Table 2.

Benchmark functions.

Test functions	L	M	Global optimum (f min)
f 1(x) = ∑l=1 L x l 2	10, 30	[−100,100]L	0
f 2(x) = ∑l=1 L|x l| + ∏l=1 L|x l|	10, 30	[−10,10]L	0
f 3(x) = ∑l=1 L(∑g=1 l x g)2	10, 30	[−100,100]L	0
f 4(x) = ∑l=1 L(⌊x l + 0.5⌋)2	10, 30	[−100,100]L	0
$f_{\mathrm{5}}(x)={{\displaystyle \sum }}_{l=\mathrm{1}}^L-x_l\sin \left(\sqrt{\left|x_l\right|}\right)$	10, 30	[−500,500]L	−12569.5
$\begin{array}{c}{f}_{\mathrm{6}}(x)=-\mathrm{20}\exp \left(-\mathrm{0.2}\sqrt{\left({{\displaystyle \sum }}_{l=\mathrm{1}}^L{x}_l^{\mathrm{2}}\right)/L}\right)\\ -\exp \left(\left(\mathrm{1}/L\right){{\displaystyle \sum }}_{l=\mathrm{1}}^L\cos \mathrm{2}\pi x_l\right)+\mathrm{20}+e\end{array}$	10, 30	[−32,32]L	0
$f_{\mathrm{7}}(x)=\left(\mathrm{1}/\mathrm{4000}\right){{\displaystyle \sum }}_{l=\mathrm{1}}^L{x}_l^{\mathrm{2}}-{\prod }_{l=\mathrm{1}}^L\cos \left(x_l/\sqrt{l}\right)+\mathrm{1}$	10, 30	[−600,600]L	0