NO

Functions

D

Search space

$\text{fmin}$

F1

$F_1\left(x\right)={\displaystyle {\sum }_{i=1}^n{x}_i^2}$

30

${\left[-100,100\right]}^D$

0

F2

$F_2\left(x\right)={\displaystyle {\sum }_{i=1}^n\left|x_i\right|}+{\displaystyle {\prod }_{i=1}^n\left|x_i\right|}$

30

${\left[-10,10\right]}^D$

0

F3

$F_3\left(x\right)={\displaystyle {\sum }_{i=1}^n{\left({\displaystyle {\sum }_{j=1}^i{x}_j}\right)}^2}$

30

${\left[-100,100\right]}^D$

0

F4

$F_4\left(x\right)={\max }_i\left\{\left|x_i\right|,1\le i\le n\right\}$

30

${\left[-100,100\right]}^D$

0

F5

$F_5\left(x\right)={\displaystyle {\sum }_{i=1}^{n-1}\left[100{\left(x_{i+1}-x_i\right)}^2+{\left(x_i-1\right)}^2\right]}$

30

${\left[-30,30\right]}^D$

0

F6

$F_6\left(x\right)={{\displaystyle {\sum }_{i=1}^n\left(\left[x_i+0.5\right]\right)}}^2$

30

${\left[-100,100\right]}^D$

0

F7

F8

$F_8\left(x\right)={\displaystyle {\sum }_{i=1}^n\left[x_i^2-10\cos \left(2\pi x_i\right)+10\right]}$

30

${\left[-5.12,5.12\right]}^D$

0

F9

$F_9\left(x\right)=-20\exp \left(-0.2\sqrt{\frac{1}{n}{\displaystyle {\sum }_{i=1}^n{x}_i^2}}\right)-\exp \left(\frac{1}{n}{\displaystyle {\sum }_{i=1}^n\cos \left(2\pi x_i\right)}\right)+20+e$

30

${\left[-32,32\right]}^D$

0

F10

$F_{10}\left(x\right)=\frac{1}{4000}{\displaystyle {\sum }_{i=1}^n{x}_i^2}-{\displaystyle {\prod }_{i=1}^n\cos \left(\frac{x_i}{\sqrt{i}}\right)}+1$

30

${\left[-600,600\right]}^D$

0

F11

$\begin{array}{l}{F}_{11}\left(x\right)={\displaystyle {\sum }_{i=1}^{n}u\left(x_i,5,100,4\right)}\\ +0.1\left\{{\sin }^2\left(3\pi x_1\right)+{\displaystyle {\sum }_{i=1}^{n-1}{\left(x_i-1\right)}^2\left[1+{\sin }^2\left(3\pi x_1{}_{i+1}\right)\right]+{\left(x_n-1\right)}^2\left[1+{\sin }^2\left(3\pi x_n\right)\right]}\right\}\end{array}$

30

${\left[-50,50\right]}^D$

0

F12

$F_{12}\left(x\right)={\left(\frac{1}{500}+{\displaystyle {\sum }_{j=1}^{25}\frac{1}{j+{\displaystyle {\sum }_{i=1}^2{\left(x_i-a_{ij}\right)}^6}}}\right)}^{-1}$

2

${\left[-65.536,65.536\right]}^D$

0.998

F13

$F_{13}\left(x\right)=4x_1^2-2.1x_1^4+\frac{1}{3}{x}_1^6+x_1{x}_2-4x_2^2+4x_2^4$

2

${\left[-5,5\right]}^D$

−1.0316285

F14

$F_{14}\left(x\right)={\left(x_2-\frac{5.1}{4{\pi }^2}{x}_1^2+\frac{5}{\pi }{x}_1-6\right)}^2+10\left(1-\frac{1}{8\pi }\right)\cos x_1+10$

2

$\left[-5,10\right]\times \left[0,15\right]$

0.398

F15

$\begin{array}{l}{F}_{15}\left(x\right)=\left[1+{\left(x_1+x_2+1\right)}^2\left(19-14x_1+3x_1^2-14x_2+6x_1{x}_2+3x_2^2\right)\right]\\ \times \left[30+{\left(2x_1-3x_2\right)}^2\left(18-32x_1+12x_1^2+48x_2-36x_1{x}_2+27x_2^2\right)\right]\end{array}$

2

${\left[-2,2\right]}^D$

3