Table 1.

UFs and MFs benchmark functions.

Function	Range	n (Dim)
$F_1\left(X\right)={\sum }_{i=1}^n{x}_i^2$	${\left[-100,100\right]}^n$	30
$F_2\left(X\right)={\sum }_{i=1}^n\left|x_i\right|+{\prod }_{i=1}^n\left|x_i\right|$	${\left[-10,10\right]}^n$	30
$F_3\left(X\right)={\sum }_{i=1}^n{\left({\sum }_{j=1}^i{x}_j\right)}^2$	${\left[-100,100\right]}^n$	30
$F_4\left(X\right)=\underset{i}{\max }\left\{\left|x_i\right|,1\le i\le n\right\}$	${\left[-100,100\right]}^n$	30
$F_5\left(X\right)={\sum }_{i=1}^n{\left(\left[x_i+0.5\right]\right)}^2$	${\left[-100,100\right]}^n$	30
$F_6\left(X\right)={\sum }_{i=1}^{n}i{x}_i^4+random[\mathrm{0,1})$	${\left[-1.28,1.28\right]}^n$	30
$F_7\left(X\right)=\sum _{i-1}^n-x_i\sin \left(\sqrt{\left|x_i\right|}\right)$	${\left[-500,500\right]}^n$	30
$F_8\left(X\right)={\sum }_{i=1}^n\left[x_i^2-10\cos \left(2\pi x_i\right)+10\right]$	${\left[-5.12,5.12\right]}^n$	30
$F_9\left(X\right)=-20\exp \left(-0.2\sqrt{\frac{1}{n}{\sum }_{i=1}^n{x}_i^2}\right)-\mathit{exp}\left(\frac{1}{n}{\sum }_{i=1}^n\cos \left(2\pi x_i\right)\right)+20+e$	${\left[-32,32\right]}^n$	30
$F_{10}\left(X\right)=\frac{1}{4000}{\sum }_{i=1}^n{x}_i^2-{\prod }_{i=1}^n\cos \left(\frac{x_i}{\sqrt{i}}\right)+1$	${\left[-600,600\right]}^n$	30
$F_{11}\left(X\right)=0.1\left\{{\sin }^2\left(3\pi x_1\right)+{\sum }_{i=1}^n{\left(x_i-1\right)}^2\left[1+{\sin }^2\left(3\pi x_i+1\right)\right]+{\left(x_n-1\right)}^2\left[1+{\sin }^2\left(2\pi x_n\right)\right]\right\}+{\sum }_{i=1}^{n}u\left(x_i,5,100,4\right)$	${\left[-50,50\right]}^n$	30
$F_{12}\left(X\right)=$ $\frac{\pi }{n}\left\{10\sin \left(\pi y_1\right)+{\sum }_{i=1}^{n-1}{\left(y_i-1\right)}^2\left[1+10{\sin }^2\left(\pi y_{i+1}\right)\right]+{\left(y_n-1\right)}^2\right\}+{\sum }_{i=1}^{n}u\left(x_i,10,100,4\right)$ $y_i=1+\frac{x_{i+4}}{4}$$u\left(x_i,a,k,m\right)=\{\begin{array}{c}k{\left(x_i-a\right)}^m{x}_i>a\\ 0a<x_i<a\\ k{\left(-x_i-a\right)}^m{x}_i<-a\end{array}$	${\left[-50,50\right]}^n$	30