函数名称

特征

维度

区间

最优值

$F_1\left(x\right)={\displaystyle \sum _{i=1}^n{x}_i^2}$

单峰

100

[−100, 100]

0

$F_2\left(x\right)={\displaystyle \sum _{i=1}^n\left[100{\left(x_{\left(i+1\right)}-x_i^2\right)}^2+{\left(x_i-1\right)}^2\right]}$

单峰

100

[−10, 10]

0

$F_3\left(x\right)={\displaystyle \sum _{i=1}^n\left[x_i^2-10\cos \left(2\pi x_i\right)+10\right]}$

多峰

100

[−32, 32]

0

$F_4\left(x\right)=-20\exp \left(-0.2\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^n{x}_i^2}}\right)-\exp \left\{\frac{1}{n}{\displaystyle \sum _{i=1}^n\cos \left(2\pi x_i\right)}\right\}+20+e$

多峰

100

[6, 6]

0

$F_5\left(x\right)=\frac{1}{4000}{\displaystyle \sum _{i=1}^n{X}_i^2}-{\displaystyle \prod _{i=1}^n\cos \left(x_i/\sqrt{i}\right)}+1$

多峰

100

[−600, 600]

0

$F_6\left(x\right)={\displaystyle \sum _{i=1}^n{X}_i^2}+{\left({\displaystyle \sum _{i=1}^{n}0.5i{X}_i}\right)}^2+{\left({\displaystyle \sum _{i=1}^{n}0.5i{X}_i}\right)}^4$

多峰

100

[−100, 100]

0

$\begin{array}{c}{F}_7\left(x\right)={\displaystyle \sum _{i=1}^n({\left(x_{4i-2}^2-10x_{4i-2}\right)}^2}+5{\left(x_{\left(4i-1\right)}-x_{4}i\right)}^2\\ +{\left(x_{\left(4i-2\right)}-2x_{\left(4i-1\right)}\right)}^4+10{\left(x_{\left(4i-3\right)}-2x_{4}i\right)}^4)\end{array}$

多峰

100

[−1000, 1000]

0

$F_8\left(x\right)={\displaystyle \sum _{i=1}^{D-1}\left(100{\left(x_i^2-x_{i+1}\right)}^2+{\left(x_i-1\right)}^2\right)}$

多峰

100

[−100, 100]

0

$F_9\left(x\right)={\displaystyle \sum _{i=1}^D{\left({10}^6\right)}^{\frac{i-1}{D-1}{x}_i^2}}$

多峰

100

[−1300, 1300]

0

$F_{10}\left(x\right)=g\left(x_1,x_2\right)+g\left(x_2,x_3\right)+\cdots +g\left(x_{D-1},x_D\right)+g\left(x_D,x_1\right)$

多峰

100

[−600, 600]

0