Table 1.

Test functions.

Function	Equation	Dimension	Bounds	Optimum
F1	${{\displaystyle \sum _{i=1}^d\left({\displaystyle \sum _{j=1}^i{x}_j}\right)}}^2$	30	[−100, 100]	0
F2	$\max \left\{\left|x_i\right|,1\le i\le d\right\}$	30	[−100, 100]	0
F3	${\displaystyle \sum _{i=1}^d\left|x_i\sin (x_i)+0.1x_i\right|}$	30	[−10, 100]	0
F4	$-20\exp \left(-0.2\sqrt{\frac{1}{d}{\displaystyle \sum _{i=1}^d{x}^2}}\right)-\exp \left(\frac{1}{d}{\displaystyle \sum _{i=1}^d\cos (2\pi x_i)}\right)+20+\exp (1)$	30	[−5.12, 5.12]	0
F5	$-{\displaystyle \sum _{i=1}^4{c}_i\exp \left(-{\displaystyle \sum _{j=1}^3{a}_{ij}{(x_j-p_{ij})}^2}\right)}$	30	[1, 3]	−3.86
F6	$-{\displaystyle \sum _{i=1}^7{[(X-a_i){(X-a_i)}^T+c_i]}^{-1}}$	30	[0, 10]	−10.4
F7	$-{\displaystyle \sum _{i=1}^{10}{[(X-a_i){(X-a_i)}^T+c_i]}^{-1}}$	30	[0, 10]	−10.5
F8	$-{\displaystyle \sum _{i=1}^5{[(X-a_i){(X-a_i)}^T+c_i]}^{-1}}$	30	[0, 10]	−10.1