贾永楠 , 田似营 , 李擎 . 无人机集群研究进展综述 [J ] . 航空学报 , 2020 , 41 ( 增刊1 ): 4 - 14 .

JIA Y N , TIAN S Y , LI Q . Recent development of unmanned aerial vehicle swarms [J ] . Acta Aeronautica et Astronautica Sinica , 2020 , 41 ( S1 ): 4 - 14 . (in Chinese)

NIU W , HUANG J Q , MIU L F . Research on the concept and key technologies of unmanned aerial vehicle swarm concerning naval attack [J ] . Command Control & Simulation , 2018 , 40 ( 1 ): 20 - 27 .

MAVROVOUNIOTIS M , LI C , YANG S . A survey of swarm intelligence for dynamic optimization: algorithms and applications [J ] . Swarm and Evolutionary Computation , 2017 , 33 : 1 - 17 . DOI: 10.1016/j.swevo.2016.12.005 http://doi.org/10.1016/j.swevo.2016.12.005 https://linkinghub.elsevier.com/retrieve/pii/S2210650216302541 https://linkinghub.elsevier.com/retrieve/pii/S2210650216302541

甄子洋 , 江驹 , 孙绍山 , 等 . 无人机集群作战协同控制与决策 [M ] . 北京 : 国防工业出版社 , 2022 : 1 - 35 .

ZHEN Z Y , JIANG J , SUN S S , et al . Cooperative control and decision of UAV operations [M ] . Beijing : National Defense Industry Press , 2022 : 1 - 35 . (in Chinese)

贾高伟 , 王建峰 . 无人机集群任务规划方法研究综述 [J ] . 系统工程与电子技术 , 2019 , 43 ( 1 ): 99 - 111 .

JIA G W , WANG J F . Research review of UAV swarm mission planning method [J ] . Systems Engineering and Electronics , 2021 , 43 ( 1 ): 99 - 111 . (in Chinese)

DHEIN G , NETO A F K , DE ARAÚJO O C B . The multiple traveling salesman problem with backup coverage [J ] . Electronic Notes in Discrete Mathematics , 2018 , 66 : 135 - 142 . DOI: 10.1016/j.endm.2018.03.018 http://doi.org/10.1016/j.endm.2018.03.018 https://linkinghub.elsevier.com/retrieve/pii/S1571065318300647 https://linkinghub.elsevier.com/retrieve/pii/S1571065318300647

MINH A N , GIANG T D , MINH H H , et al . The mincost parallel drone scheduling vehicle routing problem [J ] . European Journal of Operational Research , 2021 , 229 ( 3 ): 910 - 930 .

AFONSO R , MAXIMO M , GALVĀO R . Task allocation and trajectory planning for multiple agents in the presence of obstacle and connectivity constraints with mixed-integer linear programming [J ] . International Journal of Robust and Nonlinear Control , 2020 , 30 ( 14 ): 5464 - 5491 . DOI: 10.1002/rnc.v30.14 http://doi.org/10.1002/rnc.v30.14 https://onlinelibrary.wiley.com/toc/10991239/30/14 https://onlinelibrary.wiley.com/toc/10991239/30/14

KONG X Q , LU N , LI B . Optimal scheduling for unmanned aerial vehicle networks with flow-level dynamics [J ] . IEEE Transactions on Mobile Computing , 2021 , 20 ( 3 ): 1186 - 1197 . DOI: 10.1109/TMC.7755 http://doi.org/10.1109/TMC.7755 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7755 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7755

朱云冲 , 梁彦刚 , 黎克波 , 等 . 基于PSO和RRT的智能弹群任务分配算法 [J/OL ] . 航空学报 , 2022 .( 2022 - 07 - 12 ) [ 2022 - 08 - 22 ] . http://kns.cnki.net/kcms/detail/11.1929.V.20220710.1634.028.html http://kns.cnki.net/kcms/detail/11.1929.V.20220710.1634.028.html http://kns.cnki.net/kcms/detail/11.1929.V.20220710.1634.028.html .

ZHU Y C , LIANG Y G , LI K B , et al . Algorithm to solve the task assignment problem of intelligent missile swarm based on PSO and RRT [J/OL ] . Acta Aeronautica et Astronautica Sinica , 2022 . ( 2022 - 07 - 12 ) [ 2022 - 08 - 22 ] . http://kns.cnki.net/kcms/detail/11.1929.V.20220710.1634.028.html http://kns.cnki.net/kcms/detail/11.1929.V.20220710.1634.028.html http://kns.cnki.net/kcms/detail/11.1929.V.20220710.1634.028.html . (in Chinese)

李桂亮 , 毕海洋 , 洪雪健 , 等 . 基于DE-DPSO-GT-SA算法的协同多任务分配 [J ] . 北京航空航天大学学报 , 2021 , 47 ( 1 ): 90 - 96 .

LI G L , BI H Y , HONG X J , et al . Cooperative multi-task assignment based on DE-DPSO-GT-SA algorithm [J ] . Journal of Beijing University of Aeronautics and Astronautics , 2021 , 47 ( 1 ): 90 - 96 . (in Chinese)

CHEN Y B , YANG D , YU J Q . Multi-UAV task assignment with parameter and time-sensitive uncertainties using modified two-part wolf pack search algorithm [J ] . IEEE Transactions on Aerospace and Electronic Systems , 2018 , 54 ( 6 ): 2853 - 2872 . DOI: 10.1109/TAES.2018.2831138 http://doi.org/10.1109/TAES.2018.2831138 https://ieeexplore.ieee.org/document/8351958/ https://ieeexplore.ieee.org/document/8351958/

WANG Z , LIU L , LONG T , et al . Multi-UAV reconnaissance task allocation for heterogeneous targets using an opposition based genetic algorithm with double-chromosome encoding [J ] . Chinese Journal of Aeronautics , 2018 , 31 ( 2 ): 339 - 350 . DOI: 10.1016/j.cja.2017.09.005 http://doi.org/10.1016/j.cja.2017.09.005 https://linkinghub.elsevier.com/retrieve/pii/S1000936117302224 https://linkinghub.elsevier.com/retrieve/pii/S1000936117302224

JIA Z Y , YU J Q , AI X L , et al . Cooperative multiple task assignment problem with stochastic velocities and time windows for heterogeneous unmanned aerial vehicles using a genetic algorithm [J ] . Aerospace Science and Technology , 2018 , 76 : 112 - 125 . DOI: 10.1016/j.ast.2018.01.025 http://doi.org/10.1016/j.ast.2018.01.025 https://linkinghub.elsevier.com/retrieve/pii/S1270963817301220 https://linkinghub.elsevier.com/retrieve/pii/S1270963817301220

XIA C , LIANG Y T , YUAN L Y , et al . Cooperative task assignment and track planning for multi-UAV attack mobile targets [J ] . Journal of Intelligent & Robotic Systems , 2020 , 100 ( 3 ): 1383 - 1400 .

WANG J Q , ZHANG M X , SONG H H , et al . Improvement and application of hybrid firefly algorithm [J ] . IEEE Access , 2019 , 7 : 165458 - 165477 . DOI: 10.1109/ACCESS.2019.2952468 http://doi.org/10.1109/ACCESS.2019.2952468 Aiming at the problem of poor global search ability and slow convergence speed when solving optimization problems, this paper proposes improved hybrid firefly algorithm (HFA). HFA improves the position updating method, mutation strategy, chaotic search method and evolution strategy of the population. Specifically, the improved position update formula considers both the effect of high-brightness fireflies on position-updated fireflies, and the effects of the optimal firelfy on position-updated fireflies. At the same time, a method of adaptive adjustment parameters in the position update formula is presented, which makes the position update method exhibit strong global search ability and local search ability in the initial stage and the later stage of iteration, respectively. In addition, a combined mutation operator is introduced into HFA, which effectively takes the local search and global search ability of the algorithm into account. Since chaotic search exhibits good ergodicity, an operation of randomly moving all fireflies in the population according to chaotic search is given, which enhances the ability of the algorithm to traverse the whole search space, and further improves the global search ability of the algorithm. To verify the effectiveness of HFA, 28 CEC2017 test problems are selected. The calculation results of 28 CEC2017 test problems show that compared with other algorithms, the accuracy of HFA is obviously better than that of other algorithms. Finally, HFA and other intelligent optimization methods in the literatures are used to optimize the structural parameters of cantilever beams. The optimization results show that the weight of the cantilever beam obtained by HFA is obviously smaller than other algorithms. The calculation results of CEC2017 test problems and practical problem show that the solving quality of HFA is obviously better than other algorithms.

WANG M , MA T M , LI G L , et al . Ant colony optimization with an improved pheromone model for solving MTSP with capacity and time window constraint [J ] . IEEE Access , 2020 , 8 : 106872 - 106879 . DOI: 10.1109/Access.6287639 http://doi.org/10.1109/Access.6287639 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639

KIM K S , KIM H Y , CHOI H L . A bid-based grouping method for communication-efficient decentralized multi-UAV task allocation [J ] . International Journal of Aeronautical and Space Sciences , 2020 , 21 ( 1 ): 290 - 302 . DOI: 10.1007/s42405-019-00205-1 http://doi.org/10.1007/s42405-019-00205-1

SUJIT P , GEORGE J , BEARD R . Multiple UAV task allocation using particle swarm optimization [C ] // Proceedings of AIAA Guidance, Navigation and Control Conference and Exhibit. Honolulu, HI, US:AIAA , 2008 : 6837 .

刘重 , 高晓光 , 符小卫 , 等 . 未知环境下异构多无人机协同搜索打击中的联盟组建 [J ] . 兵工学报 , 2015 , 36 ( 12 ): 2284 - 2297 . DOI: 10.3969/j.issn.1000-1093.2015.12.011 http://doi.org/10.3969/j.issn.1000-1093.2015.12.011 为了提高多架异构无人机在未知环境下协同执行搜索打击任务时的效能，提出了一种未知环境下的异构多无人机协同搜索打击中的联盟组建方法，研究了实时性较高且适应于未知环境下的任务分配机制。以最小化目标打击时间和最小化联盟规模为优化指标，以满足同时打击和资源需求为约束条件，建立了联盟组建模型；为了提高联盟组建的实时性，提出了一种分阶次优联盟快速组建算法(MSOCFA)。算法复杂度分析说明了该算法是一个多项式时间算法，并且通过与粒子群优化算法进行仿真对比，验证了该算法具有较低的计算复杂度，满足实时性要求。为了使得多架无人机能自主协同完成搜索打击任务，设计了基于有限状态机(FSM)的多无人机分布式自主协同控制策略。仿真验证了未知环境下的异构多无人机协同搜索打击中的联盟组建方法的合理性和可行性。使用蒙特卡洛法验证了无人机数量和目标数量对联盟组建的影响，即无人机数量越多，目标数量越少，其平均任务完成时间越短。 为了提高多架异构无人机在未知环境下协同执行搜索打击任务时的效能，提出了一种未知环境下的异构多无人机协同搜索打击中的联盟组建方法，研究了实时性较高且适应于未知环境下的任务分配机制。以最小化目标打击时间和最小化联盟规模为优化指标，以满足同时打击和资源需求为约束条件，建立了联盟组建模型；为了提高联盟组建的实时性，提出了一种分阶次优联盟快速组建算法(MSOCFA)。算法复杂度分析说明了该算法是一个多项式时间算法，并且通过与粒子群优化算法进行仿真对比，验证了该算法具有较低的计算复杂度，满足实时性要求。为了使得多架无人机能自主协同完成搜索打击任务，设计了基于有限状态机(FSM)的多无人机分布式自主协同控制策略。仿真验证了未知环境下的异构多无人机协同搜索打击中的联盟组建方法的合理性和可行性。使用蒙特卡洛法验证了无人机数量和目标数量对联盟组建的影响，即无人机数量越多，目标数量越少，其平均任务完成时间越短。

LIU Z , GAO X G , FU X W , et al . Coalition formation of multiple heterogeneous unmanned aerial vehicles in cooperative search and attack in unknown environment [J ] . Acta Armamentarii , 2015 , 36 ( 12 ): 2284 - 2297 . (in Chinese)

符小卫 , 魏可 , 李斌 , 等 . 基于联盟的无人机集群编队控制方法 [J ] . 系统工程与电子技术 , 2019 , 41 ( 11 ): 2559 - 2572 .

FU X W , WEI K , LI B , et al . Formation control method of UAV cluster based on alliance [J ] . Systems Engineering and Electronics , 2019 , 41 ( 11 ): 2559 - 2572 . (in Chinese)

ZHEN Z Y , WEN L D , WANG B L , et al . Improved contract network protocol algorithm based cooperative target allocation of heterogeneous UAV swarm [J ] . Aerospace Science and Technology , 2021 , 119 ( 6 ): 107054 . DOI: 10.1016/j.ast.2021.107054 http://doi.org/10.1016/j.ast.2021.107054 https://linkinghub.elsevier.com/retrieve/pii/S1270963821005642 https://linkinghub.elsevier.com/retrieve/pii/S1270963821005642

SUJIT P B , MANATHARA J G , GHOSE D , et al . Decentralized multi-UAV coalition formation with limited communication ranges [M ] . VALAVANIS K P, VACHTSEVANOS G J. Handbook of unmanned aerial vehicles . Dordrecht, the Netherlands : Springer , 2014 : 2021 - 2048 .

陈璞 , 严飞 , 刘钊 , 等 . 通信约束下异构多无人机任务分配方法 [J ] . 航空学报 , 2021 , 42 ( 8 ): 313 - 326 .

CHEN P , YAN F , LIU Z , et al . Heterogeneous unmanned aerial vehicles task allocation with communication constraints [J ] . Acta Aeronautica et Astronautica Sinica , 2021 , 42 ( 8 ): 313 - 326 . (in Chinese)

DENG Q B , YU J Q , WANG N F . Cooperative task assignment of multiple heterogeneous unmanned aerial vehicles using a modified genetic algorithm with multi-type genes [J ] . Chinese Journal of Aeronautics , 2013 , 26 ( 5 ): 1238 - 1250 . DOI: 10.1016/j.cja.2013.07.009 http://doi.org/10.1016/j.cja.2013.07.009 https://linkinghub.elsevier.com/retrieve/pii/S1000936113001453 https://linkinghub.elsevier.com/retrieve/pii/S1000936113001453

WU W N , WANG X G , CUI N G . Fast and coupled solution for cooperative mission planning of multiple heterogeneous unmanned aerial vehicles [J ] . Aerospace Science and Technology , 2018 , 79 : 131 - 144 . DOI: 10.1016/j.ast.2018.05.039 http://doi.org/10.1016/j.ast.2018.05.039 https://linkinghub.elsevier.com/retrieve/pii/S1270963817306934 https://linkinghub.elsevier.com/retrieve/pii/S1270963817306934

吴钟博 , 易建强 . 无人机编队支撑网络的协同通信中继策略 [J ] . 航空学报 , 2020 , 41 ( 增刊2 ): 187 - 194 .

WU Z B , YI J Q . Cooperative communication relay selection method for UAV formation support networks [J ] . Acta Aeronautica et Astronautica Sinica , 2020 , 41 ( S2 ): 187 - 194 . (in Chinese)

陈清阳 , 辛宏博 , 王玉杰 , 等 . 一种多机协同打击的快速航迹规划方法 [J ] . 北京航空航天大学学报 , 2019 , 48 ( 7 ): 1145 - 1153 .

CHEN Q Y , XIN H B , WANG Y J , et al . A rapid path planning method for multiple UAVs to cooperative strike [J ] . Journal of Beijing University of Aeronautics and Astronautics , 2019 , 48 ( 7 ): 1145 - 1153 . (in Chinese)

苏菲 , 陈岩 , 沈林成 . 基于蚁群算法的无人机协同多任务分配 [J ] . 航空学报 , 2008 , 29 ( 增刊 ): 184 - 191 .

SU F , CHEN Y , SHEN L C . UAV cooperative multi-task assignment based on ant colony algorithm [J ] . Acta Aeronautica et Astronautica Sinica , 2008 , 29(S) : 184 - 191 . (in Chinese)