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融合多策略的黄金正弦黑猩猩优化算法

刘成汉 何庆

刘成汉, 何庆. 融合多策略的黄金正弦黑猩猩优化算法. 自动化学报, 2021, 47(x): 1−14 doi: 10.16383/j.aas.c210313
引用本文: 刘成汉, 何庆. 融合多策略的黄金正弦黑猩猩优化算法. 自动化学报, 2021, 47(x): 1−14 doi: 10.16383/j.aas.c210313
Liu Cheng-Han, He Qing. Golden sine chimp optimization algorithm integrating multiple strategies. Acta Automatica Sinica, 2021, 47(x): 1−14 doi: 10.16383/j.aas.c210313
Citation: Liu Cheng-Han, He Qing. Golden sine chimp optimization algorithm integrating multiple strategies. Acta Automatica Sinica, 2021, 47(x): 1−14 doi: 10.16383/j.aas.c210313

融合多策略的黄金正弦黑猩猩优化算法

doi: 10.16383/j.aas.c210313
基金项目: 贵州省科技计划项目重大专项项目(黔科合重大专项字[2021] 335), 贵州省公共大数据重点实验室开放课题(2017BDKFJJ004)
详细信息
    作者简介:

    刘成汉:贵州大学大数据与信息工程学院研究生. 主要研究方向为智能优化算法, 深度学习. E-mail: lzttym@163.com

    何庆:副教授, 贵州大学大数据与信息工程学院硕士生导师. 主要研究方向为认知无线电、智能算法. 本文通信作者. E-mail: qhe@gzu.edu.cn

Golden Sine Chimp Optimization Algorithm Integrating Multiple Strategies

Funds: Supported by Major Special Project of Guizhou Science and Technology Planning Project (Major Special Project of Guizhou Science and Technology Cooperation [2021] 335), Open project of Guizhou Provincial Key Laboratory of Public Big Data (2017BDKFJJ004)
More Information
    Author Bio:

    LIU Cheng-Han Postgraduate student at College of Big Data and Information Engineering, Guizhou University. His research interests in clude Intelligent optimization algorithm, deep learning

    HE Qing Associate professor, Master supervisor of College of Big Data and Information Engineering, Guizhou University. His research interest covers cognitive radio and intelligent algorithms. Corresponding author of this paper

  • 摘要: 针对黑猩猩优化算法(Chimp optimization algorithm, ChOA)存在收敛速度慢、精度低和易陷入局部最优值的问题, 提出一种融合多策略的黄金正弦黑猩猩优化算法(IChOA). 引入Halton序列初始化种群, 提高初始化种群的多样性, 加快算法收敛, 提高收敛精度; 考虑到收敛因子和权重因子对于平衡算法勘探和开发能力的重要作用, 引入改进的非线性收敛因子和自适应权重因子, 平衡算法的搜索能力; 结合黄金正弦算法相关思想更新个体位置, 提高算法对于局部极值的处理能力. 通过对23个基准测试函数的寻优对比分析和Wilcoxon秩和统计检验以及部分CEC2014测试函数寻优结果对比可知, 改进的算法具有更好的鲁棒性, 最后, 通过2个实际工程优化问题的实验对比分析, 进一步验证了IChOA在处理现实优化问题上的优越性.
  • 图  1  种群随机分布图

    Fig.  1  Population random distribution diagram

    图  2  种群Halton分布图

    Fig.  2  Population Halton distribution map

    图  3  收敛因子对比图

    Fig.  3  Contrast diagram of convergence factors

    图  4  自适应权重ω曲线

    Fig.  4  Adaptive weight ω curve

    图  5  ChOA算与HChOA收敛对比图

    Fig.  5  convergence curve of ChOA and HChOA

    图  6  ChOA与WChOA收敛对比图

    Fig.  6  convergence curve of ChOA and WChOA

    图  7  ChOA与GChOA收敛对比图

    Fig.  7  convergence curve of ChOA and GChOA

    图  8  各算法寻优对比曲线(500维)

    Fig.  8  convergence curve of each algorithm (500dim)

    图  9  焊接梁模型

    Fig.  9  Welded beam model

    图  10  拉压弹簧设计模型

    Fig.  10  Tension/compression spring model

    表  1  算法参数设置

    Table  1  Algorithm Parameter Setting

    算法参数
    ChOAm = chaos (3, 1, 1)
    PSOc1 = 1.5, c2 = 2, w = 1, wdamp = 0.99
    GWO
    WOAb = 1
    IChOAm = chaos(3, 1, 1), δ1 = 0.3, δ2 = 300, δ3 = 1.8,
    ρ1 = 0.1, ρ2 = 0.05, ρ3 = 0.3, ε = 300
    下载: 导出CSV

    表  2  基准测试函数介绍

    Table  2  Introduction to Benchmark Functions

    编号函数名定义域维度最优值绝对精度误差ε
    f1Sphere[−100, 100]3001.00×10−03
    f2Schwefel’problem 2.22[−10, 10]3001.00×10−03
    f3Schwefel’problem 1.2[−100, 100]3001.00×10−03
    f4Schwefel’problem 2.21[−100, 100]3001.00×10−03
    f5Generalized Rosenbrock's Function[−30, 30]3001.00×10−02
    f6Step Function[−100, 100]3001.00×10−02
    f7Quartic Function[−1.28, 1.28]3001.00×10−02
    f8Generalized Schwefel’s problem 2.26[−500, 500]30−12569.51.00×10+02
    f9Generalized Rastrigin’s Function[−5.12, 5.12]3001.00×10−02
    f10Ackley’s Function[−32, 32]3001.00×10−02
    f11Ceneralized Criewank Function[−600, 600]3001.00×10−02
    f12Ceneralized Penalized Function 1[−50, 50]3001.00×10−02
    f13Ceneralized Penalized Function 2[−50, 50]3001.00×10−02
    f14Shekell’s Foxholes Function[−65, 65]211.00×10−02
    f15Kowalik's Function[−5, 5]40.00031.00×10−02
    f16Six-Hump Camel-Back Function[−5, 5]2−1.031.00×10−02
    f17Branin Function[−5, 5]20.3981.00×10−02
    f18Goldstein-Price Function[−2, 2]231.00×10−02
    f19Hatman’s Function1[0, 1]3−3.861.00×10−02
    f20Hatman’s Function2[0, 1]6−3.321.00×10−02
    f21Shekel's Family 1[0, 10]4−101.00×10−02
    f22Shekel's Family 2[0, 10]4−101.00×10−02
    f23Shekel's Family 3[0, 10]4−101.00×10−02
    下载: 导出CSV

    表  3  各算法寻优结果对比(30维)

    Table  3  Comparison of optimization results of each algorithm (30dim)

    函数ChOA算法PSO算法[19]GWO算法[20]SChOA算法[21]IChOA算法
    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
    f11.34×10−51.19×10−201.40×10−42.11×10−45.95×10−286.85×10−285.66×10−335.68×10300
    f21.42×10−58.55×10−214.21×10−24.54×10−27.95×10−174.97×10−171.72×10−201.91×101000
    f36.31×1001.40×10−177.01×1012.21×1012.83×10−51.12×10−46.19×10−82.25×10400
    f42.75×10−25.95×10−281.08×1003.17×10−15.69×10−75.55×10−72.75×10−101.26×10000
    f52.87×1012.51×10−149.67×1016.01×1012.70×1018.26×10−12.85×1021.00×1073.13×10−45.26×10−17
    f63.72×1004.48×10−151.10×10−48.28×10−57.64×10−13.58×10−13.01×1005.62×1036.51×10−33.25×10−4
    f71.72×10−31.09×10−181.22×10−14.49×10−21.72×10−37.51×10−41.00×10−35.77×1017.81×10−71.02×10−12
    f8−5648.582.75×10−12−4841.281152.84−6084.021.02×103−9867.01180.01−12555.731.83×10−11
    f91.41×10104.67×1011.16×1013.22×1004.16×10007.77×10100
    f101.96×1011.79×10−142.76×10−15.09×10−11.05×10−132.39×10−141.50×10−141.76×1018.88×10−160
    f114.79×10−27.00×10−179.21×10−37.74×10−35.14×10−39.98×10−308.30×10100
    f123.98×10−15.60×10−176.92×10−31.19×10−25.99×10−29.78×10−21.62×10−13.31×1076.46×10−44.39×10−18
    f132.82×1001.76×10−156.68×10−38.91×10−36.27×10−13.06×10−16.76×10−15.16×1072.97×10−54.56×10−16
    f140.997011.12×10−153.627172.5×1005.086614.34×1000.99801.04×1010.9884.48×10−16
    f150.001364.39×10−190.000582.21×10−40.005738.98×10−30.000681.70×10−30.000235.46×10−19
    f16−1.031606.72×10−15−1.031626.25×10−16−1.03162.42×10−8−1.03162.21×10−1−1.03165.60×10−16
    f170.398053.36×10−160.3978900.3978900.39794.90×10−30.397898.98×10−16
    f183.0001003.182401.33×10−155.700031.47×1013.00001.92×10−13.00000
    f19−3.853102.69×10−15−3.862782.58×10−15−3.861682.17×10−3−3.86499.16×10−2−3.72321.34×10−18
    f20−1.920741.12×10−15−3.261346.05×10−2−3.230368.433×10−2−3.32191.24×10−1−2.89545.23×10−15
    f21−4.924782.69×10−15−6.865113.01×100−8.799562.2×100−10.09443.34×10−1−10.12372.38×10−15
    f22−4.994542.69×10−15−8.456533.08×100−10.223849.70×10−1−5.17595.74×10−2−9.78338.79×10−15
    f23−5.025304.48×10−16−8.952911.78×100−9.905001.96×100−10.51394.95×10−2−9.93358.97×10−16
    下载: 导出CSV

    表  4  Wilcoxon秩和检验结果

    Table  4  Wilcoxon rank sum test results

    编号PSO(p1)GWO(p2)WOA(p3)ChOA(p4)GChOA(p5)
    f13.31×10−203.31×10−203.31×10−203.31×10−203.31×10−20
    f23.31×10−203.31×10−203.31×10−203.31×10−203.25×10−20
    f33.31×10−203.31×10−203.31×10−203.31×10−203.31×10−20
    f43.31×10−203.31×10−203.31×10−203.31×10−203.31×10−20
    f51.01×10−172.47×10−171.04×10−152.29×10−157.96×10−18
    f67.06×10−181.28×10−171.38×10−152.13×10−167.06×10−18
    f74.20×10−177.06×10−186.88×10−141.36×10−171.27×10−16
    f87.06×10−187.06×10−182.21×10−107.06×10−187.06×10−18
    f93.31×10−203.31×10−20NaN1.17×10−193.31×10−20
    f103.31×10−203.31×10−202.39×10−162.91×10−202.62×10−23
    f113.31×10−203.31×10−203.27×10−012.50×10−043.31×10−20
    f127.06×10−189.37×10−111.83×10−177.96×10−187.06×10−18
    +/=/−12/0/012/0/010/1/112/0/012/0/0
    下载: 导出CSV

    表  5  部分CEC2014函数介绍

    Table  5  Part of the CEC2014 function

    函数维度特征定义域最佳值
    CEC0330UN[−100, 100]300
    CEC0530MF[−100, 100]500
    CEC0630MF[−100, 100]600
    CEC1630MF[−100, 100]1600
    CEC1930HF[−100, 100]1900
    CEC2230HF[−100, 100]2200
    CEC2530CF[−100, 100]2500
    CEC2730CF[−100, 100]2700
    下载: 导出CSV

    表  6  CEC2014函数优化对比

    Table  6  CEC2014 function optimization comparison

    函数PSO算法[24]SCA算法[25]L-SHADE算法[26]HChOA算法GChOA算法IChOA算法
    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平均值标准差
    CEC034.87×1016.61×1018.83×1001.36×100007.78×1047.44×1037.54×1046.58×1037.35×1046.23×103
    CEC052.09×1018.52×10-22.21×1002.72×1002.01×1011.70×10-25.22×1026.67×10-25.26×1024.21×10-25.20×1021.02×10-2
    CEC061.08×1012.53×1006.63×1013.74×1011.67×10-29.17×10-26.33×1022.42×1006.33×10-52.42×1006.31×1022.39×100
    CEC161.13×1017.05×10-12.27×1011.66×10-18.48×1002.97×10-11.62×1032.81×10-11.61×1031.88×10-11.61×1031.24×10-1
    CEC197.76×1001.87×1002.88×1022.99×1013.59×1007.22×10-12.56×1032.46×1001.76×1032.39×1002.32×1031.96×100
    CEC222.31×1021.04×1022.43×1013.03×1013.69×1013.36×1013.57×1039.65×1014.21×1031.48×1023.56×1037.48×101
    CEC252.09×1021.65×1002.69×1022.71×1012.03×1024.97×10-22.71×1039.49×1002.71×1033.21×1002.70×1030
    CEC275.36×1028.15×1032.08×1021.89×1013.00×1021.34×10-132.93×1035.36×1002.91×1038.12×1002.90×1030
    下载: 导出CSV

    表  7  基准函数寻优平均时间及成功率对比

    Table  7  Comparison of average time and success rate for optimization of benchmark function

    函数ChOAHChOAWChOAGChOAIChOA
    平均值标准差成功率平均值标准差成功率平均值标准差成功率平均值标准差成功率平均值标准差成功率
    f11.97320.0136100%1.98240.0088100%1.93020.0155100%1.41130.0181100%1.39160.0101100%
    f21.95460.0101100%1.98410.0181100%1.79620.0063100%1.41760.0101100%1.40860.0081100%
    f32.29990.008302.29880.0077100%2.06160.0906100%2.12720.0128100%2.11500.0275100%
    f42.04560.010701.98840.0309100%1.99550.0676100%1.43810.0330100%1.42080.0446100%
    f52.06960.066302.06910.064901.99660.032633.3%1.46700.053096.6%1.45740.0244100%
    f62.01270.043501.96170.010736.6%1.96040.013816.6%1.41220.011143.3%1.40060.012190%
    f72.05670.0089100%2.03640.0190100%2.05200.0147100%1.54070.0070100%1.53560.0098100%
    f82.02460.012702.01950.031001.97840.029401.46380.008673.3%1.46250.013283.3%
    f92.01380.034302.02030.011296.6%1.98550.0096100%1.43160.0184100%1.41690.0141100%
    f102.00110.011302.00450.014373.3%1.99990.0086100%1.45210.0113100%1.43950.0089100%
    f112.02930.008163.3%2.03010.0144100%2.01550.0095100%1.47760.0119100%1.47350.0116100%
    f122.20400.011402.19300.014233.3%2.16970.016986.6%1.83540.011043.3%1.84220.0530100%
    f132.18730.011202.17920.011536.6%2.18110.018456.6%1.81800.014066.6%1.81400.0084100%
    f140.78930.0090100%0.79160.0068100%0.78980.0073100%1.38300.0100100%1.35710.0064100%
    f150.31310.003900.31410.003450.0%0.31740.002463.3%0.27920.002790.0%0.27880.002496.6%
    f160.17300.0038100%0.17430.0034100%0.17280.0037100%0.16470.0037100%0.16470.0013100%
    f170.16900.0012100%0.17090.0043100%0.16890.0013100%0.15560.0061100%0.15240.0022100%
    f180.16730.0025100%0.16990.0035100%0.16890.0021100%0.15160.0012100%0.15100.0020100%
    f190.28040.0045100%0.28470.0031100%0.28490.0019100%0.30210.0064100%0.25800.0017100%
    f200.47510.004246.6%0.47370.002470.0%0.47240.002863.3%0.43040.005363.3%0.42780.003376.6%
    f210.40460.025116.6%0.40680.003520.0%0.40120.002870.0%0.45810.002976.6%0.40350.005583.3%
    f220.44470.004300.44580.003036.6%0.44030.005053.3%0.53910.004873.3%0.43490.005180.0%
    f230.50870.002900.50890.003643.3%0.50800.002136.6%0.66100.003476.6%0.63470.003986.6%
    下载: 导出CSV

    表  8  焊接梁设计问题结果对比

    Table  8  Comparison of welded beam design

    算法hltb平均值
    GA0.24556.19868.12640.22472.4412
    PSO0.20273.47059.03660.20571.7249
    WOA0.20243.47729.04350.21891.7299
    GWO0.20223.48939.05410.21551.7265
    RO[21]0.20363.52849.00420.20721.7353
    MOV[21]0.20543.47319.04450.20561.7246
    HSSAHHO[21]0.20573.47059.03670.20571.7248
    ChOA0.22143.53588.91150.21271.7737
    SChOA[21]0.20573.47059.03060.20561.7229
    IChOA0.20383.47139.03000.20601.7228
    下载: 导出CSV

    表  9  拉力/压力弹簧优化设计问题结果对比

    Table  9  Comparison of tension/compression spring design

    算法dDP平均值
    GA0.05280.352311.59800.0125
    PSO0.05000.317414.02780.0127
    WOA0.51190.345212.00520.0126
    GWO0.51560.356211.55600.0125
    RO[21]0.04130.349011.76200.0126
    MFO[21]0.05100.364110.86840.0126
    HSSAHHO[21]0.05140.353511.35460.0124
    ChOA0.05000.315914.26290.0128
    SChOA[21]0.05240.348910.65430.01187
    IChOA0.05100.337411.50680.01185
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-04-12
  • 录用日期:  2021-09-17
  • 网络出版日期:  2021-10-13

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