Table 1.

Detailed description of the test functions F1–F15.

No.	Function	Dimension	Interval	fmin
F1	$f\left(x\right)={\displaystyle \sum _{i=1}^d}{x}_i{}^2$	30, 50	[−100, 100]	0
F2	$f\left(x\right)={\displaystyle \sum _{i=1}^d}\left|x_i\right|+{\displaystyle \prod _{i=1}^d}\left|x_i\right|$	30, 50	[−10, 10]	0
F3	$f\left(x\right)={\displaystyle \sum _{i=1}^d}\left({\displaystyle \sum _{j=1}^i}{x}_j^2\right)$	30, 50	[−100, 100]	0
F4	$f\left(x\right)={\max }_i\left\{\left|x_{i }\right|,1\le i\le n\right\}$	30, 50	[−100, 100]	0
F5	$f\left(x\right)={\displaystyle \sum _{i=1}^{d-1}}\left[100{\left(x_{i+1}-x_i{}^2\right)}^2+{\left(x_i-1\right)}^2\right]$	30, 50	[−30, 30]	0
F6	$f\left(x\right)={\displaystyle \sum _{i=1}^d}{\left(\left[x_i+0.5\right]\right)}^2$	30, 50	[−100, 100]	0
F7	$f\left(x\right)={\displaystyle \sum _{i=1}^d}i{x}_i{}^4+random\left(0,1\right)$	30, 50	[−1.28, 1.28]	0
F8	$f\left(x\right)={\displaystyle \sum _{i=1}^d}-x_i\sin \left(\sqrt{\left|x_i\right|}\right)$	30, 50	[−500, 500]	−418.9829 × 5
F9	$f\left(x\right)={\displaystyle \sum _{i=1}^d}\left[x_i{}^2-10\cos \left(2\Pi x_i\right)+10\right]$	30, 50	[−5.12, 5.12]	0
F10	$\begin{array}{l}f\left(x\right)=-20\exp \left(-0.2\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^d}{x}_i{}^2}\right)-\\ \exp \left(\frac{1}{n}{\displaystyle \sum _{i=1}^d}\cos \left(2\Pi x_i\right)\right)+20+e\end{array}$	30, 50	[−32, 32]	0
F11	$f\left(x\right)=\frac{1}{4000}{\displaystyle \sum _{i=1}^d}{x}_i{}^2-{\displaystyle \prod _{i=1}^d}\cos \left(\frac{x_i}{\sqrt{i}}\right)+1$	30, 50	[−600, 600]	0
F12	$f(x)={\displaystyle {\sum }_{i=1}^{d-1}}\left[\begin{array}{c}{x}_i^2+2x_{i+1}^2-0.3\cos \left(3\pi x_i\right)\\ -0.4\cos \left(4\pi x_{i+1}\right)+0.7\end{array}\right]$	30, 50	[−15, 15]	0
F13	$f(x)={\displaystyle {\sum }_{i=1}^d}|x_i\sin \left(x_i\right)+0.1x_i|$	30, 50	[−10, 10]	0
F14	$f(x)={\displaystyle {\sum }_{i=1}^{d/4}}\left[\begin{array}{c}{(x_{4i-3}+10x_{4i-2})}^2+5{(x_{4i-1}-x_{4i})}^2\\ +{(x_{4i-2}-2x_{4i-1})}^4+10{(x_{4i-3}-x_{4i})}^4\end{array}\right]$	30, 50	[−4, 5]	0
F15	$\begin{array}{l}f(x)=\left\{\left[{\displaystyle \sum _{i=1}^d}{\sin }^2\left(x_i\right)\right]-exp\left(-{\displaystyle \sum _{i=1}^d}{x}_i{}^2\right)\right\}\\ ·exp\left[-{\displaystyle \sum _{i=1}^d}{\sin }^2\sqrt{\left|x_i\right|}\right]\end{array}$	30, 50	[−10, 10]	−1