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一种基于欧氏距离的种群规模动态控制方法

季伟东 倪婉璐

季伟东, 倪婉璐. 一种基于欧氏距离的种群规模动态控制方法[J]. 电子与信息学报, 2022, 44(6): 2195-2206. doi: 10.11999/JEIT210322
引用本文: 季伟东, 倪婉璐. 一种基于欧氏距离的种群规模动态控制方法[J]. 电子与信息学报, 2022, 44(6): 2195-2206. doi: 10.11999/JEIT210322
JI Weidong, NI Wanlu. A Dynamic Control Method of Population Size Based on Euclidean Distance[J]. Journal of Electronics & Information Technology, 2022, 44(6): 2195-2206. doi: 10.11999/JEIT210322
Citation: JI Weidong, NI Wanlu. A Dynamic Control Method of Population Size Based on Euclidean Distance[J]. Journal of Electronics & Information Technology, 2022, 44(6): 2195-2206. doi: 10.11999/JEIT210322

一种基于欧氏距离的种群规模动态控制方法

doi: 10.11999/JEIT210322
基金项目: 国家自然科学基金(31971015),哈尔滨市科技局科技创新人才研究专项项目(2017RAQXJ050),哈尔滨师范大学计算机科学与信息工程学院科研项目(JKYKYY202001),2021年度黑龙江省自然科学基金(LH2021F037)
详细信息
    作者简介:

    季伟东:男,1978年生,博士,教授,研究方向为大数据、群体智能

    倪婉璐:女,1996年生,硕士生,研究方向为群体智能

    通讯作者:

    季伟东 kingjwd@126.com

  • 中图分类号: TP301

A Dynamic Control Method of Population Size Based on Euclidean Distance

Funds: The National Natural Science Foundation of China (31971015), Harbin Science and Technology Bureau’s Special Subsidy for Scientific and Technological Innovation Talents Research (2017RAQXJ050), The Research Project of School of Computer Science and Information Engineering,Harbin Normal University (JKYKYY202001), The Natural Science Foundation of Heilongjiang Province in 2021 (LH2021F037)
  • 摘要: 种群规模是决定算法性能最重要的参数,其大小会引发算法过早收敛或效率低下等问题。该文提出一种基于欧氏距离的种群规模动态控制方法(EDPS),通过引入欧氏距离建立核心圆域,利用核心圆域反馈的信息动态控制种群规模,提出基于核心圆域的增加/删除个体数目的方法。将该方法运用到粒子群算法、遗传算法和差分进化算法中,对收敛性进行分析,在测试函数上对其性能进行测试,实验结果表明了所提新策略的有效性。
  • 图  1  动态控制流程图

    图  2  算法流程图

    图  3  增删的不同个体数的收敛图

    图  4  收敛曲线

    图  5  收敛曲线

    表  1  函数F1和F5基于激活阈值K和判定阈值θ的平均结果

    F1F5
    激活阈值KK=02.4785×10–92.2471×10–04
    K=102.7143×10–192.3246×10–09
    K=205.4301×10–233.2744×10–11
    K=301.1969×10–245.4805×10–12
    K=401.1569×10–243.7871×10–12
    K=501.7930×10–245.0300×10–12
    判定阈值θθ=1/22.9332×10–246.7745×10–12
    θ=2/32.0541×10244.8624×10–12
    θ=3/43.5091×10–243.2218×10–12
    θ=4/53.9844×10–252.5269×10–12
    θ=5/62.1254×10–246.2672×10–12
    下载: 导出CSV

    表  2  适应度值的平均值与标准差

    测试函数 PSOSaDCPS+PSOMSMPSOGDIWPSOEDPS+PSO
    F1Mean
    Std
    0.0048(5)
    0.0036
    5.2678E-05(2)
    1.9733E-04
    0.0035(4)
    0.0048
    5.4229E-04(3)
    6.9283E-04
    4.2030E-22(1)
    5.4355E-22
    F2Mean
    Std
    321.6227(5)
    757.5841
    305.9853(4)
    612.6810
    37.8965(2)
    20.8848
    295.3553(3)
    646.0457
    1.1286(1)
    1.2517
    F3Mean
    Std
    11.4856(3)
    57.4760
    35.6888(5)
    96.4784
    1.6279(2)
    1.3055
    15.3413(4)
    59.2914
    0.6667(1)
    5.3114E-13
    F4Mean
    Std
    7.1478(4)
    18.5511
    24.8610(5)
    39.5939
    0.0869(2)
    0.1725
    6.5236(3)
    21.1265
    3.5356E-06(1)
    1.6043E-06
    F5Mean
    Std
    2.8480(3)
    0.6077
    0.0794(2)
    0.3244
    4.2122(5)
    1.8981
    3.2137(4)
    0.4853
    4.0041E-12(1)
    3.1655E-12
    F6Mean
    Std
    0.3953(2)
    0.3879
    4.7684(5)
    8.2253
    0.6478(3)
    0.4967
    0.7580(4)
    0.4689
    4.8769E-23(1)
    6.2365E-23
    F7Mean
    Std
    0.0037(2)
    0.0041
    6.6792(4)
    35.8988
    0.6468(3)
    0.6773
    10.1297(5)
    29.9757
    1.1530E-14(1)
    2.8465E-14
    F8Mean
    Std
    0.0364(2)
    0.0198
    0.0824(3)
    0.2486
    0.6663(5)
    0.2804
    0.2826(4)
    0.1051
    0.0133(1)
    0.0205
    F9Mean
    Std
    41.3446(5)
    12.1342
    17.7337(2)
    13.9827
    24.1869(3)
    10.0910
    45.9872(4)
    14.3957
    1.3145E-14(1)
    5.7943E-15
    F10Mean
    Std
    2.0873(4)
    4.0499
    3.0617(5)
    4.6183
    1.4784(3)
    1.1296
    1.4486(2)
    4.4262
    6.0354E-07(1)
    1.0596E-06
    F11Mean
    Std
    0.0069(2)
    0.0083
    0.4674(4)
    0.1805
    1.1304(5)
    1.2018
    0.1760(3)
    0.1348
    1.8818E-21(1)
    3.2949E-21
    Num000011
    Ave.R3.363.183.363.541
    T.R32451
    下载: 导出CSV

    表  3  适应度值的平均值与标准差

    测试函数 GAEDPS+GADEEDPS+DE
    F1Mean
    Std
    6.1788×10–4
    4.3273×10–4
    1.6779×10–23
    9.0360×10–23
    3.6639
    1.3679
    3.8710×10–108
    1.6719×10–107
    F2Mean
    Std
    27.2667
    0.7982
    37.3328
    24.9148
    3.9463×103
    3.7519×103
    57.1605
    34.2014
    F3Mean
    Std
    0.6668
    9.7515×10–5
    0.6667
    3.0891×10–6
    839.0467
    813.5188
    0.7655
    0.4595
    F4Mean
    Std
    0.0081
    0.0020
    0.0013
    2.8946×10–04
    28.8509
    18.4569
    9.6287×10–4
    4.9931×10–4
    F5Mean
    Std
    0.0059
    0.0021
    2.2649×10–13
    3.2758×10–13
    7.6543
    1.0717
    1.5099×10–14
    3.8918×10–15
    F6Mean
    Std
    2.5529×10–5
    1.4647×10–5
    1.2247×10–06
    1.5500×10–06
    2.5036
    1.3115
    0.0322
    0.0509
    F7Mean
    Std
    1.1032×10–04
    8.6325×10–05
    1.5921×10–26
    8.5642×10–26
    159.1248
    69.8944
    3.1682×10–106
    9.8938×10–106
    F8Mean
    Std
    0.0106
    0.0112
    0.0087
    0.0162
    13.4697
    5.7995
    0.0041
    0.0054
    F9Mean
    Std
    7.4007×10–4
    4.0655×10–4
    0
    0
    140.2000
    19.1678
    0
    0
    F10Mean
    Std
    0.0020
    5.5404×10–4
    7.9361×10–15
    4.0250×10–14
    14.9866
    3.2050
    1.7483×10–52
    3.7124×10–52
    F11Mean
    Std
    5.9413×10–4
    4.0894×10–4
    2.5991×10–6
    1.6006×10–6
    1.3808×103
    526.4687
    0.1605
    0.1092
    下载: 导出CSV

    表  4  适应度值的平均结果对比

    测试函数EDPS+GAGAVaPSAPAGAPL-GAGPS-GAEDPS+DEdynNP-DESAMDE
    F18.09×10–3105.02×10–55.01×10–55.02×10–55.04×10–505.02×10–55.02×10–5
    F80.01974.94×10–25.14×10–25.74×10–24.91×10–20.02095.08×10–23.87×10–2
    F90–1.02×101–1.02–1.03×–1.020–1.03–1.03
    F111.67×10–80.11×100.11000.350800.00
    下载: 导出CSV

    表  5  适应度值的运行平均结果

    函数PSOEDPS+PSOGAEDPS+GADEEDPS+DE
    F11.84×1035.46×10–136.38×10–32.74×10-25.69×1036.96×102
    F29.82×1061.12×1056.24×1066.66×1061.00×1076.84×106
    F59.39×1021.83×10–41.91×10–26.03×10-21.50×1025.00×101
    F61.54×1021.08×1017.57×1016.19×1012.79×1031.16×102
    F103.99×1021.08×1011.461.615.08×1021.45×102
    F111.41×1025.02×1011.82×10–14.87×1021.67×1021.24×101
    F142.83×1031.38×1031.25×1014.16×10–16.51×1037.62×102
    F161.329.32×10–11.271.742.531.82
    F171.38×1023.47×1014.24×1013.06×1012.45×1023.18×101
    F194.91×1022.951.258.88×10–12.23×1024.72
    F203.86×1023.35×1025.14×1023.24×10+029.91×1026.08×102
    F213.64×1031.72×1031.29×1021.04×10+026.74×1037.10×102
    F232.87×1022.80×1022.94×1023.16×1022.41×1022.33×102
    F242.98×1022.95×1023.50×1023.43×10+022.65×1022.63×102
    F253.33×1022.05×1022.02×1022.25×1022.002×1022.001×102
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-04-19
  • 修回日期:  2021-11-18
  • 录用日期:  2021-11-18
  • 网络出版日期:  2021-12-23
  • 刊出日期:  2022-06-21

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