Table 2.

Benchmark functions.

Function	Definition	Range
F1	$F1=\sum _{i=1}^D{x}_i^2$	[− 100, 100]
F2	$F2=\sum _{i=1}^D{({10}^6)}^{\frac{i-1}{D-1}}{x}_i^2$	[− 100, 100]
F3	$F3=x_1^2+{10}^6\sum _{i=2}^D{x}_i^2$	[− 100, 100]
F4	$F4={10}^6{x}_1^2+\sum _{i=2}^D{x}_i^2$	[− 100, 100]
F5	$F5=\sqrt{\sum _{i=1}^D{|x_i|}^{2+4\frac{i-1}{D-1}}}$	[− 100, 100]
F6	$F6=\sum _{i=1}^{D-1}\left(100{\left(x_i^2-x_{i+1}\right)}^2+{\left(x_i-1\right)}^2\right)$	[− 2.048, 2.048]
F7	$F7=20+e-20exp\left(-0.2\sqrt{\frac{1}{D}\sum _{i=1}^D{x}_i^2}\right)+exp\left(\frac{1}{D}\sum _{i=1}^{D}cos\left(2\pi x_i\right)\right)$	[− 32, 32]
F8	$F8=\sum _{i=1}^D|x_{i}sin\left(x_i\right)+0.1x_i|$	[− 10, 10]
F9	$F9=\sum _{i=1}^D\frac{x_i^2}{4000}-\prod _{i=1}^{D}cos\left(\frac{x_i}{\sqrt{i}}\right)+1$	[− 600, 600]
F10	$F10=\sum _{i=1}^D\left(x_i^2-10cos\left(2\pi x_i\right)+10\right)$	[− 5.12, 5.12]
F11	$F11=\sum _{i=1}^D|x_i|+\prod _{i=1}^D|x_i|$	[− 100, 100]
F12	$F12=max|x_i|,(1<i<D)$	[− 100, 100]
F13	$F13=\sum _{i=1}^D{x}_i^{10}$	[− 10, 10]
F14	$F14=\sum _{i=1}^D|x_i|$	[− 100, 100]
F15	$F15=\sum _{i=2}^D\left({\left(x_i-1\right)}^2+{\left(x_1-x_i^2\right)}^2\right)$	[0, 10]