Table 3.

Multi-peak test functions.

F	Function	Range	Dim	fmin
F8	$f_8\left(x\right)={\displaystyle \sum _{i=1}^n-x_i}\sin (\sqrt{\left|x_i\right|})$	[−500, 500]	30	−418.9829 × n
F9	$f_9\left(x\right)={\displaystyle \sum _{i=1}^n{x}_i^2}-10 \cos (2\pi x_i)+10$	[−5.12, 5.12]	30	0
F10	$\begin{array}{l}{f}_{10}\left(x\right)=-20\exp (-0.2\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^n{x}_i^2}})-\\ \exp (\frac{1}{n}{\displaystyle \sum _{i=1}^n\cos (2\pi x_i)})+20+e\end{array}$	[−32, 32]	30	0
F11	$f_{11}\left(x\right)={\displaystyle \sum _{i=1}^n\frac{x_i^2}{4000}}-{\displaystyle \prod _{i=1}^n\cos (\frac{x_i}{\sqrt{i}})}-1$	[−600, 600]	30	0
F12	$\begin{array}{l}{f}_{12}\left(x\right)=\frac{\pi }{n}\left\{\begin{array}{c}10{\sin }^2(\pi y_i)+{\displaystyle \sum _{i=1}^{n-1}{(y_i-1)}^2}\\ [1+10{\sin }^2(\pi y_{i+1})]+{(y_n-1)}^2\end{array}\right\}+\\ {\displaystyle \sum _{i=1}^{n}u(x_i,10,100,4)}\end{array}$	[−50, 50]	30	0
F13	$\begin{array}{l}{f}_{13}\left(x\right)=0.1\left\{\begin{array}{c}{\sin }^2(3\pi x_i)+{\displaystyle \sum _{i=1}^n{(x_i-1)}^2}\\ \left[1+{\sin }^2(3\pi x_i+1)\right]+\\ {\left(x_n-1\right)}^2\left[1+{\sin }^2(2\pi x_n)\right]\end{array}\right\}\\ +{\displaystyle \sum _{i=1}^{n}u(x_i,5,100,4)}\end{array}$	[−50, 50]	30	0