Table 2.

Unimodal benchmark functions.

Function	Expression	n	Range	fmin
Sphere	$f_1(x)={{\displaystyle {\sum }_{i=1}^{n}x}}_i$	5	[−100,100]	0
Schwefel 2.22	$f_2(x)={\displaystyle {\sum }_{i=1}^n\left|x_i\right|}+{\displaystyle {\prod }_{i=1}^n\left|x_i\right|}$	5	[−10,10]	0
Schwefel 1.2	$f_3(x)={\displaystyle {\sum }_{i=1}^n({\displaystyle {\sum }_{j=1}^i{x}_j}}{)}^2$	5	[−100,100]	0
Schwefel 2.21	$f_4(x)=\{\left|x_i\right|,1\le i\le n\}$	5	[−100,100]	0
Rosenbrock	$f_5(x)={\displaystyle {\sum }_{i=1}^{n-1}[100(x_{i+1}-x_i{}^2)+{(x_i-1)}^2]}$	5	[−30,30]	0
Step	$f_6(x)={\displaystyle {\sum }_{i=1}^n([x_i+0.5]}{)}^2$	5	[−100,100]	0
Quartic	$f_7(x)=i{x}_i{}^4+random[0,1)$	5	[−1.28,1.28]	0