Table A2.

Test functions.

Function Name	Test Function	Variable Domain	Global Optimum
Sphere	$f\left(x\right)={\displaystyle \sum _{i=1}^d{x}_i^2}$	$x_i\in \left[-100,100\right]$	$f_{min}\left(0,0,0\cdots 0\right)=0$
Rosenbrock	$f\left(x\right)={\displaystyle \sum _{i=1}^{d-1}\left[100{\left(x_i^2-x_{i+1}\right)}^2+{\left(x_i-1\right)}^2\right]}$	$x_i\in \left[-30,30\right]$	$f_{min}\left(1,1,1\cdots 1\right)=0$
Rastrigin	$f\left(x\right)={\displaystyle \sum _{i=1}^d\left(x_i^2-10cos\left(2\pi x_i\right)+10\right)}$	$x_i\in \left[-5.12,5.12\right]$	$f_{min}\left(0,0,0\cdots 0\right)=0$
Shaffer	$f(x)=0.5+\frac{{\left(sin\sqrt{{\displaystyle \sum _{i=1}^d{x_i}^2}}\right)}^2-0.5}{{\left(1+0.001{\displaystyle \sum _{i=1}^d{x_i}^2}\right)}^2}$	$x_i\in \left[-100,100\right]$	$f_{min}\left(0,0,0\cdots 0\right)=0$
Griewank	$f(x)=\frac{1}{4000}{\displaystyle \sum _{i=1}^d{x_i}^2-{\displaystyle \prod _{i=1}^{d}cos(\frac{x_i}{\sqrt{i}})}}+1$	$x_i\in \left[-600,600\right]$	$f_{min}\left(0,0,0\cdots 0\right)=0$
Ackley	$\begin{array}{l}f(x)=-a\exp \left(-b\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^d{x_i}^2}}\right)-\exp \left(\frac{1}{n}{\displaystyle \sum _{i=1}^{d}cos(2\pi x_j)}\right)+a+e\\ a=20,b=0.2,e=2.7128\end{array}$	$x_i\in \left[-32,32\right]$	$f_{min}\left(0,0,0\cdots 0\right)=0$