Table 2.

The equations and the boundaries of the studied benchmarks in the analysis.

Function	Equation	Constraint
Rastrigin	f 1(x)=10  D+∑i=1D(xi2 − 10  cos(2πxi))	[30,50]D
Rosenbrock	f 2(x)=∑i=1D−1(100(xi2 − xi+1)+(xi − 1)2)	[−2.045, 2.045]D
Ackley	$f_3\left(x\right)=-20\exp \left(-0.2\sqrt{\left(1/D\right){\displaystyle {\sum }_{i=1}^D\left(x_i^2\right)}}\right)-\exp \left(\left(1/D\right){\displaystyle {\sum }_{i=1}^D\left(\cos \left(2\pi x_i\right)\right)}\right)+20+e$	[−10,10]D
Sphere	f 4(x)=∑i=1Dxi2	[−512,512]D