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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2022, Vol. 56 Issue (5): 977-986    DOI: 10.3785/j.issn.1008-973X.2022.05.015
    
Dragonfly algorithm based on clustering and detection elite guidance
Xiao-xin DU(),Hao WANG,Lian-he CUI,Jin-qi LUO,Yan LIU,Jian-fei ZHANG,Yi-ping WANG
School of Computer and Control Engineering, Qiqihar University, Heilongjiang 161006, China
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Abstract  

Aiming at the shortcomings of the dragonfly algorithm (DA), i.e., slow convergence speed, low convergence accuracy, and poor global search ability, a new DA algorithm was proposed. Firstly, tent chaos was used to initialize the population and K-Means++ clustering was performed on the population. According to the results of clustering, reverse learning and Gaussian mutation were performed on the individuals of the population respectively to enhance the diversity of the population and improve the search efficiency. Secondly, the nonlinear adaptive factor was introduced to accelerate the convergence speed, and the probing elite guiding strategy was used to enhance the ability of jumping out of local convergence. Finally, square hash detection was introduced to increase the convergence accuracy. The optimization algorithm was applied to eight typical complex function optimization problems, and compared with the original dragonfly algorithm and other bionic algorithms. Experimental results show that the improved algorithm has good global convergence and optimization accuracy.

Key words： dragonfly algorithm      clustering      detection elite guidance strategy      square hash detection      tent chaos     
Received: 12 June 2021      Published: 31 May 2022
CLC:  TP 301.6  
Fund:  2020年度黑龙江省省属高等学校基本科研业务费面上资助项目（135509112）
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Xiao-xin DU
Hao WANG
Lian-he CUI
Jin-qi LUO
Yan LIU
Jian-fei ZHANG
Yi-ping WANG
Cite this article:

Xiao-xin DU,Hao WANG,Lian-he CUI,Jin-qi LUO,Yan LIU,Jian-fei ZHANG,Yi-ping WANG. Dragonfly algorithm based on clustering and detection elite guidance. Journal of ZheJiang University (Engineering Science), 2022, 56(5): 977-986.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2022.05.015     OR     https://www.zjujournals.com/eng/Y2022/V56/I5/977


基于聚类和探测精英引导的蜻蜓算法

针对蜻蜓算法（DA）收敛速度慢、收敛精度低、全局搜索能力差等不足，提出新的蜻蜓优化算法. 利用tent混沌初始化种群并对种群进行K-Means++聚类，根据聚类的结果分别对种群个体进行反向学习和高斯变异以增强种群的多样性，提高搜索效率. 引入非线性自适应因子加快收敛速度，使用探测精英引导策略增强算法跳出局部收敛的能力. 引入平方散列探测增加收敛精度. 将该优化算法应用于8个典型复杂函数优化问题，并与原蜻蜓算法，以及其他仿生计算算法对比，实验结果表明该改进算法具有良好的全局收敛性和寻优精度.


关键词： 蜻蜓算法,  聚类,  探测精英引导策略,  平方散列探测,  tent混沌 
Fig.1 Weight comparison curve of flight step
Fig.2 Illustration of probing elite guiding strategy
Fig.3 Illustration of square hash detection replacement
Fig.4 Flow chart of dragonfly algorithm based on clustering and detection elite guidance
函数名 表达式 维度 搜索区域
Sphere ${f_1}(x) = \displaystyle \sum\limits_{i = 1}^n {{x_i}^2} $ 10 [?100, 100]
Roscnbrock ${f_2}(x) = \displaystyle \sum\limits_{i = 1}^{n - 1} {(100{{({x_{i + 1}} - x_i^2)}^2})} $ 10 [?30, 30]
Step ${f_3}(x) = \displaystyle \sum\limits_{i = 1}^n { { {({x_i} + 0.5)}^2} }$ 10 [?100, 100]
Rastrigin ${f_4}(x) = \displaystyle \sum\limits_{i = 1}^n {[x_i^2 - 10\cos\; (2\pi {x_i}) + 10]}$ 10 [?5.12, 5.12]
Ackley $\begin{gathered} {f_5}(x) = - 20\exp\; \left( - 0.2\sqrt {\dfrac{1}{n}\displaystyle \sum\limits_{i = 1}^n {x_i^2} } \right) - \exp\; (\dfrac{1}{n}\displaystyle \sum\limits_{i = 1}^n {\cos \;(2\pi {x_i})} ) + 20 + {\rm{e}} \end{gathered}$ 10 [?32, 32]
Griewank ${f_6}(x) = \dfrac{1}{ {4\;000} }\displaystyle \sum\limits_{i = 1}^n {x_i^2 - \prod\limits_{i = 1}^n {\cos\; (\dfrac{ { {x_i} } }{ {\sqrt i } })} } + 1$ 10 [?600, 600]
Penalized1 $\begin{gathered} {f_7}(x) = \dfrac{\pi }{n}\left\{ {\left. {10\sin\; (\pi {y_1}) + \displaystyle \sum\limits_{i = 1}^{n - 1} { { {({y_i} - 1)}^2} } \left[ {1 + 10{ {\sin }^2}\;(\pi {y_{i + 1} })} \right] + { {({y_n} - 1)}^2} } \right\} } \right. + \displaystyle \sum\limits_{i = 1}^n {\mu ({x_i},10,100,4),\;{y_i} = 1 + \dfrac{ { {x_i} + 1} }{4} } \hfill \\ \end{gathered}$ 10 [?50, 50]
Penalized2 $\begin{gathered} {f_8}(x) = \displaystyle \sum\limits_{i = 1}^n {0.1\left\{ { { {\sin }^2}\;(3\pi {x_1}) + \displaystyle \sum\limits_{i = 1}^n { { {({x_i} - 1)}^2} } \left[ {1 + { {\sin }^2}(3\pi {x_i} + 1)} \right]} \right.} + \left. { { {({x_n} - 1)}^2}\left[ {1 + { {\sin }^2}\;(2\pi {x_n})} \right]} \right\} + \displaystyle \sum\limits_{i = 1}^n {\mu ({x_i},5,100,4)} \hfill \\ \end{gathered}$ 10 [?50, 50]
Tab.1 Eight typical complex functions
函数 算法 Xbest Xmean $\sigma $
f1 CEDA 2.36×10?93 5.43×10?90 1.05×10?89
DA 1.54×10?3 5.15×100 9.82×100
GWO 5.78×10?69 3.36×10?63 2.11×10?62
FOA 1.38×10?4 2.39×10?4 5.73×10?5
DE 2.40×10?20 4.52×10?19 4.93×10?19
ABC 4.61×10?10 4.61×10?10 1.25×10?07
PSO 1.28×10?5 4.82×10?4 1.10×10?3
f2 CEDA 1.39×10?6 2.37×10?2 1.21×10?1
DA 5.86×100 7.36×102 1.25×103
GWO 5.12×100 6.58×100 6.32×10?1
FOA 8.07×100 8.75×100 1.86×10?1
DE 6.74×100 7.81×100 3.61×100
ABC 4.70×100 7.25×100 1.47×100
PSO 1.80×10?2 6.83×101 1.15×102
f3 CEDA 0 0 0
DA 1.49×10?5 5.66×100 1.06×101
GWO 1.21×10?6 5.00×10?3 3.53×10?2
FOA 2.53×100 2.54×100 5.30×10?3
DE 2.32×10?20 4.19×10?19 4.75×10?19
ABC 3.46×10?10 4.13×10?8 9.69×10?8
PSO 3.87×10?5 5.50×10?4 5.58×10?4
Tab.2 Results of 2 000 independent runs of unimodal function
函数 算法 Xbest Xmean $\sigma $
f4 CEDA 0 0 0
DA 5.26×100 2.54×101 1.26×101
GWO 0 8.65×101 1.75×100
FOA 1.03×101 1.66×101 3.64×100
DE 1.40×10?10 4.13×10?6 1.46×10?6
ABC 1.20×101 2.62×101 4.46×100
PSO 5.07×100 2.35×101 1.23×101
f5 CEDA 8.88×10?16 2.55×10?15 1.98×10?15
DA 8.79×10?16 2.34×100 1.27×100
GWO 4.44×10?15 6.60×10?15 1.74×10?15
FOA 5.78×10?2 7.62×10?2 1.40×10?2
DE 9.33×10?11 2.66×10?10 1.16×10?10
ABC 6.51×10?5 8.02×10?5 6.47×10?4
PSO 1.27×10?2 1.05×100 8.33×10?1
f6 CEDA 0 0 0
DA 0 4.34×10?1 2.86×10?1
GWO 0 1.99×10?2 2.05×10?2
FOA 4.35×10?7 9.32×10?7 2.47×10?7
DE 1.74×10?11 3.60×10?3 8.10×10?3
ABC 2.02×10?1 3.72×10?1 7.03×10?2
PSO 1.49×10?2 1.24×10?1 6.18×10?2
f7 CEDA 4.71×10?32 4.71×10?32 4.95×10?47
DA 9.10×10?4 1.24×100 1.22×100
GWO 2.73×10?7 2.50×10?3 7.20×10?3
FOA 2.69×100 2.70×100 7.98×10?3
DE 8.36×10?22 3.06×10?20 4.18×10?20
ABC 2.49×10?9 8.45×10?7 2.03×10?6
PSO 5.62×10?5 6.94×10?2 2.09×10?1
f8 CEDA 1.34×10?32 1.34×10?32 1.34×10?48
DA 2.30×10?3 6.38×10?1 9.37×10?1
GWO 1.46×10?6 7.70×10?3 2.64×10?2
FOA 8.11×10?1 8.93×10?1 2.66×10?2
DE 7.95×10?21 1.11×10?19 1.33×10?19
ABC 4.10×10?8 6.83×10?6 1.08×10?5
PSO 1.33×10?4 7.70×10?3 9.10×10?3
Tab.3 Results of 2 000 independent runs of multimodal function
Fig.5 Comparison of convergence effect of CEDA algorithm and other classical algorithms
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