides, the necessity of a strike is weighed against the cost of tactical intent exposure. To solve that WTA model, an improved artificial bee colony algorithm is proposed. This algorithm improves the search directionality of the algorithm and the ability to escape local optimum at the end of each iteration. At the same time, a population initialization strategy based on the Weapon Target Combination Library is adopted to improve the initial population quality of the algorithm. Simulation examples show the soundness of the proposed model and the advantages of the improved algorithm in terms of convergence speed, convergence accuracy, and robustness.

周奕丽 . 多武器平台协同火力打击任务规划问题研究 [D ] . 长沙 : 国防科技大学 , 2016 .

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刘昊 , 张策 , 丁文韬 . 基于智能对抗进化的联合火力打击任务规划方法 [J ] . 兵工学报 , 2019 , 40 ( 6 ): 1287 - 1296 . DOI: 10.3969/j.issn.1000-1093.2019.06.020 http://doi.org/10.3969/j.issn.1000-1093.2019.06.020 针对常规联合火力打击任务规划方法很少涉及敌我对抗，导致评估环境发生变化的问题，提出一种基于敌我对抗进化的智能对抗进化算法。该算法以遗传算法为基础，将模拟生物竞争机制引入敌我双种群，互为评估条件实施对抗进化。依据敌我战场态势图构建观察-判断-决策-打击（OODA）超网络，计算OODA循环效率、确定敌我打击排序,通过多代对抗进化获得能够适应战场动态变化的任务规划最优个体。仿真结果表明：多代进化后的最优个体相比于标准优化结果，战场动态适应性更强，联合火力打击胜率更高，应对突发情况的响应机制更完善，能够有效地解决联合火力打击任务规划的评估优化问题。

LIU H , ZHANG C , DING W T . Joint fire attack mission planning method based on intelligent confrontation evolution [J ] . Acta Armamentarii , 2019 , 40 ( 6 ): 1287 - 1296 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2019.06.020 http://doi.org/10.3969/j.issn.1000-1093.2019.06.020 In view of the fact that the conventional joint fire attack mission planning method rarely involves an issue of friend-foe confrontation leading to the change in evaluation environment, a smart confrontation evolution algorithm based on the evolution of friend-foe confrontation is proposed. The proposed algorithm is based on genetic algorithm, in which the simulation of biological competition mechanism is introduced into the two populations of friend and foe for implementing the confrontational evolution. An observe-orient-decide-act (OODA) super-network is constructed based on the battlefield situation map, and then the OODA cycle efficiency is calculated to determine the order of friend and foe attacks. The task-planning optimal individuals can adapt to the dynamic changes of the battlefield through the confrontation evolution of multiple generations. The simulated results show that the multi-generation evolutionary optimal individual has stronger dynamic adaptability, and the joint firepower strike rate is higher. The response mechanism to respond to the emergencies is more perfect, which can effectively solve the evaluation optimization issues of joint firepower mission planning. Key

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 . Modeling and optimization of weapon-target assignment for group targets defense based on NSGA-Ⅲ algorithm [J ] . Acta Armamentarii , 2021 , 42 ( 8 ): 1771 - 1779 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2021.08.022 http://doi.org/10.3969/j.issn.1000-1093.2021.08.022 As an important part of the task planning of group targets defense, the modeling and optimization of weapon-target assignment are of great significance to improve the defense effect and ensure the quality of task completion. In view of a basic trend that the defense strategy changes from the traditional point-to-point saturation attack to a reasonable firepower coverage, a weapon-group targets assignment model is established by considering the effects of damage threshold, total weapon resources and 0-1 integer constraints. The proposed model is based on the principles of maximum attack effectiveness, its own maximum surplus value and minimum weapon consumption. The optimization framework of weapon-group targets assignment based on NSGA-Ⅲ is proposed, and the specific optimization process of the algorithm is given. The simulation of combat mission is realized, and the convergence metric and spacing metric are used to compare the performances of NSGA-Ⅲ, SPEA2 and NSGA-Ⅱ. The simulated results demonstrate that NSGA-Ⅲ has better performance, which can effectively solve the weapon-target assignment modeling and optimization problem of group targets defense.

CHANG X N , SHI J M , LUO Z H , et al . Adaptive large neighborhood search algorithm for multi-stage weapon target assignment problem [J ] . Computers & Industrial Engineering , 2023 , 181 : 109303 .

刘昊 , 谢鹏 , 李玥 . 联合火力打击中的多目标组合排序算法 [J ] . 兵工学报 , 2020 , 41 ( 12 ): 2570 - 2578 . DOI: 10.3969/j.issn.1000-1093.2020.12.023 http://doi.org/10.3969/j.issn.1000-1093.2020.12.023 针对联合火力打击中的目标排序问题，建立多目标组合火力打击排序数学模型。通过对比和借鉴同类的体系评估算法，设计基于信息流循环效率的多目标组合排序算法，研究多目标组合在联合火力打击中的体系价值及在火力打击排序中的规律特点；按照固定目标组合和动态目标组合方式分别设计仿真模型，提出并验证联合火力打击目标排序的基本原则。实验结果表明：基于信息流循环算法的多目标组合排序符合联合火力打击的目标排序战场需求，具备战场普遍性和应用性。

LIU H , XIE P , LI Y . Combined sorting algorithm for multi-target sorting in joint firepower strike [J ] . Acta Armamentarii , 2020 , 41 ( 12 ): 2570 - 2578 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2020.12.023 http://doi.org/10.3969/j.issn.1000-1093.2020.12.023 A multi-target combined firepower striking mathematical model is established for target sorting in joint firepower strike. A multi-target combined sorting algorithm based on information flow loop efficiency is designed by comparing and referring to the similar system evaluation algorithm. The system value in the joint firepower strike and the regularity of the firepower strike sorting are studied. The simulation models are designed for the fixed target combination and the dynamic target combination, respectively，and the basic principles of the joint firepower target sorting are proposed and verified. The experimental results show that the multi-target combined sorting based on the information flow loop algorithm meets the target sorting battlefield requirements of the joint firepower strike，and has the universality and applicability in the battlefield.

XING H X , XING Q H . An air defense weapon target assignment method based on multi-objective artificial bee colony algorithm [J ] . Computers,Materials & Continua , 2023 , 76 ( 3 ): 2685 - 2705 .

吴巍 , 任成坤 , 张成 , 等 . 非饱和打击场景下考虑附带毁伤的火力分配方法 [J ] . 兵工自动化 , 2024 , 43 ( 6 ): 61 - 66 .

WU W , REN C K , ZHANG C , et al . Firepower allocation method considering collateral damage in unsaturated strike scenario [J ] . Ordnance Industry Automation , 2024 , 43 ( 6 ): 61 - 66 . (in Chinese)

季顺松 , 黄炎焱 , 张寒 , 等 . 基于改进遗传算法的火力分配寻优模型研究 [J ] . 南京理工大学学报 , 2023 , 47 ( 1 ): 33 - 40 .

JI S X , HUANG Y Y , ZHANG H , et al . Research on optimization model of firepower allocation based on improved genetic algorithm [J ] . Journal of Nanjing University of Science and Technology , 2023 , 47 ( 1 ): 33 - 40 . (in Chinese)

张安 , 徐双飞 , 毕文豪 , 等 . 空地多目标攻击武器-目标分配与制导序列优化 [J ] . 兵工学报 , 2023 , 44 ( 8 ): 2233 - 2244 . DOI: 10.12382/bgxb.2022.0326 http://doi.org/10.12382/bgxb.2022.0326 武器-目标分配(WTA)与空地导弹的接力制导规划是远距离空地多目标攻击中亟需解决的难题,具有参数复杂、约束多、非线性强等特点。为此,建立多目标、多约束武器-目标分配与制导序列优化模型,优化目标为目标综合生存概率最小和总用弹量最少,约束条件涉及攻击机导弹配置、导弹毁伤能力、目标毁伤要求、制导站性能。对带精英策略的非支配排序遗传算法(NSGA-Ⅱ)进行改进,提出基于双序列编码的多种群NSGA-Ⅱ(DSMPNSGA-Ⅱ),通过优化WTA序列和制导站序列,实现WTA方案及各导弹制导序列的优化。在DSMPNSGA-Ⅱ中,使用深度优先搜索-Dijkstra算法搜索空地导弹制导序列,改进交叉和变异操作,以减少非可行解的产生,引入多种群策略提升算法性能。仿真结果表明,DSMPNSGA-Ⅱ能够获得有效的WTA与空地导弹接力制导方案,并且求解质量优于单种群NSGA-Ⅱ和多目标粒子群优化算法。

ZHANG A , XU S F , BI W H , et al . Weapon-target assignment and guidance sequence optimization in air-to-ground multi-target attack [J ] . Acta Armamentarii , 2023 , 44 ( 8 ): 2233 - 2244 . (in Chinese) DOI: 10.12382/bgxb.2022.0326 http://doi.org/10.12382/bgxb.2022.0326 Weapon-target assignment (WTA) and relay guidance of air-to-ground missiles are difficult problems to be solved urgently in long-range air-to-ground multi-target attack, and are characterized by complex parameters, multiple constraints, and strong nonlinearity. A multi-target and multi-constraint optimization model of WTA and guidance sequence is established, in which the objective includes the minimum comprehensive survival probability of targets and the minimum number of used missiles, and the constraints involve missile configuration of the attack aircraft, damage capability of the missiles, damage requirements of the targets, performance of the guidance stations, etc. A double sequence coding multi-population non-dominated sorting genetic algorithm Ⅱ (DSMPNSGA-Ⅱ) is proposed by improving NSGA-Ⅱ, which optimizes the scheme of WTA and every missile’s guidance sequence through optimizing the WTA sequence and guidance stations sequence. In DSMPNSGA-Ⅱ, the depth-first search Dijkstra (DFS-DJ) algorithm is used to search for missiles’ guidance sequences and improve crossover and mutation operations so as to reduce the production of infeasible solutions, and the multi-population strategy is introduced to improve the performance of DSMPNSGA-Ⅱ. The simulation results show that the DSMPNSGA-Ⅱ can obtain effective schemes of WTA and air-to-ground missile relay guidance, and that its solution quality is better than that of the single-population NSGA-Ⅱ and the multi-objective discrete particle swarm optimization (MODPSO) algorithm.

赵文飞 , 陈健 , 王 , 等 . 基于强化学习的海上要地群协同防空动态火力分配 [J ] . 兵工学报 , 2023 , 44 ( 11 ): 3516 - 3528 . DOI: 10.12382/bgxb.2022.1276 http://doi.org/10.12382/bgxb.2022.1276 针对海上要地群协同防空作战动态火力分配问题,综合分析海上要地防空作战过程的特点,建立基于马尔可夫决策模型的动态火力分配问题,构建以海上要地毁伤期望、拦截成本为指标的优化模型。考虑到马尔可夫决策模型求解易陷入维数灾难的问题,提出利用近似动态规划方法来探究解的有效性,并给出基于强化学习的最小二乘时序差分算法来求解该问题。通过4种典型的攻防场景共80个案例仿真结果表明,相比传统的匹配算法、遗传算法和粒子群优化算法,新构建的模型和算法更加科学合理有效,可为海上要地群协同防空作战火力分配提供一定的理论依据。

ZHAO W F , CHEN J , WANG Y , et al . Dynamic firepower allocation for cooperative air defense of strategic locations on the sea based on reinforcement learning [J ] . Acta Armamentarii , 2023 , 44 ( 11 ): 3516 - 3528 . (in Chinese) DOI: 10.12382/bgxb.2022.1276 http://doi.org/10.12382/bgxb.2022.1276 For the dynamic firepower allocation in the cooperative air defense operation of strategic locations on the sea, the characteristics of air defense operations in strategic locations on the sea are comprehensively analyzed to establish the dynamic firepower allocation problem based on the Markov decision model, and an optimization model with the damage expectation and interception cost as the indexes is constructed. Considering the problem that the Markov decision model is easy to fall into the disaster of dimensionality, an approximate dynamic programming method is proposed to explore the validity of the solution, and a least squares temporal difference algorithm based on reinforcement learning is given to solve the problem. The simulated results of 80 cases in four typical offensive and defensive scenarios show that, compared with the traditional matching algorithm, genetic algorithm and particle swarm optimization algorithm, the proposed model and algorithmin this paper are more scientific, reasonable and effective, which can provide a certain basis for the firepower allocation in the cooperative air defense operations of strategic locations on the sea.

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