Function

Range

$f_{\min }$

$f_1\left(x\right)={\displaystyle \sum _{i=1}^n{x}_i^2}$

$\left[-100,100\right]$

0

$f_2\left(x\right)={\displaystyle \sum _{i=1}^n\left|x_i\right|+{\displaystyle \prod _{i=1}^n\left|x_i\right|}}$

$\left[-10,10\right]$

0

$f_3\left(x\right)={\displaystyle \sum _{i=1}^n{\left({\displaystyle \sum _{j=1}^i{x}_j}\right)}^2}$

$\left[-100,100\right]$

0

$f_4\left(x\right)={\max }_i\left\{\left|x_i\right|,1\le i\le n\right\}$

$\left[-100,100\right]$

0

$f_5\left(x\right)={\displaystyle \sum _{i=1}^{n-1}\left[100{\left(x_{i+1}-x_i^2\right)}^2+{\left(x_i-1\right)}^2\right]}$

$\left[-30,30\right]$

0

$f_6\left(x\right)={\displaystyle \sum _{i=1}^{n}i{x}_i^4}+random\left[0,1\right)$

$\left[-1.28,1.28\right]$

0

$f_7\left(x\right)={\displaystyle \sum _{i=1}^n\left[x_i^2-10\cos \left(2\pi x_i\right)+10\right]}$

$\left[-5.12,5.12\right]$

0

$f_8\left(x\right)=-20\exp \left(-0.2\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^n{x}_i^2}}\right)-\exp \left(\frac{1}{n}\cos \left(2\pi x_i\right)\right)+20+e$

$\left[-32,32\right]$

0

$f_9\left(x\right)=\frac{1}{4000}{\displaystyle \sum _{i=1}^n{x}_i^2-{\displaystyle \prod _{i=1}^n\cos \left(\frac{x_i}{\sqrt{i}}\right)+1}}$

$\left[-600,600\right]$

0

$\begin{array}{l}{f}_{10}\left(x\right)=\frac{\pi }{n}\left\{10{\sin }^2\left(\pi y_i\right)+{\displaystyle \sum _{i=1}^{n-1}{\left(y_i-1\right)}^2\left[1+{\sin }^2\left(\pi y_{i+1}\right)\right]+{\left(y_n-1\right)}^2}\right\}\\ +{\displaystyle \sum _{i=1}^{n}u\left(x_i,10,100,4\right),}\\ y_i=1+\frac{1}{4}\left(x_i+1\right)\\ u\left(x_i,a,k,m\right)=\{\begin{array}{l}k{\left(x_i-a\right)}^m,x_i>a\\ 0,-a\le x_i\le a\\ k{\left(-x_i-a\right)}^m,x_i<-a\end{array}\end{array}$

$\left[-50,50\right]$

0