Table A2.

High-dimensional multimodal test functions.

Objective Function	Range	Dimensions	Fmin
$F_8\left(x\right)=\sum _{i=1}^m-x_i \sin \left(\sqrt{\left|x_i\right|}\right)$	$\left[-500, 500\right]$	30	−12,569
$F_9\left(x\right)=\sum _{i=1}^m\left[ x_i^2-10\cos \left(2\pi x_i\right)+10\right]$	[−5.12, 5.12]	30	0
$F_{10}\left(x\right)=-20\exp (-0.2\sqrt{\frac{1}{m}\sum _{i=1}^m{x}_i^2})-\exp \left(\frac{1}{m}\sum _{i=1}^m\cos \right(2\pi x_i\left)\right)+20+e$	$\left[-32, 32\right]$	30	0
$F_{11}\left(x\right)=\frac{1}{4000}\sum _{i=1}^m{x}_i^2-\prod _{i=1}^m\cos \left(\frac{x_i}{\sqrt{i}}\right)+1$	$\left[-600, 600\right]$	30	0
$F_{12}\left(x\right)=\frac{\pi }{m} \left\{10\sin \left(\pi y_1\right)+\sum _{i=1}^m{\left(y_i-1\right)}^2\left[1+10 {\sin }^2\left(\pi y_{i+1}\right)\right]+{\left(y_n-1\right)}^2\right\}+\sum _{i=1}^{m}u\left(x_i,10,100,4\right)$ $u\left(x_i,a,i,n\right)=\{\begin{array}{cc}k{\left(x_i-a\right)}^n,& x_i>-a;\\ 0,& -a<x_i<a\\ k{\left(-x_i-a\right)}^n, & x_i<-a\end{array};$	$\left[-50, 50\right]$	30	0
$\begin{array}{l}{F}_{13}\left(x\right)=0.1\{{\sin }^2\left(3\pi x_1\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+\sum _{i=1}^m{\left(x_i-1\right)}^2\left[1+{\sin }^2\left(3\pi x_i+1\right)\right]+{\left(x_n-1\right)}^2\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left[1+{\sin }^2\left(2\pi x_m\right)\right]\}+\sum _{i=1}^{m}u\left(x_i,5,100,4\right)\end{array}$	$\left[-50, 50\right]$	30	0