F_min

Range

Dim

Function

0

[−100, 100]

30

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

0

[−10, 10]

30

$F_2\left(x\right)={\displaystyle \sum }_{i=1}^n\left|x\right|+{\displaystyle \prod }_{i=1}^n\left|x_i\right|$

0

[−100, 100]

30

$F_3\left(x\right)={\displaystyle \sum _{i=1}^n{\left({\displaystyle {\sum }_{j-1}^n{x}_i}\right)}^2}$

0

[−100, 100]

30

$F_4\left(x\right)={\max }_i\left\{\left|x_i\right|,1\le i\le n\right\}$

0

[−30, 30]

30

$F_5\left(x\right)={\displaystyle {\sum }_{i=1}^{n-1}\left[100{\left(x_{i+1}-x_i^2\right)}^2+{\left(x_i-1\right)}^2\right]}$

[−5.12, 5.12]

30

$F_6\left(x\right)={\displaystyle {\sum }_{i=1}^n\left[x_i^2-10\cos \left(2\pi x_i\right)+10\right]}$

0

[−32, 32]

30

$F_7\left(x\right)=-20\exp \left(-0.2\sqrt{\frac{1}{n}{\displaystyle {\sum }_{i=1}^n{x}_i^2}}\right)-\exp \left(\frac{1}{n}{\displaystyle {\sum }_{i=1}^n\cos \left(2\pi x_i\right)}\right)+20+e$

0

[−600, 600]

30

$F_8\left(x\right)={\displaystyle {\sum }_{i=1}^n{x}_i^2}-{\displaystyle {\prod }_{i=1}^n\cos \left(\frac{x_i}{\sqrt{i}}\right)}+1$

0.00030

[−5, 5]

4

$F_9\left(x\right)={\displaystyle {\sum }_{i=1}^{11}{\left[a_i-\frac{x_1\left(b_i^2+b_i{x}_2\right)}{b_i^2+b_i{x}_3+x_4}\right]}^2}$

−1.0316

[−5, 5]

2

$F_{10}=4x_1^2-2.1x_1^4+\frac{1}{3}{x}_1^6+x_1{x}_2-4x_2^2+4x_2^4$