基于改进粒子群优化和Stackelberg博弈的武器部署

刘富樯; 刘中阳; 周伦; 皮阳军; 蒲华燕; 罗均

doi:10.16383/j.aas.c240257

基于改进粒子群优化和Stackelberg博弈的武器部署

doi: 10.16383/j.aas.c240257 cstr: 32138.14.j.aas.c240257

刘富樯^{1, 2,},
刘中阳^{1, 2,},
周伦^{1, 2,},
皮阳军^{1, 2,},
蒲华燕^{1, 2,},
罗均^{1, 2,}

1.
重庆大学机械与运载工程学院重庆 400044
2.
重庆大学高端装备机械传动全国重点实验室重庆 400044

基金项目: 国家自然科学基金(62033001), 重庆市技术创新与应用发展重点项目(CSTB2023TIAD-KPX0057) 资助

详细信息

作者简介:
刘富樯：重庆大学机械与运载工程学院副教授. 2015年获得西北工业大学博士学位. 他的主要研究方向为机器人系统设计, 博弈决策与容错控制. 本文通信作者. E-mail: liufq@cqu.edu.cn

刘中阳：重庆大学机械与运载工程学院硕士. 2021年获得吉林大学学士学位. 他的主要研究方向为智能设备决策规划. E-mail: liuzhongyang0323@163.com

周伦：重庆大学机械与运载工程学院博士研究生. 2020年获得石河子大学硕士学位. 他的主要研究方向为智能设备决策规划和深度强化学习. E-mail: Lunz0630@163.com

皮阳军：重庆大学机械与运载工程学院教授. 2010年获得浙江大学博士学位. 他的主要研究方向为分布式参数系统的控制, 智能无人系统和振动控制. E-mail: cqpp@cqu.edu.cn

蒲华燕：重庆大学机械与运载工程学院教授. 2011年获得华中科技大学博士学位. 她的主要研究方向为智能无人系统, 振动控制和机器人学. E-mail: phygood_2001@shu.edu.cn

罗均：重庆大学机械与运载工程学院教授. 2000年获得上海交通大学博士学位. 他的主要研究方向为包括人工智能, 传感技术, 智能无人系统和特种机器人. E-mail: luoj@cqu.edu.cn

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- 文章访问数: 17
- HTML全文浏览量: 20
- 被引次数: 0
出版历程
- 收稿日期: 2024-05-10
- 录用日期: 2025-02-08
- 网络出版日期: 2025-03-16

Weapon Deployment Based on Improved Particle Swarm Optimization and Stackelberg Game

LIU Fu-Qiang^{1, 2
,},
LIU Zhong-Yang^{1, 2
,},
ZHOU Lun^{1, 2
,},
PI Yang-Jun^{1, 2
,},
PU Hua-Yan^{1, 2
,},
LUO Jun^{1, 2
,}

1.
College of Mechanical and Vehicle Engineering, Chongqing University, Chongqing 400044
2.
State Key Laboratory of Mechanical Transmission for Advanced Equipment, Chongqing 400044

Funds: Supported by National Natural Science Foundation of China (62033001) and Key Project of Technological Innovation and Application Development of Chongqing (CSTB2023TIAD-KPX0057)

More Information

Author Bio:
LIU Fu-Qiang　Associate professor at the College of Mechanical and Vehicle Engineering, Chongqing University. He received his Ph.D. degree from Northwestern Polytechnical University in 2015. His research interest covers robotic system design, game decision making, and fault-tolerant control. Corresponding author of this paper

LIU Zhong-Yang　Master student at the College of Mechanical and Vehicle Engineering, Chongqing University. He received his bachelor degree from the Jilin University in 2021. His main research interest is intelligent equipment decision planning

ZHOU Lun　Ph.D. candidate at the College of Mechanical and Vehicle Engineering, Chongqing University. He received his master degree from Shihezi University in 2023. His research interest covers intelligent equipment decision planning and deep reinforcement learning

PI Yang-Jun　Professor at the College of Mechanical and Vehicle Engineering, Chongqing University. He received his Ph.D. degree from Zhejiang University in 2010. His research interest covers control of distributed parameter systems, intelligent unmanned systems, and vibration control

PU Hua-Yan　Professor at the College of Mechanical and Vehicle Engineering, Chongqing University. She received her Ph.D. degree from Huazhong University of Science and Technology in 2011. Her research interest covers intelligent unmanned system, vibration controlling, and robotics

Luo Jun　Professor at the College of Mechanical and Vehicle Engineering, Chongqing University. He received his Ph.D. degree from Shanghai Jiao Tong University in 2000. His research interest covers artiffcial intelligence, sensing technology, intelligent unmanned systems, and special robotics

摘要

摘要: 为应对来袭目标的机动调整对防区防御能力的影响, 针对性设计全新的部署优化模型和求解算法. 首先, 从战术层面出发, 提出一种考虑攻防信息变化的新型武器部署模型, 该模型能够动态调整部署策略以提高防御系统的整体效能; 其次, 设计基于混沌映射机制和$K$均值聚类与重心法的算法初始化方案, 以应对资源紧缺和充足两种情况, 降低算法陷入局部最优的风险; 然后, 设计基于Metropolis准则的个体最优更新方法和基于Stackelberg博弈模型的全局最优更新方法用以指导种群的进化方向; 最后, 通过提供多规模场景仿真实验, 验证了新模型和所提算法的有效性, 对比实验结果表明, 新模型能够更准确地反映部署方案之间的差异, 所提算法在求解质量与收敛性方面均有显著提高.
- 武器部署 /
- Stackelberg博弈 /
- 粒子群算法 /
- K均值聚类 /
- 重心法
Abstract: In order to cope with the impact of incoming target's maneuvering adjustment on the defensive capability of the defense zone, a new deployment optimization model and a solution algorithm are designed. Firstly, at the tactical level, a new weapon deployment model is proposed that takes into account changes in offensive and defensive information, allowing for dynamic adjustment of the deployment strategy to improve the overall effectiveness of the defense system; Secondly, an initialization scheme for the algorithm, based on chaotic mapping mechanism and $K$-means clustering and center-of-gravity method, is designed to cope with both limited and ample resources, reducing the risk of the algorithm falling into local optima; Then, an individual optimal renewal method based on the Metropolis criterion and a global optimal renewal method based on the Stackelberg game model are designed to guide the evolutionary directions of the population; Finally, the effectiveness of the new model and the proposed algorithm is verified through multi-scale scenario simulation experiments. The results of the comparative experiments show that the new model reflects deployment scheme differences more accurately and the proposed algorithm significantly improves the solution quality and convergence.
- Weapon deployment /
- Stackelberg game /
- particle swarm optimization /
- K-means clustering /
- centre-of-gravity method

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图 1 投弹线

Fig. 1 Bombing lines

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图 2 火力重叠

Fig. 2 Firepower overlap

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图 3 初始化种群方法框架

Fig. 3 Framework for population initialization methods

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图 4 场景1进攻路径规划结果

Fig. 4 Path planning results in the scenario 1

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图 6 场景3进攻路径规划结果

Fig. 6 Path planning results in the scenario 3

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图 5 场景2进攻路径规划结果

Fig. 5 Path planning results in the scenario 2

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图 7 三种场景下防御部署方案适应度值收敛曲线

Fig. 7 Convergence curves of fitness values for defence deployment schemes in three scenarios

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图 8 两种部署模型评价指标值对比

Fig. 8 Comparison of the evaluation indicator values of two deployment models

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表 1 最优进攻路径代价对比

Table 1 Comparison of optimal attack path costs

仿真实例	对比指标	PSO	AGAPSO	SSGWO	IPSO
规模场景1	最大值	87.9157	90.1453	83.7577	81.1419
	最小值	84.7922	85.7749	79.3922	78.6324
	平均值	85.9452	87.0357	81.1712	79.4218
	均方差	6.3320	6.9340	7.0318	7.8558
规模场景2	最大值	84.1190	72.7094	72.0462	71.9816
	最小值	79.1262	70.2760	70.4387	70.1361
	平均值	82.4984	71.6797	71.1869	70.8235
	均方差	3.9597	3.6551	4.4898	3.9926
规模场景3	最大值	53.3404	52.7513	52.6991	52.6948
	最小值	51.2769	51.2769	51.2769	51.2769
	平均值	52.8909	51.9593	51.9407	51.9171
	均方差	1.3500	2.8143	2.2543	1.9502

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表 2 各算法计算时间对比

Table 2 Comparison of computation time

算法	规模场景1	规模场景2	规模场景3
PSO	0.6864	0.8446	0.9469
AGAPSO	0.6314	0.8430	0.9308
SSGWO	0.6437	0.8236	0.9107
IPSO	0.6357	0.7909	0.8991

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表 3 两种模型在对比模型评价指标中的差异

Table 3 Differences between two models in comparing model evaluation indicators

规模	组别	评价指标均值	平均值差	t	显著性
场景1	对比模型	0.5927	0.0288	−1.6265	0.1212
场景1	本文模型	0.6215	0.0288	−1.6265	0.1212
场景2	对比模型	0.6438	0.0088	0.3301	0.7451
场景2	本文模型	0.6350	0.0088	0.3301	0.7451
场景3	对比模型	0.7500	0.0036	−0.9334	0.3629
场景3	本文模型	0.7536	0.0036	−0.9334	0.3629

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表 4 两种模型在本文模型评价指标中的差异

Table 4 Differences between two models in the model evaluation indicators of this paper

规模	组别	评价指标均值	平均值差	t	显著性
场景1	对比模型	75.5000	3.5126	−2.4348	0.0255*
场景1	本文模型	79.0126	3.5126	−2.4348	0.0255*
场景2	对比模型	73.4573	2.6694	2.2003	0.0411*
场景2	本文模型	76.1267	2.6694	2.2003	0.0411*
场景3	对比模型	63.1573	1.9786	−1.7206	0.1025
场景3	本文模型	65.1359	1.9786	−1.7206	0.1025

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