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融合收敛因子和樽海鞘群的蝴蝶优化算法

郑洪清 彭石燕 周永权

郑洪清, 彭石燕, 周永权. 融合收敛因子和樽海鞘群的蝴蝶优化算法[J]. 微电子学与计算机, 2021, 38(10): 28-34. doi: 10.19304/J.ISSN1000-7180.2021.0022
引用本文: 郑洪清, 彭石燕, 周永权. 融合收敛因子和樽海鞘群的蝴蝶优化算法[J]. 微电子学与计算机, 2021, 38(10): 28-34. doi: 10.19304/J.ISSN1000-7180.2021.0022
ZHENG Hongqing, Peng Shiyan, ZHOU Yongquan. Butterfly optimization algorithm based on convergence factor and salp swarm[J]. Microelectronics & Computer, 2021, 38(10): 28-34. doi: 10.19304/J.ISSN1000-7180.2021.0022
Citation: ZHENG Hongqing, Peng Shiyan, ZHOU Yongquan. Butterfly optimization algorithm based on convergence factor and salp swarm[J]. Microelectronics & Computer, 2021, 38(10): 28-34. doi: 10.19304/J.ISSN1000-7180.2021.0022

融合收敛因子和樽海鞘群的蝴蝶优化算法

doi: 10.19304/J.ISSN1000-7180.2021.0022
基金项目: 

国家自然科学基金资助项目 61463007

详细信息
    作者简介:

    郑洪清   男,(1978-),硕士,副教授,研究方向为智能计算

    周永权   男,(1962-),博士,教授.研究方向为智能计算与神经网络

    通讯作者:

    彭石燕(通讯作者)   女,(1986-),硕士,讲师,研究方向为计算机应用. E-mail:237296281@qq.com

  • 中图分类号: TP391

Butterfly optimization algorithm based on convergence factor and salp swarm

  • 摘要: 针对蝴蝶优化算法存在收敛速度慢、寻优精度差和易陷入局部最优等缺陷,提出融合收敛因子和樽海鞘群的蝴蝶优化算法.受灰狼算法和樽海鞘群算法的启发分别将收敛因子融入全局位置和局部位置更新处,提高算法的寻优精度;再结合樽海鞘群领导机制,平衡了算法的全局搜索和局部勘探能力.通过17个基准函数的测试,所有实验结果表明采用综合改进策略的算法在收敛速度、寻优精度和鲁棒性方面具有一定优势.
  • 图  1  A收敛因子曲线

    图  2  c1收敛因子曲线

    图  3  f3函数收敛曲线

    图  4  f4函数收敛曲线

    图  5  f5函数收敛曲线

    图  6  f6函数收敛曲线

    图  7  f9函数收敛曲线

    表  1  基准函数

    Function Range 理论值
    $ \text { Sphere: } f_{1}(x)=\sum\limits_{i=1}^{n} x_{i}^{2} $ [-100, 100] 0
    $ \text { Schwefel 2. } 22: f_{2}(x)=\sum\limits_{i=1}^{n}\left|x_{i}\right|+\prod_{i=1}^{n}\left|x_{i}\right| $ [-10, 10] 0
    $ \text { Schwefel 1. } 2: f_{3}(x)=\sum\limits_{i=1}^{n}\left(\sum\limits_{j=1}^{i} x_{j}\right)^{2} $ [-100, 100] 0
    $ \text { Schwefel 2. 21: } f_{4}(x)=\max\limits _{i}\left\{\left|x_{i}\right|, 1 \leqslant i \leqslant n\right\} $ [-100, 100] 0
    $ \text { Rosenbrock: } f_{5}(x)=\sum\limits_{i=1}^{n-1}\left[100\left(x_{i+1}-x_{i}^{2}\right)^{2}+\left(x_{i}-1\right)^{2}\right] $ [-30, 30] 0
    $ \text { Step: } f_{6}(x)=\sum\limits_{i=1}^{n}\left(x_{i}+0.5\right)^{2} $ [-100, 100] 0
    $ \text { Quartic: } f_{7}(x)=\sum\limits_{i=1}^{n} i x_{i}^{4}+rand(0, 1) $ [-1.28, 1.28, ] 0
    $ \text { Schwefel: } f_{8}(x)=\sum\limits_{i=1}^{n}\left[x_{i}^{2} \sin \left(\sqrt{\mid x_{i}} \mid\right)\right] $ [-500, 500] -418.983×n
    $ \text { Rastrigin: } f_{9}(x)=\sum\limits_{i=1}^{n}\left[x_{i}^{2}-10 \cos \left(2 \pi x_{i}\right)+10\right] $ [-5.12, 5.12] 0
    $ \text { Ackley: } f_{10}(x)=-20 \exp \left(-0.2 \sqrt{\frac{1}{n} \sum\limits_{i}^{n} x_{i}^{2}}\right)-\exp \left(\frac{1}{n} \sum\limits_{i}^{n} \cos 2 \pi x_{i}\right)+20+e $ [-32, 32] 0
    $ \text { Griewank: } f_{11}(x)=1+\frac{1}{4000} \sum\limits_{i=1}^{n} x_{i}^{2}-\prod_{i=1}^{n} \cos \left(\frac{x_{i}}{\sqrt{i}}\right) $ [-600, 600] 0
    $ \text { Penalized: } f_{12}(x)=\frac{\pi}{n}\left\{10 \sin \left(\pi y_{1}\right)+\sum\limits_{i=1}^{n-1}\left(y_{i}-1\right)^{2}\left[1+10 \sin ^{2}\left(\pi y_{i}+1\right)\right]+\left(y_{n}-1\right)^{2}\right\}+\sum\limits_{i=1}^{n} u\left(x_{i}, 10, 100, 4\right) $ [-50, 50] 0
    $ \begin{array}{l} \text { Penalized2 }: f_{13}(x)=0.1 \sin ^{2}\left(3 \pi x_{1}\right)+\sum\limits_{i=1}^{n-1}\left(x_{i}-1\right)^{2}\left[1+\sin ^{2}\left(3 \pi x_{i}+1\right)\right]+\left(x_{n}-1\right)^{2} \times\left[1+\sin ^{2}\left(2 \pi x_{n}\right)\right]+ \\ \sum\limits_{i=1}^{n} u\left(x_{i}, 5, 100, 4\right) \end{array} $ [-50, 50] 0
    $ \text { Foxholes: } f_{14}(x)=\left(\frac{1}{500}+\sum\limits_{j=1}^{25}\left(1 / j+\sum\limits_{i=1}^{2}\left(x_{i}-a_{i j}\right)^{6}\right)\right)^{-1} $ [-65, 65] 1
    $ \text { Kowalik: } f_{15}(x)=\sum\limits_{i=1}^{11}\left[a_{i}-\frac{x_{i}\left(b_{i}^{2}+b_{i} x_{2}\right)}{b_{i}^{2}+b_{i} x_{3}+x_{4}}\right]^{2} $ [-5, 5] 0.0003
    $ \text { Six-Hump Camel : } f_{16}(x)=4 x_{1}^{2}-2.1 x^{4}+\frac{1}{3} x_{1}^{6}+x_{1} x_{2}-4 x_{2}^{2}+4 x^{4} $ [-5, 5] -1.0316
    $ \text { Alpine: } f_{17}(x)=\sum\limits_{i=1}^{n}\left|x_{i} \sin \left(x_{i}\right)+0.1 x_{i}\right| $ [-10, 10] 0
    下载: 导出CSV

    表  2  基准函数的实验结果

    f Index CFSSBOA BOA SSA LECUSSA RCSSA 文献[6] 文献[7] 文献[9] 文献[10]
    f1(x) Mean 0 1.306 7e-11 3.153 3e-07 1.553 2e-009 0 1.28e-166 0 0 1.73e-299
    Std 0 7.233 4e-13 8.425 1e-07 2.252 8e-009 0 0 0 0 -
    f2(x) Mean 0 4.669 1e-09 0.002 1 8.543 6e-006 6.57e-173 8.80e-77 1.36e-81 3.86e-134 1.37e-150
    Std 0 5.749 7e-10 0.009 4 6.700 6e-006 0 3.68e-76 7.43e-81 1.52e-133 -
    f3(x) Mean 0 1.081 2e-11 1.992 9e-06 1.480 8e-009 0 5.51e-162 - - -
    Std 0 1.420 5e-12 6.501 9e-06 1.964 7e-009 0 0 - - -
    f4(x) Mean 0 5.191 3e-09 2.194 9e-05 7.138 7e-006 1.31e-173 7.96e-79 - 3.29e-134 -
    Std 0 5.178 0e-10 7.744 7e-06 6.849 4e-006 0 5.25e-78 - 1.80e-133 -
    f5(x) Mean 3.792 1e-12 8.938 8 212.516 0 1.495 1e-007 98.2 - - - 2.31e-09
    Std 3.131 5e-12 0.024 7 472.779 1 9.289 0e-008 0.039 6 - - - -
    f6(x) Mean 3.949 0e-13 1.083 3 9.854 6e-10 3.833 5e-009 3.2 - - - -
    Std 3.736 0e-13 0.371 7 4.710 8e-10 1.086 4e-009 0.643 - - - -
    f7(x) Mean 9.860 0e-05 0.001 2 0.013 5 5.810 6e-004 7.12e-5 2.93e-05 - 1.57e-04 -
    Std 1.091 2e-04 5.781 7e-04 0.006 2 5.894 2e-004 7.08e-5 3.52e-05 - 1.35e-04 -
    f8(x) Mean -4.155 9e+03 -2.102 0e+03 -2.800 1e+03 -3.106 0e+003 -2.36e+4 - - - -
    Std 186.028 8 226.083 7 384.973 2 275.879 7 4.02e+4 - - - -
    f9(x) Mean 0 32.404 0 17.544 4 5.533 5e-010 0 0 0 - 0
    Std 0 17.912 9 9.056 9 7.962 5e-010 0 0 0 - -
    f10(x) Mean 8.881 8e-16 2.754 4e-09 0.697 9 5.879 3e-006 8.881 8e-16 8.88e-16 8.88e-16 - 8.88e-16
    Std 2.005 9e-31 1.275 9e-09 0.887 6 5.781 9e-006 2.005 9e-31 0.00e+0 0.00e+0 - -
    f11(x) Mean 0 1.919 3e-13 0.197 8 1.365 4e-009 0 0 0 - 0
    Std 0 1.730 4e-13 0.129 9 1.830 6e-009 0 0 0 - -
    f12(x) Mean 1.705 3e-14 0.121 3 0.348 5 0.035 5 0.163 - - - -
    Std 1.629 1e-14 0.052 4 0.634 6 0.104 6 0.045 3 - - - -
    f13(x) Mean 8.472 3e-14 0.410 9 0.004 7 3.288 5e-009 9.91 - - - -
    Std 9.566 3e-14 0.162 9 0.006 7 9.707 1e-009 4.07e-3 - - - -
    f14(x) Mean 0.998 0 1.646 9 1.229 8 2.400 3 1.53 - - - -
    Std 6.775 2e-16 1.146 4 0.500 5 1.603 4 0.964 - - - -
    f15(x) Mean 0.001 2 3.959 6e-04 0.005 5 3.577 7e-004 2.05e-3 - - - -
    Std 0.002 7 7.333 7e-05 0.008 4 4.528 5e-005 4.99e-3 - - - -
    f16(x) Mean -1.031 6 -1.031 5 -1.031 6 -1.0316 -1.03 - - - -
    Std 2.423 4e-04 1.061 7e-04 0 0 7.92e-14 - - - -
    f17(x) Mean 0 1.123 1e-09 4.313 6 - - - 2.99e-86 2.13e-137 -
    Std 0 1.433 1e-09 2.932 7 - - - 1.64e-85 8.15e-137 -
    下载: 导出CSV
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  • 收稿日期:  2021-01-06
  • 修回日期:  2021-02-01
  • 刊出日期:  2021-10-05

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