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Journal of ZheJiang University (Engineering Science)  2025, Vol. 59 Issue (8): 1698-1707    DOI: 10.3785/j.issn.1008-973X.2025.08.017
    
Improved slime mould bee colony algorithm for multi-UAVs cooperative path planning
Hui XIONG1,2(),Banglu GE1,2,Jinzhen LIU1,2,Jiaxing WANG3
1. School of Control Science and Engineering, Tiangong University, Tianjin 300387, China
2. Tianjin Key Laboratory of Intelligent Control of Electrical Equipment, Tiangong University, Tianjin 300387, China
3. Shenyang Aircraft Design and Research Institute, Aviation Industry Corporation of China, Shenyang 110000, China
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Abstract  

An improved slime mold algorithm with artificial bee colony (ISMABC) was proposed aiming at the problem of cooperative path planning for multiple unmanned aerial vehicles (UAVs). A path planning cost model was established, and the path planning problem in a three-dimensional environment was transformed into an optimization problem by introducing a fitness function and constraint conditions, which was solved by the proposed algorithm to obtain the optimal path. The slime mold algorithm was improved by employing the good point set strategy and a nonlinear convergence factor. Then the population diversity was increased, and the convergence speed of the algorithm was accelerated. An elite opposition-based learning strategy was applied to the global best individual in order to enhance population quality. A global best position guidance was introduced based on the exploration capability of the artificial bee colony in order to improve the exploitation capability of the slime mold algorithm. Comparative analysis of optimization on 14 test functions and some functions from the CEC2017 test suite showed that the optimization ability and convergence speed of the ISMABC algorithm were significantly enhanced. The algorithm was applied to solve the problem of cooperative path planning for multiple UAVs in order to verify the feasibility of the ISMABC algorithm. Comparative analysis shows that the ISMABC algorithm can be used to plan paths with minimal cost that satisfies the constraints for each UAV.



Key wordsmultiple UAVs      path planning      slime mould algorithm      artificial bee colony algorithm      good point set      nonlinear convergence factor     
Received: 11 March 2024      Published: 28 July 2025
CLC:  TP 393  
Fund:  国家自然科学基金资助项目(62071329).
Cite this article:

Hui XIONG,Banglu GE,Jinzhen LIU,Jiaxing WANG. Improved slime mould bee colony algorithm for multi-UAVs cooperative path planning. Journal of ZheJiang University (Engineering Science), 2025, 59(8): 1698-1707.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2025.08.017     OR     https://www.zjujournals.com/eng/Y2025/V59/I8/1698


用于多无人机协同路径规划的改进黏菌蜂群算法

针对多无人机(UAV)协同路径规划的问题,提出改进黏菌人工蜂群算法(ISMABC). 建立路径规划代价模型,通过引入适应度函数和约束条件,将三维环境中的路径规划问题转化为优化问题,利用所提算法求解模型,获得最优路径. 采用佳点集策略和非线性收敛因子,对黏菌算法进行改进,在增加种群多样性的同时,提高算法的收敛速度. 对全局最优个体采用精英反向学习策略,提高种群质量. 在人工蜂群探索能力的基础上,引入全局最优位置引导,提高黏菌算法的开发能力. 通过对14个测试函数和CEC2017测试函数集中部分函数的寻优对比分析可知,ISMABC算法的寻优能力和收敛速度都有了较大的提升. 为了验证ISMABC算法的可行性,采用所提算法求解多无人机协同路径规划问题. 通过对比分析可知,利用ISMABC算法能够为每架UAV规划出满足约束且代价最小的路径.


关键词: 多无人机,  路径规划,  黏菌算法,  人工蜂群算法,  佳点集,  非线性收敛因子 
Fig.1 Schematic diagram of path planning
Fig.2 Schematic of change in heading angle
Fig.3 Flowchart of ISMABC algorithm
算法函数最优值平均值方差耗时均值/s
HHO$ {F_1} $4.21×10?753.49×10?581.16×10?1133.07×10?2
$ {F_2} $1.95×10?393.49×10?313.33×10?603.09×10?2
$ {F_3} $3.67×10?708.87×10?437.78×10?830.151
$ {F_4} $4.22×10?399.78×10?312.44×10?593.76×10?2
$ {F_5} $1.23×10?52.55×10?47.59×10?86.01×10?2
ABC$ {F_1} $2.65×10?221.51×10?181.43×10?690.192
$ {F_2} $2.20×10?222.77×10?193.43×10?420.197
$ {F_3} $2.22×10?292.35×10?252.21×10?540.304
$ {F_4} $2.99×10?187.12×10?153.32×10?390.199
$ {F_5} $0.2120.5772.82×10?20.208
GWO$ {F_1} $5.09×10?174.35×10?154.33×10?294.02×10?2
$ {F_2} $2.05×10?104.19×10?92.25×10?144.09×10?2
$ {F_3} $5.69×10?40.6152.30×10?28.93×10?2
$ {F_4} $5.53×10?58.75×10?43.44×10?74.01×10?2
$ {F_5} $9.95×10?43.60×10?32.40×10?64.63×10?2
WOA$ {F_1} $5.21×10?532.36×10?414.39×10?801.44×10-2
$ {F_2} $1.12×10?352.77×10?292.57×10?401.52×10-2
$ {F_3} $3.04×1046.45×1042.73×1086.36×10-2
$ {F_4} $3.60×10252.37.00×1021.44×10-2
$ {F_5} $7.07×10?55.80×10?34.50×10?52.07×10-2
SSA$ {F_1} $01.09×10?691.16×10?1369.31×10?2
$ {F_2} $01.26×10?341.60×10?669.49×10?2
$ {F_3} $01.38×10?591.29×10?1160.191
$ {F_4} $02.13×10?322.25×10?629.28×10?2
$ {F_5} $1.50×10?54.18×10?41.05×10?70.105
SMA$ {F_1} $07.77×10?22200.120
$ {F_2} $1.00×10?1966.40×10?994.75×10?1900.120
$ {F_3} $08.09×10?23900.170
$ {F_4} $4.21×10?2169.06×10?1128.21×10?2210.120
$ {F_5} $7.77×10?52.74×10?44.81×10?80.129
ISMABC$ {F_1} $0000.113
$ {F_2} $0000.115
$ {F_3} $0000.216
$ {F_4} $0000.113
$ {F_5} $2.01×10-78.65×10-55.52×10-90.127
Tab.1 Test result of single peak function
算法函数最优值平均值方差耗时均值/s
HHO$ {F_8} $?1.26×104?1.25×1042.92×1056.25×10?2
$ {F_9} $0005.10×10?2
$ {F_{10}} $8.88×10?168.88×10?1605.22×10?2
$ {F_{11}} $0006.22×10?2
ABC$ {F_8} $?6.28×103?4.84×1031.50×1052.21×10?2
$ {F_9} $1.94×1022.42×1022.70×1020.211
$ {F_{10}} $3.905.310.5130.211
$ {F_{11}} $1.432.080.1210.219
GWO$ {F_8} $?8.42×103?5.85×1038.44×1054.77×10?2
$ {F_9} $2.05×10?126.9728.24.30×10?2
$ {F_{10}} $2.25×10?91.15×10?84.08×10?174.33×10?2
$ {F_{11}} $2.66×10?156.00×10?31.19×10?44.81×10?2
WOA$ {F_8} $?1.26×104?1.01×1043.32×1062.14×10?2
$ {F_9} $01.00×10?21.10×10?21.67×10?2
$ {F_{10}} $8.88×10?166.32×10?151.13×10?291.76×10?2
$ {F_{11}} $01.40×10?24.00×10?32.18×10?2
SSA$ {F_8} $?1.26×104?8.64×1036.05×1060.106
$ {F_9} $0009.66×10?2
$ {F_{10}} $8.88×10?168.88×10?1609.83×10?2
$ {F_{11}} $0000.106
SMA$ {F_8} $?1.26×104?1.26×1042.270.131
$ {F_9} $0000.124
$ {F_{10}} $8.88×10?168.88×10?1600.126
$ {F_{11}} $0000.130
ISMABC$ {F_8} $?1.26×104?1.26×1043.70×10?20.132
$ {F_9} $0000.117
$ {F_{10}} $8.88×10?168.88×10?1600.119
$ {F_{11}} $0000.128
Tab.2 Test result of multi-peak function
算法函数最优值平均值方差耗时均值/s
HHO$ {F_{14}} $0.9981.561.524.02×10?1
$ {F_{15}} $?1.03?1.032.90×10?163.68×10?2
$ {F_{21}} $?10.1?5.230.8374.92×10?2
$ {F_{22}} $?10.3?5.270.8925.53×10?2
$ {F_{23}} $?5.13?4.990.3606.28×10?2
ABC$ {F_{14}} $0.9981.017.00×10?30.519
$ {F_{15}} $?1.03?1.035.09×10?130.192
$ {F_{21}} $?10.2?9.452.700.210
$ {F_{22}} $?10.4?10.20.7130.218
$ {F_{23}} $?10.5?10.53.86×10?80.227
GWO$ {F_{14}} $0.9984.8417.60.159
$ {F_{15}} $?1.03?1.033.19×10?151.36×10?2
$ {F_{21}} $?10.2?9.045.541.98×10?2
$ {F_{22}} $?10.410.40.8262.25×10?2
$ {F_{23}} $?10.5?1.02×1012.212.53×10?2
WOA$ {F_{14}} $0.9983.2610.30.158
$ {F_{15}} $?1.03?1.037.56×10?171.28×10?2
$ {F_{21}} $?10.2?7.707.741.72×10?2
$ {F_{22}} $?10.4?7.248.812.00×10?2
$ {F_{23}} $?10.5?6.6310.32.28×10?2
SSA$ {F_{14}} $0.9989.2422.60.320
$ {F_{15}} $?1.03?1.037.08×10?172.99×10?2
$ {F_{21}} $?10.2?9.931.004.33×10?2
$ {F_{22}} $?10.4?10.30.6584.85×10?2
$ {F_{23}} $?10.5?10.50.2825.47×10?2
SMA$ {F_{14}} $0.9980.9983.29×10?230.206
$ {F_{15}} $?1.03?1.036.22×10?175.79×10?2
$ {F_{21}} $?10.2?10.23.85×10?76.85×10?2
$ {F_{22}} $?10.4?10.48.64×10?77.13×10?2
$ {F_{23}} $?10.5?10.53.25×10?77.45×10?2
ISMABC$ {F_{14}} $0.9980.9982.18×10?280.359
$ {F_{15}} $?1.03?1.032.65×10?206.03×10?2
$ {F_{21}} $?10.2?10.27.85×10?97.64×10?2
$ {F_{22}} $?10.4?10.43.61×10?98.12×10?2
$ {F_{23}} $?10.5?10.59.01×10?98.77×10?2
Tab.3 Test result of fixed dimension function
函数WOASSAHHOSMAISMABC
平均值标准差平均值标准差平均值标准差平均值标准差平均值标准差
CEC011.73×10105.77×1091.23×10105.78×1092.19×1072.40×1075.38×1061.56×1075.98×1027.72×102
CEC036.81×1049.62×1034.62×1041.79×1046.41×1041.58×1044.58×1049.99×1032.02×1042.56×103
CEC066.06×1026.516.93×1021.216.39×10218.66.24×1028.636.13×1021.57×10?13
CEC071.53×10362.31.73×10350.31.98×10251.69.42×10251.97.69×1021.85
CEC129.31×1081.95×1091.16×1091.86×1091.99×1061.31×1061.13×1069.47×1054.21×1052.05×105
CEC141.29×1061.97×1062.37×1042.76×1043.14×1043.79×1044.74×1045.67×1041.39×1056.21×104
CEC191.09×1071.13×1071.45×1061.92×1068.65×1037.32×1039.73×1031.97×1043.91×1031.85×103
CEC266.13×1036.25×1027.18×1031.64×1035.48×1031.23×1032.89×10379.53.31×1032.17×102
CEC283.92×1032.99×1024.48×1034.27×1023.46×10339.13.27×1031.29×1033.20×10313.9
CEC304.86×1073.66×1071.44×1078.41×1062.94×1043.83×1041.23×1052.67×1057.16×1031.49×103
Tab.4 Comparison result of CEC2017 test set algorithm
Fig.4 Convergence curve of ISMABC and six comparison algorithms
UAV起点坐标目标点坐标
UAV1(50, 150, 50)(900, 900, 50)
UAV2(150, 150, 50)(900, 900, 50)
UAV3(150, 50, 50)(900, 900, 50)
Tab.5 UAV starting point and target point m
环境威胁位置坐标rh
场景21(800, 300)180200
2(400, 200)120200
3(300, 700)220200
4(800, 850)80200
场景31(400, 500)60200
2(800, 300)80200
3(400, 200)100200
4(300, 700)90200
5(800, 850)70200
6(200, 400)60200
7(800, 500)50200
8(600, 800)70200
9(900, 650)50200
10(550, 450)70200
Tab.6 Parameter of threat source m
Fig.5 Path planning result of scenario 1
场景1l/mT/s
UAV11 174.3[58.715, 117.43]
UAV21 202.8[60.14, 120.28]
UAV31 172.9[58.645, 117.29]
Tab.7 Path length and arrival time for scenario 1
Fig.6 Data result of scenario 1
Fig.7 Path planning result of scenario 2
场景2l/mT/s
UAV11 235.6[61.78, 123.56]
UAV21 235.5[61.775, 123.55]
UAV31 235.7[61.785, 123.57]
Tab.8 Path length and arrival time for scenario 2
Fig.8 Data result of scenario 2
Fig.9 Path planning result of scenario 3
Fig.10 Data result of scenario 3
场景3l/mT/s
UAV11 453.8[72.69, 145.38]
UAV21 228.1[61.405, 122.81]
UAV31 228.3[61.415, 122.83]
Tab.9 Path length and arrival time for scenario 3
Fig.11 Variation of pitch angle and heading angle of three UAVs in scenario 3
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