基于聚类和探测精英引导的蜻蜓算法

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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

表 1 8个典型的复杂函数

Tab.1 Eight typical complex functions

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]