Table 1. Details of benchmarks.

NO.	Func.name	Expression	Box constraint	optimum
F1	Sphere	$f\left(x\right)={\displaystyle \sum _{i=1}^n}{x}_i^2$	[−100, 50]D	[0, 0]D
F2	Rosenbrock	$f\left(x\right)={\displaystyle \sum _{i=1}^{n-1}}{100(x_{i+1}-x_i^2)}^2+{(x_i-1)}^2$	[−30, 30]D	[0, 0]D
F3	Step	$f\left(x\right)={\displaystyle \sum _{i=1}^n}{(x_i^{}+0.5)}^2$	[−100, 100]D	[0, 0]D
F4	Schwefel’s P2.22	$f\left(x\right)={\displaystyle \sum _{i=1}^n\left|x_i\right|}+{\displaystyle \prod _{i=1}^n\left|x_i\right|}$	[−10, 10]D	[0, 0]D
F5	Noise Quadric	$f\left(x\right)={\displaystyle \sum _{i=1}^{n}i{x}_i^4}+random(0,1)$	[−1.28, 1.28]D	[0, 0]D
F6	A generalized penalized	$\begin{array}{c}f\left(x\right)=\frac{\pi }{n}(10{sin}^2\left(\pi y_1\right)\hfill \\ +{\displaystyle \sum _{i=1}^n}(y_i-1)(1+10{sin}^2\left(\pi y_{i+1}\right))+{(y_n-1)}^2)\hfill \\ +{\displaystyle \sum _{i=1}^n}u(x_i,10),\hfill \\ y_i=1+(x_i+1)/4,u(x_i,a)\hfill \\ =\{\begin{array}{c}100{(x_i-a)}^4,if{x}_i>a\\ 0,if-a\le x_i\le a\\ 100{(-x_i-a)}^{4}if{x}_i<-a\end{array}\hfill \end{array}$	[−50, 50]D	[0, 0]D
F7	Another generalized penalized	$\begin{array}{c}f\left(x\right)=({sin}^2\left(3\pi x_1\right)+{(x_n-1)}^2(1+{sin}^2\left(2\pi x_n\right)\hfill \\ +{\displaystyle \sum _{i=1}^{n-1}}{(x_i-1)}^2(1+sin3\pi x_i))/10+{\displaystyle \sum _{i=1}^n}u(x_i,5)\hfill \end{array}$	[−50, 50]D	[0, 0]D
F8	Ackley	$\begin{array}{c}f\left(x\right)=20+\mathrm{e}-20*exp(-0.2\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^n}{x}_i^2})\hfill \\ -exp\left(\frac{1}{n}{\displaystyle \sum _{i=1}^n}cos\left(2\pi x_i\right)\right)\hfill \end{array}$	[−32, 32]D	[0, 0]D
F9	Rastrigin	$f\left(x\right)={\displaystyle \sum _{i=1}^n}{x}_i^2-10cos2\pi x_i+10$	[−5, 5]D	[0, 0]D
F10	Griewank	$f\left(x\right)=1+\frac{{\displaystyle \sum _{i=1}^n}{(x_i-100)}^2}{4000}-{\displaystyle \prod _{i=1}^n}cos\left(\frac{x_i-100}{\sqrt{i}}\right)$	[−600, 200]D	[0, 0]D
F11	Schwefel	$f\left(x\right)=418.9829-{\displaystyle \sum _{i=1}^n}{x}_{i}sin\left(\sqrt{\left|x_i\right|}\right)$	[−500, 500]D	[420, 96]D
F12	Ackley-Rotated	f12(y) = f8(y), y = Mx	[−32, 32]D	[0, 0]D
F13	Rastrigin-Rotated	f13(y) = f9(y), y = Mx	[−5, 5]D	[0, 0]D
F14	Griewank-Rotated	f14(y) = f10(y), y = Mx	[−600, 200]D	[0, 0]D
F15	Ackley-Rotated-shifted	$f_{15}\left(y\right)=f_8\left(y\right)+f\_bias,y=M(\overrightarrow{x}-\overrightarrow{o})$	[−32, 32]D	$\overrightarrow{o}$
F16	Rastrigin-Rotated-shifted	$f_{16}\left(y\right)=f_8\left(y\right)+f\_bias,y=M(\overrightarrow{x}-\overrightarrow{o})$	[−5, 5]D	$\overrightarrow{o}$
F17	Griewank-Rotated-shifted	$f_{17}\left(y\right)=f_{10}\left(y\right)+f\_bias,y=M(\overrightarrow{x}-\overrightarrow{o})$	[−600, 200]D	$\overrightarrow{o}$