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自适应变异麻雀搜索优化算法

唐延强 李成海 宋亚飞 陈晨 曹波

唐延强,李成海,宋亚飞,等. 自适应变异麻雀搜索优化算法[J]. 北京航空航天大学学报,2023,49(3):681-692 doi: 10.13700/j.bh.1001-5965.2021.0282
引用本文: 唐延强,李成海,宋亚飞,等. 自适应变异麻雀搜索优化算法[J]. 北京航空航天大学学报,2023,49(3):681-692 doi: 10.13700/j.bh.1001-5965.2021.0282
TANG Y Q,LI C H,SONG Y F,et al. Adaptive mutation sparrow search optimization algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(3):681-692 (in Chinese) doi: 10.13700/j.bh.1001-5965.2021.0282
Citation: TANG Y Q,LI C H,SONG Y F,et al. Adaptive mutation sparrow search optimization algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(3):681-692 (in Chinese) doi: 10.13700/j.bh.1001-5965.2021.0282

自适应变异麻雀搜索优化算法

doi: 10.13700/j.bh.1001-5965.2021.0282
基金项目: 国家自然科学基金(61703426); 中国博士后科学基金(2018M633680);陕西省高校科协青年人才托举计划(20190108)
详细信息
    通讯作者:

    E-mail:lichenghai_ns@163.com

  • 中图分类号: TP301.6

Adaptive mutation sparrow search optimization algorithm

Funds: National Natural Science Foundation of China (61703426); China Postdoctoral Science Foundation (2018M633680); Young Talent Fund of University Association for Science and Technology in Shaanxi Province (20190108)
More Information
  • 摘要:

    针对麻雀搜索算法前期易陷入局部极值点、后期寻优精度不高等问题,提出一种自适应变异麻雀搜索算法(AMSSA)。先通过猫映射混沌序列初始化种群,增强初始种群的随机性、遍历性,提高算法的全局搜索能力;再引入柯西变异和Tent混沌扰动,拓展局部搜索能力,使陷入局部极值点的个体跳出限制继续搜索;最后,提出探索者-跟随者数量自适应调整策略,利用各阶段探索者和跟随者数量的改变增强算法前期的全局搜索能力和后期的局部深度挖掘能力,提高算法的寻优精度。选取16个基准函数和Wilcoxon检验进行验证,实验结果表明:所提算法与其他算法相比,寻优精度、收敛速度和稳定性都取得较大提升。

     

  • 图 1  c变化曲线

    Figure 1.  Variation curves of c

    图 2  AMSSA流程

    Figure 2.  Flow chart of AMSSA

    图 3  基准函数平均收敛曲线

    Figure 3.  Average convergence curve of benchmark function

    表  1  参数 ${\boldsymbol{m}}$ 对SSA2的影响

    Table  1.   Influence of parameter ${\boldsymbol{m}}$ on SSA2

    m最佳值平均值标准差平均收敛次数
    1.005.509×10−723.120×10−71891
    1.5000723
    2.0000151
    2.507.505×10−354.747×10−34289
    3.0000224
    3.5000557
    4.0000292
    下载: 导出CSV

    表  2  基准函数

    Table  2.   Benchmark function

    编号函数名称函数式维度定义域最佳值
    f1Sphere${f_1}(x) = \displaystyle\sum\limits_{i = 1}^N{x_i^2}$30[−100,100]0
    f2Schwefel’s${f_2}(x) = \displaystyle\sum\limits_{i = 1}^N {\left| { {x_i} } \right|} + \displaystyle\prod\limits_{i = 1}^N {\left| { {x_i} } \right|}$30[−10,10]0
    f3Quadric${f_3}(x) = {\displaystyle\sum\limits_{i = 1}^N {\left( {\displaystyle\sum\limits_{j = 1}^N { {x_j} } } \right)} ^2}$30[−100,100]0
    f4Rosenbrock${f_4}(x){\text{ = } }\displaystyle\sum\limits_{i = 1}^{N - 1} {\left[ {100{ {({x_{i + 1} } - x_i^2)}^2} + { {({x_i} - 1)}^2} } \right]}$30[−30,30]0
    f5Step${f_5}(x){\text{ = } }\displaystyle\sum\limits_{i = 1}^N { { {(\left| { {x_i} + 0.5} \right|)}^2} }$30[−100,100]0
    f6Quartic${f_6}(x){\text{ = } }\displaystyle\sum\limits_{i = 1}^N {ix_i^4} + {\rm{random} }[0,1]$30[−1.28,1.28]0
    f7Schwefel${f_7}(x){\text{ = } }\displaystyle\sum\limits_{i = 1}^N { - {x_i} } \sin \left( {\sqrt {\left| { {x_i} } \right|} } \right)$30[−500,500]−418.9829N
    f8Rastrigrin${f_8}(x){\text{ = } }\displaystyle\sum\limits_{i = 1}^N {\left[ {x_i^2 - 10\cos\; (2{\text{π}} {x_i}) + 10} \right]}$30[−5.12,5.12]0
    f9Ackley${f_9}(x) = - 20{\rm{exp} }\left( - 0 { {.2} }\sqrt {\dfrac{1}{N}\displaystyle\sum\limits_{i = 1}^N {x_i^2} } \right) - {\rm{exp}} \left( \dfrac{1}{N}\displaystyle\sum\limits_{i = 1}^N {\cos \;(2\text{π} {x_i})} \right) + 20 + {\rm{e} }$30[−32,32]0
    f10Griewing${f_{10} }(x){\text{ = } }\dfrac{1}{ {4\;000} }\displaystyle\sum\limits_{i = 1}^N {x_i^2} - \displaystyle\prod\limits_{i = 1}^N {\cos \left( {\dfrac{ { {x_i} } }{ {\sqrt i } } } \right)} + 1$30[−600,600]0
    f11Generalized penalized${f_{11} }(x){\text{ = } }\dfrac{\text{π} }{N}\left\{ {10{ {\sin }^2}(\text{π} {y_1}) + \displaystyle\sum\limits_{i = 1}^{N - 1} { { {({y_i} - 1)}^2}\left[ {1 + 10{ {\sin }^2}(\text{π} {y_{i + 1} })} \right]} } \right\} + {({y_N} - 1)^2}$30[−50,50]0
    f12Foxholes${f_{12} }(x){\text{ = } }{\left( {\dfrac{1}{ {500} }{\text{ + } }\displaystyle\sum\limits_{j = 1}^{25} {\dfrac{1}{ {j + \displaystyle\sum\limits_{i = 1}^2 { { {({x_i} - {a_{ij} })}^6} } } } } } \right)^{ - 1} }$2[−65,65]1
    f13Hartmann 6-D${f_{13} }(x){{ = - } }\displaystyle\sum\limits_{i = 1}^4 { {c_i} } \exp \left( { - \displaystyle\sum\limits_{j = 1}^6 { {a_{ij} }{ {\left( { {x_j} - {p_{ij} } } \right)}^2} } } \right)$6[0,1]−3.32237
    f14Schkel${f_{14} }(x){ { = - } }{\displaystyle\sum\limits_{i = 1}^{10} {\left[ {\left( { {\boldsymbol{X} } - {{\boldsymbol{a}}_i} } \right){ {\left( { {\boldsymbol{X} } - {{\boldsymbol{a}}_i} } \right)}^{\rm{T} } } + {c_i} } \right]} ^{ - 1} }$4[0,10]−10.5363
    f15Six-Hump Camel${f_{15} }(x){\text{ = 4} }x_1^2 - 2.1x_1^4 + \dfrac{1}{3}x_1^6 + {x_1}{x_2} - 4x_2^2 - 4x_2^4$2[−5,5]−1.0316
    f16Kowalik${f_{16} }(x){\text{ = } }{\displaystyle\sum\limits_{i = 1}^{11} {\left[ { {a_i} - \dfrac{ { {x_1}\left( {b_i^2 + {b_i}{x_2} } \right)} }{ {b_i^2 + {b_i}{x_3} + {x_4} } } } \right]} ^2}$4[−5,5]0.000307
    下载: 导出CSV

    表  3  基准函数测试结果对比

    Table  3.   Comparison of benchmark function test results

    编号算法最佳值平均值标准值编号算法最佳值平均值标准值
    f1PSO1.057×10−51.422×10−42.013×10−4f9PSO2.200×10−31.381×10−13.759×10−1
    GWO2.026×10−291.522×10−271.998×10−27GWO7.550×10−141.021×10−131.668×10−14
    WOA2.579×10−876.403×10−732.573×10−72WOA8.882×10−164.530×10−152.955×10−15
    SSA12.628×10−81.302×10−71.163×10−7SSA19.313×10−12.6481.245
    SSA201.227×10−517.761×10−51SSA28.882×10−168.882×10−160
    AMSSA01.010×10−1820AMSSA8.882×10−168.882×10−160
    f2PSO5.100×10−34.260×10−26.160×10−2f10PSO1.354×10−61.030×10−19.200×10−3
    GWO2.312×10−178.104×10−173.908×10−17GWO03.200×10−38.000×10−3
    WOA4.803×10−581.678×10−517.650×10−51WOA000
    SSA14.260×10−22.3711.860SSA16.545×10−41.330×10−21.050×10−2
    SSA21.129×10−1185.065×10−313.185×10−30SSA2000
    AMSSA04.831×10−352.656×10−34AMSSA000
    f3PSO2.569×107.363×103.642×10f11PSO9.907×10−81.040×10−23.930×10−2
    GWO2.630×10−57.351×10−51.307×10−5GWO1.280×10−24.300×10−21.470×10−2
    WOA3.610×1034.822×1041.793×104WOA4.500×10−32.920×10−24.220×10−2
    SSA12.330×1021.467×1037.677×102SSA12.1156.8323.754
    SSA22.774×10−54.129×10−51.628×10−5SSA22.785×10−169.587×10−133.536×10−12
    AMSSA01.168×10−1670AMSSA1.335×10−223.992×10−158.391×10−15
    f4PSO1.563×109.915×105.719×10f12PSO9.980×10−13.6352.619
    GWO2.610×102.693×106.457×10−1GWO9.980×10−13.7923.810
    WOA2.707×102.798×104.642×10−1WOA9.980×10−12.8383.215
    SSA12.430×101.659×1022.593×102SSA19.980×10−11.0973.762×10−1
    SSA26.711×10−93.419×10−51.144×10−4SSA29.980×10−14.8475.242
    AMSSA1.658×10−138.871×10−73.077×10−6AMSSA9.980×10−19.6114.962
    f5PSO1.008×10−51.894×10−43.878×10−4f13PSO−3.322−3.2745.900×10−2
    GWO7.462×10−57.011×10−13.678×10−1GWO−3.322−3.2548.450×10−2
    WOA7.440×10−24.005×10−12.182×10−1WOA−3.322−3.2091.158×10−1
    SSA12.344×10−82.011×10−72.792×10−7SSA1−3.322−3.2206.150×10−2
    SSA21.179×10−141.538×10−113.735×10−11SSA2−3.322−3.2805.740×10−2
    AMSSA2.101×10−237.744×10−151.533×10−14AMSSA−3.322−3.2163.114×10−2
    f6PSO4.340×10−21.793×10−15.150×10−2f14PSO−1.054×10−9.1652.805
    GWO3.836×10−41.900×10−38.773×10−4GWO−1.054×10−1.033×101.283
    WOA3.416×10−52.700×10−33.400×10−3WOA−1.054×10−7.1193.386
    SSA16.170×10−21.766×10−16.360×10−2SSA1−1.054×10−8.4223.343
    SSA28.384×10−51.700×10−31.400×10−3SSA2−1.054×10−8.5082.652
    AMSSA2.468×10−68.001×10−47.674×10−4AMSSA−1.054×10−1.006×106.803×10−15
    f7PSO−7.082×103−4.601×1031.108×103f15PSO−1.032−1.0322.043×10−16
    GWO−7.586×103−5.865×1039.074×102GWO−1.032−1.0322.281×10−8
    WOA−1.257×104−1.057×1041.769×103WOA−1.032−1.0325.898×10−10
    SSA1−9.017×103−7.584×1036.607×102SSA1−1.032−1.0323.233×10−14
    SSA2−9.618×103−8.525×1035.415×102SSA2−1.032−1.0321.067×10−16
    AMSSA−8.839×103−6.541×1036.724×102AMSSA−1.032−1.0322.073×10−18
    f8PSO3.609×106.026×101.460×10f16PSO3.275×10−48.612×10−41.552×10−4
    GWO03.1744.412GWO3.075×10−43.900×10−37.700×10−3
    WOA000WOA3.229×10−47.261×10−44.383×10−4
    SSA12.388×105.313×102.077×10SSA14.024×10−41.400×10−33.100×10−3
    SSA2000SSA23.075×10−43.219×10−45.463×10−5
    AMSSA000AMSSA3.075×10−43.075×10−48.314×10−10
    下载: 导出CSV

    表  4  Wilcoxon秩和检验p

    Table  4.   p-value for Wilcoxon’s rank-sum test

    函数PSOGWOWOASSA1SSA2
    pRpRpRpRpR
    f18.25×10−15+8.25×10−15+8.64×10−11+9.55×10−15+5.57×10−10+
    f21.17×10−14+1.26×10−14+1.85×10−5+1.17×10−14+1.98×10−7+
    f31.29×10−14+9.55×10−15+9.55×10−15+9.55×10−15+2.69×10−7+
    f41.43×10−14+1.43×10−14+1.43×10−14+1.43×10−14+1.94×10−10+
    f51.43×10−14+1.43×10−14+1.43×10−14+1.43×10−14+8.40×10−13+
    f61.43×10−14+6.54×10−26.94×10−4+1.43×10−14+9.57×10−1
    f73.46×10−11+2.40×10−3+2.83×10−10+9.92×10−7+2.89×10−13+
    f81.96×10−16+1.90×10−16+NaN=1.96×10−16+NaN=
    f91.96×10−16+1.77×10−16+1.90×10−11+1.96×10−16+NaN=
    f101.96×10−16+4.18×10−4+NaN=1.96×10−16+NaN=
    f111.43×10−14+1.43×10−14+1.43×10−14+1.43×10−14+5.12×10−11+
    f121.17×10−5+1.12×10−15.10×10−3+2.90×10−8+7.00×10−3+
    f133.77×10−2+2.27×10−8+9.88×10−12+6.32×10−13+3.40×10−1
    f141.62×10−2+7.18×10−5+2.61×10−6+9.02×10−7+5.68×10−1
    f159.60×10−8+2.93×10−15+2.93×10−15+6.88×10−15+6.32×10−1
    f161.43×10−14+8.66×10−12+1.05×10−13+1.79×10−14+6.68×10−1
    下载: 导出CSV

    表  5  模型消融实验结果

    Table  5.   Experimental results of model ablation

    算法f1f2f3
    MeanStdMeanStdMeanStd
    SSA2.526×10−601.050×10−591.212×10−267.105×10−267.076×10−263.363×10−25
    ASSA1.690×10−751.069×10−749.746×10−296.164×10−285.576×10−291.763×10−28
    MSSA1.679×10−671.032×10−664.333×10−371.978×10−365.084×10−291.605×10−28
    AMSSA1.034×10−18101.966×10−371.243×10−361.026×10−1553.243×10−155
    算法f4f5f6
    MeanStdMeanStdMeanStd
    SSA9.633×10−52.729×10−45.003×10−111.924×10−101.600×10−31.300×10−3
    ASSA3.436×10−68.914×10−62.327×10−143.221×10−141.600×10−31.800×10−3
    MSSA3.527×10−67.135×10−62.300×10−143.999×10−142.000×10−31.800×10−3
    AMSSA4.318×10−78.616×10−72.029×10−143.859×10−141.400×10−38.627×10−4
    下载: 导出CSV
    算法f7f8f9f10
    MeanStdMeanStdMeanStdMeanStd
    SSA−8.463×1035.314×102008.882×10−16000
    ASSA−8.492×1035.921×102008.882×10−16000
    MSSA−8.726×1039.075×102008.882×10−16000
    AMSSA−8.759×1034.052×102008.882×10−16000
    下载: 导出CSV
    算法f11f12f13
    MeanStdMeanStdMeanStd
    SSA3.474×10−121.105×10−116.2605.454−3.2636.270×10−2
    ASSA6.636×10−151.377×10−147.6205.746−3.2746.140×10−2
    MSSA1.356×10−152.427×10−159.980×10−11.480×10−16−3.2985.010×10−2
    AMSSA1.045×10−158.414×10−169.980×10−11.655×10−16−3.2746.140×10−2
    算法f14f15f16
    MeanStdMeanStdMeanStd
    SSA−8.3732.793−1.0321.958×10−163.456×10−48.718×10−5
    ASSA−8.9142.612−1.0321.958×10−163.404×10−41.040×10−4
    MSSA−8.9142.612−1.0322.094×10−163.215×10−46.452×10−5
    AMSSA−9.4552.280−1.0321.958×10−163.075×10−48.442×10−10
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-05-31
  • 录用日期:  2021-08-29
  • 网络出版日期:  2021-09-15
  • 整期出版日期:  2023-03-30

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