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张进 , 郭浩 , 陈统 . 基于可适应匈牙利算法的武器-目标分配问题 [J ] . 兵工学报 , 2021 , 42 ( 6 ): 1339 - 1344 . DOI: 10.3969/j.issn.1000-1093.2021.06.025 http://doi.org/10.3969/j.issn.1000-1093.2021.06.025 当前各类智能优化算法求解武器-目标分配问题时，存在耗时长、优化结果不唯一等缺陷，而匈牙利算法具有耗时短、求解结果稳定的优势，但其适应性较差，目前尚未见二者的对比分析文献。针对此现象，对比分析传统匈牙利算法与智能优化算法的耗时性与稳定性，展现了匈牙利算法的优势；提出统一效率矩阵，创建可适用于所有类型目标分配问题的可适应匈牙利算法；通过实例应用验证了可适应匈牙利算法的正确性。

ZHANG J , GUO H , CHEN T . Weapon-target assignment based on adaptable hungarian algorithm [J ] . Acta Armamentarii , 2021 , 42 ( 6 ): 1339 - 1344 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2021.06.025 http://doi.org/10.3969/j.issn.1000-1093.2021.06.025 When various intelligent optimization algorithms are used to solve the weapon-target assignment problem, they have the disadvantages of long time-consuming and non-unique optimization results. Hungary algorithm has the advantages of short time-consuming and stable optimization results, but its adaptability is poor. Currently, the comparison and analysis of intelligent optimization algorithms and Hungarian algorithm has not been reported. For this phenomenon, the time-consuming and stability of traditional Hungarian algorithm and intelligent optimization algorithms are compared, which shows the advantages of Hungarian algorithm. An adaptable Hungarian algorithm that can be applied to all types of weapon-target assignment problems is established by proposing a unified efficiency matrix. And then some examples are used to verify the correctness of the adaptable Hungarian algorithm.

KLINE A , AHNER D , HILL R . The weapon-target assignment problem [J ] . Computers & Operations Research , 2019 , 105 : 226 - 236 . DOI: 10.1016/j.cor.2018.10.015 http://doi.org/10.1016/j.cor.2018.10.015 https://linkinghub.elsevier.com/retrieve/pii/S0305054818302740 https://linkinghub.elsevier.com/retrieve/pii/S0305054818302740

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苗李达 , 姜青山 . 基于毁伤积累的武装直升机对地火力分配 [J ] . 火力与指挥控制 , 2018 , 43 ( 5 ): 167 - 171 .

MIAO L D , JIANG Q S . Armed helicopter-to-ground attack firepower distribution based on damage accumulation [J ] . Fire Control & Command Control , 2018 , 43 ( 5 ): 167 - 171 . (in Chinese)

AHUJA R K , KUMAR A , JHA K . Exact and heuristic algorithms for the weapon-target assignment problem [J ] . Operations Research , 2007 , 55 ( 6 ): 1136 - 1146 . DOI: 10.1287/opre.1070.0440 http://doi.org/10.1287/opre.1070.0440 https://pubsonline.informs.org/doi/10.1287/opre.1070.0440 https://pubsonline.informs.org/doi/10.1287/opre.1070.0440

夏维 , 刘新学 , 范阳涛 , 等 . 基于改进型多目标粒子群优化算法的武器-目标分配 [J ] . 兵工学报 , 2016 , 37 ( 11 ): 2085 - 2093 . DOI: 10.3969/j.issn.1000-1093.2016.11.017 http://doi.org/10.3969/j.issn.1000-1093.2016.11.017 在作战中武器-目标分配(WTA)问题包含众多的变量，是典型的非确定性多项式完全问题。针对毁伤效能最大和用弹量最少两个目标函数，建立了基于改进型多目标粒子群优化(MOPSO-Ⅱ)算法的WTA模型。由于粒子群优化算法存在“维数灾难”瓶颈，应用了变量随机分解策略和合作协同进化框架，按照带精英策略的非支配排序遗传(NSGA-Ⅱ)算法中的排序方法对粒子群编码数据进行非支配排序。通过实例仿真分析，结果表明MOPSO-Ⅱ算法比NSGA-Ⅱ算法具有更好的求解精度与运行效率，能够获得满意的分配结果，且计算快速有效，比较适合较大规模的WTA问题实时求解。在作战中武器-目标分配(WTA)问题包含众多的变量，是典型的非确定性多项式完全问题。针对毁伤效能最大和用弹量最少两个目标函数，建立了基于改进型多目标粒子群优化(MOPSO-Ⅱ)算法的WTA模型。由于粒子群优化算法存在“维数灾难”瓶颈，应用了变量随机分解策略和合作协同进化框架，按照带精英策略的非支配排序遗传(NSGA-Ⅱ)算法中的排序方法对粒子群编码数据进行非支配排序。通过实例仿真分析，结果表明MOPSO-Ⅱ算法比NSGA-Ⅱ算法具有更好的求解精度与运行效率，能够获得满意的分配结果，且计算快速有效，比较适合较大规模的WTA问题实时求解。

XIA W , LIU X X , FAN Y T , et al . Weapon-target assignment with an improved multi-objective particle swarm optimization algorithm [J ] . Acta Armamentarii , 2016 , 37 ( 11 ): 2085 - 2093 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2016.11.017 http://doi.org/10.3969/j.issn.1000-1093.2016.11.017 Weapon-target assignment (WTA) with numerous variables in modern campaign is a typical non-deterministic polynomial (NP) complete problem. An optimization model based on improved multi-objective swarm optimization algorithm (MOPSO-II) is established to solve the objective functions of maximum damage probability and minimum ammunition consumption. Since “curse of dimensionality” occurs in the objective swarm optimization algorithm (PSO), the random variable decomposition strategy and cooperative co-evolution evolutionary frame are used for variable decomposition, and also all swarms are composited by using the non-dominated set algorithm in NSGA-II. The simulated results show that MOPSO-II is quicker and more effective than NSGA-II, and can give good WTA quickly, especially when the scale of WTA problem is large.

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 http://doi.org/10.3969/j.issn.1000-1093.2016.10.016 对地打击目标与武器类型复杂多样，其武器-目标分配问题难度较大，研究不足，而合理的武器-目标分配方案，可优化资源配置，用最小的代价获取最大的战场收益。为此，构建相应数学模型，并针对采用遗传算法进行解算时收敛速度慢，甚至无法得出可行解等问题，设计了一种变量取值控制方法。该方法通过约束和控制初始种群个体中变量的取值范围来缩小搜索空间，提高搜索效率；通过改进变异策略扩大变量取值范围，确保解的质量。仿真结果表明，改进的遗传算法能有效地解决大规模对地打击武器-目标分配问题，且性能较优。

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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 .

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孙海文 , 谢晓方 , 庞威 , 等 . 基于改进火力分配模型的综合防空火力智能优化分配 [J ] . 控制与决策 , 2020 , 35 ( 5 ): 1102 - 1112 .

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BOGDANOWICZ Z R , TOLANO A , PATEL K , et al . Optimization of weapon-target pairings based on kill probabilities [J ] . IEEE Transactions on Cybernetics , 2013 , 43 ( 6 ): 1835 - 1844 . DOI: 10.1109/TSMCB.2012.2231673 http://doi.org/10.1109/TSMCB.2012.2231673 In this paper, we present a novel optimization algorithm for assigning weapons to targets based on desired kill probabilities. For the given weapons, targets, and desired kill probabilities, our optimization algorithm assigns weapons to targets that satisfy the desired kill probabilities and minimize the overkill. The minimization of overkill assures that any proper subset of the weapons assigned to a target results in a kill probability that is less than the desired kill probability on such a target. Computational results for up to 120 weapons and 120 targets indicate that the performance of this algorithm yields an average improvement in quality of solutions of 26.8% over the greedy algorithms, whereas execution times remained on the order of milliseconds.

刘海鸥 , 晋磊 , 董诗瑾 , 等 . 重型自动机械变速车辆换挡序列优化 [J ] . 兵工学报 , 2015 , 36 ( 8 ): 1377 - 1383 . DOI: 10.3969/j.issn.1000-1093.2015.08.001 http://doi.org/10.3969/j.issn.1000-1093.2015.08.001 重型车辆在动力性和燃油经济性上有较大的提升空间。分析了配备自动机械变速器（AMT）的重型车辆换挡动力中断特性，在此基础上建立了AMT重型车辆整车模型，并利用动态规划（DP）求解出重型车辆在确定道路下的最优综合性能换挡序列。计算对比原有换挡规律和DP决策下的车辆运行性能，仿真结果表明，通过调整运行耗时和燃油消耗量的加权因子，可以获得兼备动力性和燃油经济性的综合性能最优换挡序列，在保证AMT重型车辆动力性的前提下改善了燃油经济性，对AMT重型车辆的自动控制具有指导意义。

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冯睽睽 , 张发平 , 王武宏 , 等 . 基于非支配排序遗传算法的涡轮发动机转子系统装配参数优化 [J ] . 兵工学报 , 2021 , 42 ( 5 ): 1092 - 1100 . DOI: 10.3969/j.issn.1000-1093.2021.05.022 http://doi.org/10.3969/j.issn.1000-1093.2021.05.022 为探究保障转子系统高温动平衡的最佳装配参数方法，掌握高温下动平衡的变化规律，提出转子系统各零件装配角矩阵的优化确定方法。基于高温工况下热-结构动平衡理论模型和零件材料特性随温度的非线性变化规律，建立转子系统动平衡随温度变化的解析方程；根据不同装配参数下系统不平衡量和偏移扭矩的差异，把高温动平衡优化问题转换为多目标多变量的优化问题，给出基于非支配排序遗传算法的解决方案；以某弹用涡轮发动机高压转子系统装配为例，在600 ℃工作环境下对所提方法进行验证，得到该工况下零件最佳装配角矩阵，以及最小化温度对转子系统动平衡的变化量影响，改善了装配质量特性。结果表明，零件装配角对高温工况下转子系统动平衡变化有很大的影响，通过装配参数优化可显著减少高温工况对多零件转子系统动平衡的影响。

FENG K K , ZHANG F P , WANG W H , et al . Assembly process parameters optimization of turbine engine rotor system based on non-dominated sorting genetic algorithm [J ] . Acta Armamentarii , 2021 , 42 ( 5 ): 1092 - 1100 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2021.05.022 http://doi.org/10.3969/j.issn.1000-1093.2021.05.022 An optimization determination method of different matrices of assembly angle was proposed to explore the optimal method for assembly process parameters to guarantee the dynamic balance of rotor system and grasp the changing law of dynamic balance at high temperature. According to the thermal-structure dynamic balance theory model at high temperature and the nonlinear change of material characteristics with temperature, a analytical equation is established for calculating the temperature change of dynamic balance of rotor system with temperature at high temperature. Then, according to the difference between system unbalance and offset torque under the different assembly parameters, the NSGA-Ⅱbased solution is presented by converting the high temperature dynamic balance optimization into multi-objective and multivariable optimization. Taking the assembly of high-pressure rotor system of a missile turbine engine as an example, the proposed method was verified in 600 ℃ working environment, and the optimal assembly angle matrix was obtained, which minimizes the influence of high temperature on the dynamic balance of rotor system and improves the assembly quality. The results show that the assembly angles have great influence on the dynamic balance of rotor system at high temperature, and the influence of high temperature conditions on the dynamic balance of multi-part rotor system can be significantly reduced through the optimization of assembly parameters.

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