Table 1.

Six test functions utilized in this experiment.

Functions	Name of function	Expression	Domain of variables
F 1	De Jong's sphere function	$f\left(x\right)={\displaystyle \sum }_{i=1}^D{x}_i^2$	[−100,100]
F 2	Schwefel 2.22 function	$f\left(x\right)={\displaystyle \sum }_{i=1}^D\left|x_i\right|+\prod _{i=1}^D\left|x_i\right|$	[−15,15]
F 3	Griewangk's function	$f\left(x\right)=-\prod _{i=1}^D\cos \left(\frac{x_i}{\sqrt{i}}\right)+{\displaystyle \sum }_{i=1}^D\frac{x_i^2}{4000}+1$	[−15,15]
F 4	Rosenbrock's function	$f\left(x\right)={\displaystyle \sum }_{i=1}^{D-1}100\ast {\left(x_{i+1}-x_i^2\right)}^2+{(x_i-1)}^2$	[−15,15]
F 5	Rastrigin's function	$f\left(x\right)=D\ast \mathrm{10}+{\displaystyle \sum }_{i=1}^D\left(x_i^2-10\ast \cos \left(2\pi x_i\right)\right)$	[−5,5]
F 6	Ackley's function	$f\left(x\right)=\mathrm{20}+e-\mathrm{20}\ast \exp \left(-0.2\ast \sqrt{\frac{1}{D}\ast {\displaystyle \sum }_{i=1}^D{x}_i^2}\right)-\exp \left(\frac{1}{D}\ast {\displaystyle \sum }_{i=1}^D\cos \left(2\pi x_i^2\right)\right)$	[−15,15]