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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, 2023, 49(11): 2360−2373 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, 2023, 49(11): 2360−2373 doi: 10.16383/j.aas.c210313
Liu Cheng-Han, He Qing. Golden sine chimp optimization algorithm integrating multiple strategies. Acta Automatica Sinica, 2023, 49(11): 2360−2373 doi: 10.16383/j.aas.c210313
Citation: Liu Cheng-Han, He Qing. Golden sine chimp optimization algorithm integrating multiple strategies. Acta Automatica Sinica, 2023, 49(11): 2360−2373 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: 国家自然科学基金(62166006), 贵州省科技计划项目重大专项项目([2021] 335), 公共大数据国家重点实验室开放课题(2017BDKFJJ004)资助
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硕士研究生. 主要研究方向为智能优化算法, 深度学习. E-mail: lzttym@163.com

    何庆:贵州大学大数据与信息工程学院教授. 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 National Natural Science Foundation of China (62166006), Major Special Project of Guizhou Science and Technology Planning Project ([2021] 335), and Open Project of State Key Laboratory of Public Big Data (2017BDKFJJ004)
More Information
    Author Bio:

    LIU Cheng-Han Master student at the College of Big Data and Information Engineering, Guizhou University. His research interest covers intelligent optimization algorithm and deep learning

    HE Qing Professor at the 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问题, 提出一种融合多策略的黄金正弦黑猩猩优化算法(Multi-strategy golden sine chimp optimization algorithm, 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  种群随机初始化个体分布图

    Fig.  1  Randomly initialized population distribution map

    图  2  使用Halton序列产生的初始种群分布图

    Fig.  2  Halton sequence initialized population distribution map

    图  3  收敛因子对比图

    Fig.  3  Contrast diagram of convergence factors

    图  4  自适应权重因子$\omega $曲线

    Fig.  4  Adaptive weighting factor$\omega $ curve

    图  5  ChOA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500维寻优对比曲线

    Fig.  8  Comparison curves of 500-dimensional optimization of each algorithm

    图  9  焊接梁模型

    Fig.  9  Welding beam model

    图  10  拉力/压力弹簧优化设计问题模型

    Fig.  10  The model of tension/pressure spring optimization design

    表  1  算法参数设置

    Table  1  Parameter setting of algorithm

    算法参数
    ChOA$m = {{chaos} } (3, 1, 1)$
    PSOc1 = 1.5, c2 = 2.0, $\omega$ = 1, wdamp = 0.99
    GWO
    WOA$b=1 $
    IChOA$m = {chaos} (3, 1, 1)$, $\delta _1=0.3,$$\delta _2=300.0, \delta _3=1.8,$
    $\rho _1=0.10,\;\rho _2=0.05, \;\rho _3=0.30, \; \varepsilon=300$
    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$\varepsilon $
    $f_1 $Sphere[−100, 100]3001.00 × 10−3
    $f_2 $Schwefel'problem 2.22[−10, 10]3001.00 × 10−3
    $f_3 $Schwefel'problem 1.2[−100, 100]3001.00 × 10−3
    $f_4 $Schwefel'problem 2.21[−100, 100]3001.00 × 10−3
    $f_5 $Generalized Rosenbrock's function[−30, 30]3001.00 × 10−2
    $f_6 $Step function[−100, 100]3001.00 × 10−2
    $f_7 $Quartic function[−1.28, 1.28]3001.00 × 10−2
    $f_8 $Generalized Schwefel's problem 2.26[−500, 500]30−12569.50001.00 × 102
    $f_9 $Generalized Rastrigin's Function[−5.12, 5.12]3001.00 × 10−2
    $f_{10} $Ackley's function[−32, 32]3001.00 × 10−2
    $f_{11} $Generalized Criewank function[−600, 600]3001.00 × 10−2
    $f_{12} $Generalized penalized function 1[−50, 50]3001.00 × 10−2
    $f_{13} $Generalized penalized function 2[−50, 50]3001.00 × 10−2
    $f_{14} $Shekell's foxholes function[−65, 65]21.00001.00 × 10−2
    $f_{15} $Kowalik's function[−5, 5]40.00031.00 × 10−2
    $f_{16} $Six-hump camel-back function[−5, 5]2−1.03001.00 × 10−2
    $f_{17} $Branin function[−5, 5]20.39801.00 × 10−2
    $f_{18} $Gold stein-price function[−2, 2]23.00001.00 × 10−2
    $f_{19} $Hatman's function1[0, 1]3−3.86001.00 × 10−2
    $f_{20} $Hatman's function 2
    [0, 1]6−3.32001.00 × 10−2
    $f_{21} $Shekel's family 1[0, 10]4−10.00001.00 × 10−2
    $f_{22}$Shekel's family 2[0, 10]4−10.00001.00 × 10−2
    $f_{23} $Shekel's family 3[0, 10]4−10.00001.00 × 10−2
    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 (30 dim)

    函数ChOAPSOGWOSChOAIChOA
    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
    $f_{1} $1.34 × 10−51.19 × 10−201.40 × 10−42.11 × 10−45.95 × 10−286.85 × 10−285.66 × 10−335.68 × 10300
    $f_{2} $1.42 × 10−58.55 × 10−214.21 × 10−24.54 × 10−27.95 × 10−174.97 × 10−171.72 × 10−201.91 × 101000
    $f_{3} $6.31 × 1001.40 × 10−177.01 × 1012.21 × 1012.83 × 10−51.12 × 10−46.19 × 10−82.25 × 10400
    $f_{4} $2.75 × 10−25.95 × 10−281.08 × 1003.17 × 10−15.69 × 10−75.55 × 10−72.75 × 10−101.26 × 10000
    $f_{5} $2.87 × 1012.51 × 10−149.67 × 1016.01 × 1012.70 × 1018.26 × 10−12.85 × 1021.00 × 1073.13 × 10−45.26 × 10−17
    $f_{6} $3.72 × 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
    $f_{7} $1.72 × 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
    $f_{8} $−5.65 × 1032.75 × 10−12−4.84 × 1031.15 × 103−6.08 × 1031.02 × 103−9.87 × 1031.80 × 102−1.26 × 1041.83 × 10−11
    $f_{9} $1.41 × 10104.67 × 1011.16 × 1013.22 × 1004.16 × 10007.77 × 10100
    $f_{10} $1.96 × 1011.79 × 10−142.76 × 10−15.09 × 10−11.05 × 10−132.39 × 10−141.50 × 10−141.76 × 1018.88 × 10−160
    $f_{11} $4.79 × 10−27.00 × 10−179.21 × 10−37.74 × 10−35.14 × 10−39.98 × 10−308.30 × 10100
    $f_{12} $3.98 × 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
    $f_{13} $2.82 × 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
    $f_{14} $1.00 × 1001.12 × 10−153.63 × 1002.50 × 1005.09 × 1004.34 × 1001.00 × 1001.04 × 1010.99 × 1004.48 × 10−16
    $f_{15} $1.36 × 10−34.39 × 10−195.80 × 10−42.21 × 10−45.73 × 10−38.98 × 10−36.80 × 10−41.70 × 10−32.30 × 10−45.46 × 10−19
    $f_{16} $−1.03 × 1006.72 × 10−15−1.03 × 1006.25 × 10−16−1.03 × 1002.42 × 10−8−1.03 × 1002.21 × 10−1−1.03 × 1005.60 × 10−16
    $f_{17} $3.98 × 10−13.36 × 10−163.98 × 10−103.98 × 10−103.99 × 10−14.90 × 10−33.99 × 10−18.98 × 10−16
    $f_{18} $3.00 × 10003.18 × 1001.33 × 10−155.70 × 1001.47 × 1013.00 × 1001.92 × 10−13.00 × 1000
    $f_{19} $−3.85 × 1002.69 × 10−15−3.86 × 1002.58 × 10−15−3.86 × 1002.17 × 10−3−3.86 × 1009.16 × 10−2−3.72 × 1001.34 × 10−18
    $f_{20} $−1.92 × 1001.12 × 10−15−3.26 × 1006.05 × 10−2−3.23 × 1008.43 × 10−2−3.32 × 1001.24 × 10−1−2.90 × 1005.23 × 10−15
    $f_{21} $−4.92 × 1002.69 × 10−15−6.87 × 1003.01 × 100−8.80 × 1002.20 × 100−1.01 × 1013.34 × 10−1−1.01 × 1012.38 × 10−15
    $f_{22} $−4.99 × 1002.69 × 10−15−8.46 × 1003.08 × 100−10.22 × 1009.70 × 10−1−5.18 × 1005.74 × 10−2−9.78 × 1008.79 × 10−15
    $f_{23} $−5.02 × 1004.48 × 10−16−8.95 × 1001.78 × 100−9.90 × 1001.96 × 100−1.05 × 1014.95 × 10−2−9.93 × 1008.97 × 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 ($p_{1} $)GWO ($p_{2} $)WOA ($p_{3} $)ChOA ($p_{4} $)GChOA ($p_{5} $)
    $f_{1} $3.31 × 10−203.31 × 10−203.31 × 10−203.31 × 10−203.31 × 10−20
    $f_{2} $3.31 × 10−203.31 × 10−203.31 × 10−203.31 × 10−203.25 × 10−20
    $f_{3} $3.31 × 10−203.31 × 10−203.31 × 10−203.31 × 10−203.31 × 10−20
    $f_{4} $3.31 × 10−203.31 × 10−203.31 × 10−203.31 × 10−203.31 × 10−20
    $f_{5} $1.01 × 10−172.47 × 10−171.04 × 10−152.29 × 10−157.96 × 10−18
    $f_{6} $7.06 × 10−181.28 × 10−171.38 × 10−152.13 × 10−167.06 × 10−18
    $f_{7} $4.20 × 10−177.06 × 10−186.88 × 10−141.36 × 10−171.27 × 10−16
    $f_{8} $7.06 × 10−187.06 × 10−182.21 × 10−107.06 × 10−187.06 × 10−18
    $f_{9} $3.31 × 10−203.31 × 10−20NaN1.17 × 10−193.31 × 10−20
    $f_{10} $3.31 × 10−203.31 × 10−202.39 × 10−162.91 × 10−202.62 × 10−23
    $f_{11} $3.31 × 10−203.31 × 10−203.27 × 10−12.50 × 10−43.31 × 10−20
    $f_{12} $7.06 × 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  Introduction of part CEC2014 function

    函数维度特征定义域最佳值
    CEC0330单峰[−100, 100]300
    CEC0530多峰[−100, 100]500
    CEC0630多峰[−100, 100]600
    CEC1630多峰[−100, 100]1600
    CEC1930混合[−100, 100]1900
    CEC2230混合[−100, 100]2200
    CEC2530复合[−100, 100]2500
    CEC2730复合[−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PSOSCAL-SHADEHChOAGChOAIChOA
    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
    (%)
    f11.97320.01361001.98240.00881001.93020.01551001.41130.01811001.39160.0101100
    f21.95460.01011001.98410.01811001.79620.00631001.41760.01011001.40860.0081100
    f32.29990.008302.29880.00771002.06160.09061002.12720.01281002.11500.0275100
    f42.04560.010701.98840.03091001.99550.06761001.43810.03301001.42080.0446100
    f52.06960.066302.06910.064901.99660.032633.31.46700.053096.61.45740.0244100
    f62.01270.043501.96170.010736.61.96040.013816.61.41220.011143.31.40060.012190.0
    f72.05670.00891002.03640.01901002.05200.01471001.54070.00701001.53560.0098100
    f82.02460.012702.01950.031001.97840.029401.46380.008673.31.46250.013283.3
    f92.01380.034302.02030.011296.61.98550.00961001.43160.01841001.41690.0141100
    f102.00110.011302.00450.014373.31.99990.00861001.45210.01131001.43950.0089100
    f112.02930.008163.32.03010.01441002.01550.00951001.47760.01191001.47350.0116100
    f122.20400.011402.19300.014233.32.16970.016986.61.83540.011043.31.84220.0530100
    f132.18730.011202.17920.011536.62.18110.018456.61.81800.014066.61.81400.0084100
    f140.78930.00901000.79160.00681000.78980.00731001.38300.01001001.35710.0064100
    f150.31310.003900.31410.003450.00.31740.002463.30.27920.002790.00.27880.002496.6
    f160.17300.00381000.17430.00341000.17280.00371000.16470.00371000.16470.0013100
    f170.16900.00121000.17090.00431000.16890.00131000.15560.00611000.15240.0022100
    f180.16730.00251000.16990.00351000.16890.00211000.15160.00121000.15100.0020100
    f190.28040.00451000.28470.00311000.28490.00191000.30210.00641000.25800.0017100
    f200.47510.004246.60.47370.002470.00.47240.002863.30.43040.005363.30.42780.003376.6
    f210.40460.025116.60.40680.003520.00.40120.002870.00.45810.002976.60.40350.005583.3
    f220.44470.004300.44580.003036.60.44030.005053.30.53910.004873.30.43490.005180.0
    f230.50870.002900.50890.003643.30.50800.002136.60.66100.003476.60.63470.003986.6
    下载: 导出CSV

    表  8  焊接梁设计问题结果对比

    Table  8  Comparative results of welding beam design problems

    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
    RO0.20363.52849.00420.20721.7353
    MVO0.20543.47319.04450.20561.7246
    HSSAHHO0.20573.47059.03670.20571.7248
    ChOA0.22143.53588.91150.21271.7737
    SChOA0.20573.47059.03060.20561.7229
    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
    GA0.05280.352311.59800.01250
    PSO0.05000.317414.02780.01270
    WOA0.51190.345212.00520.01260
    GWO0.51560.356211.55600.01250
    RO0.04130.349011.76200.01260
    MFO0.05100.364110.86840.01260
    HSSAHHO0.05140.353511.35460.01240
    ChOA0.05000.315914.26290.01280
    SChOA0.05240.348910.65430.01187
    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
  • 刊出日期:  2023-11-22

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