函数表达式

定义域

维度

最优值

$f_1\left(x\right)=0.5+\frac{{\sin }^2\left(x_1^2-x_2^2\right)-0.5}{{\left[1+0.001\left(x_1^2+x_2^2\right)\right]}^2}$

[−100, 100]

2

0

$f_2\left(x\right)=-\frac{1+\cos \left(12\sqrt{x_1^2+x_2^2}\right)}{0.5\left(x_1^2+x_2^2\right)+2}$

[−5.12, 5.12]

2

−1

$f_3\left(x\right)=-20\exp \left(-0.2\sqrt{\frac{1}{d}{\displaystyle \sum _{i=1}^d{x}_i^2}}\right)-\exp \left(\frac{1}{d}{\displaystyle \sum _{i=1}^d\cos \left(2\text{π}{x}_i\right)}\right)+20+\exp \left(1\right)$

[−32, 32]

60

0

$f_4\left(x\right)={\displaystyle {\sum }_{i=1}^d{x}_i^{i+1}}$

[−1, 1]

60

0

$f_5\left(x\right)={\displaystyle {\sum }_{i=1}^d\left[x_i^2-10\cos \left(2\text{π}{x}_i\right)+10\right]}$

[−5.12, 5.12]

60

0

$f_6\left(x\right)={\displaystyle {\sum }_{i=1}^d{x}_i^{10}}$

[−10, 10]

60

0

$f_7\left(x\right)={\displaystyle {\sum }_{i=1}^{d}i{x}_i^2}$

[−10, 10]

60

0

$f_8\left(x\right)={\displaystyle {\sum }_{i=1}^d\left|x_i\right|}$

[−100, 100]

60

0

$f_9\left(x\right)=0.5+\frac{{\sin }^2\left(\cos \left|x_1^2-x_2^2\right|\right)-0.5}{{\left[1+0.001\left(x_1^2+x_2^2\right)\right]}^2}$

[−100, 100]

2

0

$f_{10}\left(x\right)={\displaystyle {\sum }_{i=1}^d{\left(x_i-1\right)}^2}$

[−5.12, 5.12]

60

0

$f_{11}\left(x\right)=x_1^2+2x_2^2-0.3\cos \left(3\text{π}{x}_1\right)-0.4\cos \left(4\text{π}{x}_2\right)+0.7$

[−100, 100]

2

0

$f_{12}\left(x\right)={\left(x_1+2x_2-7\right)}^3+{\left(2x_1+x_2-5\right)}^2$

[−10, 10]

2

0