Table 3.

Unimodal benchmark functions.

Function	Dim	Range	fmin
$f_1(x)={\sum }_{i=1^n{x}_i^2}$	50	[−100, 100]	0
$f_2(x)={\sum }_{i=1^n|x_i|}+{\prod }_{i=1}^n|x_i|$	50	[−10, 10]	0
$f_3(x)={\sum }_{i=1^n{({\sum }_{j-1^i}{x}_j)}^2}$	50	[−100, 100]	0
$f_4(x)={\max }_i\{|x_i|,1⩽i⩽n\}$	50	[−100, 100]	0
$f_5(x)={\sum }_{i=1^{n-1}}[100{(x_{i+1}-x_i^2)}^2+{(x_i-1)}^2]$	50	[−30, 30]	0
$f_6(x)={\sum }_{i=1^n{([x_i+0.5])}^2}$	50	[−100, 100]	0
$f_7(x)={\sum }_{i=1^n{\mathit{ix}}_i^4}+\mathit{random}[0,1)$	50	[−1.28, 1.28]	0