基于遗传–模拟退火混合算法的烟幕干扰弹协同投放策略研究
Study on Cooperative Launch Strategy of Smoke Jamming Bombs Based on GA-SA Hybrid Algorithm
摘要: 现代战场精确制导武器威胁日益严峻,烟幕干扰凭借低成本、高效能优势成为重要防护手段,无人机协同投放可有效提升干扰效果,而传统经验策略难以适配复杂作战场景。本文围绕单弹遮蔽、单机优化、单机多弹、多机协同及多机多弹对抗多目标的递进式场景,构建量化优化模型开展研究。基于运动学与几何判定方法求解单弹基础遮蔽时长为1.39 s,经遗传算法优化后提升至4.68 s。采用时段并集计时法优化单机三弹投放策略,遮蔽时长可达6.45 s。引入关键阶段权重因子,依托GA-SA混合算法实现三机协同干扰,总遮蔽时长13.15 s,关键阶段覆盖率达89.5%。针对五机十五弹对抗三枚导弹的高维优化问题,通过分层优化求解,最终实现32.54 s的有效遮蔽时长,可为多机协同烟幕干扰策略制定提供技术支撑。
Abstract: In modern warfare, precision-guided weapons pose increasingly severe threats. Smoke jamming, leveraging its cost-effectiveness and high efficiency, has become an important defensive measure. Coordinated delivery by multiple UAVs can effectively enhance jamming performance, yet traditional experience-based strategies are inadequate for complex combat scenarios. This paper focuses on a progressive sequence of scenarios—single-bomb shielding, single-UAV optimization, single-UAV multi-bomb release, multi-UAV coordination, and multi-UAV multi-bomb countering multiple targets—and establishes quantitative optimization models for systematic investigation. Using kinematic equations and geometric judgment methods, the baseline shielding duration for a single smoke bomb is calculated as 1.39 s. After optimization via a genetic algorithm, this duration is extended to 4.68 s. A time-interval union timing method is adopted to optimize the release strategy for three smoke bombs from a single UAV, achieving a total shielding duration of 6.45 s. By introducing weighting factors for critical engagement phases and employing a GA-SA hybrid algorithm, three-UAV cooperative jamming achieves a total shielding duration of 13.15 s, with a critical phase coverage rate of 89.5%. For the high-dimensional optimization problem of five UAVs with fifteen smoke bombs against three incoming missiles, a hierarchical optimization method is employed to solve the problem, ultimately achieving an effective shielding duration of 32.54 s. This can provide technical support for the formulation of multi-UAV cooperative smoke jamming strategies.
文章引用:李沁航, 赵梓妤, 赵轲. 基于遗传–模拟退火混合算法的烟幕干扰弹协同投放策略研究[J]. 统计学与应用, 2026, 15(7): 336-352. https://doi.org/10.12677/sa.2026.157172

参考文献

[1] 王五, 陆毅. 数学建模方法与应用[M]. 北京: 高等教育出版社, 2022: 56-78.
[2] 薛鹏, 董文锋, 罗威. 烟幕对光电制导目标识别能力干扰效果研究[J]. 激光与红外, 2018, 48(3): 374-378.
[3] Liu, S.Y., Ruan, W.H., Qiu, L.K., Meng, W.L., Qin, X.T. and Shu, C.L. (2019) On-Line Distribution of Coordinated Attack Targets for Multi-Anti-Ship Missiles Based on Genetic Simulated Annealing Algorithm. 2019 Chinese Control and Decision Conference (CCDC), Nanchang, 3-5 June 2019, 1228-1233.
https://doi.org/10.1109/ccdc.2019.8833254
[4] 李浩民, 赵强, 王光源, 等. 无人机掩护岸舰导弹突防效果仿真分析[J]. 科学技术与工程, 2024, 24(8): 3459-3465.
[5] 宫华, 张勇, 许可, 等. 改进遗传算法的地对空防御武器系统多目标优化[J]. 兵器装备工程学报, 2022, 43(7): 87-95.
[6] Zheng, D., Zhang, Y., Li, F. and Cheng, P. (2023) UAVs Cooperative Task Assignment and Trajectory Optimization with Safety and Time Constraints. Defence Technology, 20, 149-161.
https://doi.org/10.1016/j.dt.2022.01.011
[7] Haupt, R.L. and Haupt, S.E. (2021) Practical Genetic Algorithms. 3rd Edition, Wiley, 91-105.
[8] 王凌, 郑金华. 模拟退火算法及其混合优化策略[M]. 北京: 清华大学出版社, 2018: 112-130.
[9] He, H., Huo, M., Duan, H., Deng, Y. and Wei, C. (2025) Distributed Cooperative Control of Human-UAV Swarm Based on State Observation. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 55, 7335-7345.
https://doi.org/10.1109/tsmc.2025.3584209
[10] Wang, Y., Li, K., Li, X., Wang, J. and Yu, P. (2025) Multi-UAV Cooperative Suspension Control Strategy Considering Variable Rope Length and Load Posture Coupling Effect. IEEE Access, 13, 69660-69676.
https://doi.org/10.1109/access.2025.3561954
[11] 赵军民, 聂聪, 常冠男, 等. 多约束条件下全捷联制导空地导弹弹道方案研究[J]. 西北工业大学学报, 2021, 39(1): 141-147.
[12] Muslimov, T.Z. and Munasypov, R.A. (2021) Multi-UAV Cooperative Target Tracking via Consensus-Based Guidance Vector Fields and Fuzzy MRAC. Aircraft Engineering and Aerospace Technology, 93, 1204-1212.
https://doi.org/10.1108/aeat-02-2021-0058
[13] Aminzadeh, A. and Khoshnood, A.M. (2023) Multi-UAV Cooperative Search and Coverage Control in Post-Disaster Assessment: Experimental Implementation. Intelligent Service Robotics, 16, 415-430.
https://doi.org/10.1007/s11370-023-00476-4
[14] Bai, C., Yan, P., Yu, X. and Guo, J. (2022) Learning-Based Resilience Guarantee for Multi-UAV Collaborative QoS Management. Pattern Recognition, 122, Article ID: 108166.
https://doi.org/10.1016/j.patcog.2021.108166
[15] Luo, D., Li, S., Shao, J., Xu, Y. and Liu, Y. (2022) Pigeon-Inspired Optimisation-Based Cooperative Target Searching for Multi-UAV in Uncertain Environment. International Journal of Bio-Inspired Computation, 19, 158-168.
https://doi.org/10.1504/ijbic.2022.123107
[16] Chen, X., Wan, Y., Qi, J., Zhao, Z., Ruan, Y. and Tang, J. (2025) A Bi-Subpopulation Coevolutionary Immune Algorithm for Multi-Objective Combinatorial Optimization in Multi-UAV Task Allocation. Complex & Intelligent Systems, 11, Article No. 149.
https://doi.org/10.1007/s40747-024-01720-9