函数名称

函数公式

维度

定义域

最优值

Sphere Function

30

[−100, 100]

0

Schwefel’s Problem 2.22

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

30

[−10, 10]

0

Schwefel’s Problem 1.2

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

30

[−100, 100]

0

Schwefel’s Problem 2.21

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

30

[−100, 100]

0

Generalized Rastrigin’s Function

$F_5\left(x\right)={\displaystyle \sum }_{i=1}^n\left[x_i^2-10\cos \left(2\pi x_i\right)+10\right]$

30

[−5.12, 5.12]

0

Ackley’s Function

$F_6\left(x\right)=-20\exp \left(-0.2\sqrt{\frac{1}{n}{\displaystyle \sum }_{i=1}^n{x}_i^2}\right)-\exp \left(\frac{1}{n}{\displaystyle \sum }_{i=1}^n\cos \left(2\pi x_i\right)\right)+20+e$

30

[−32, 32]

0

Generalized Griewank’s Function

$F_7\left(x\right)=\frac{1}{4000}{\displaystyle \sum }_{i=1}^n{x}_i^2-{\displaystyle \prod }_{i=1}^n\cos \frac{x_i}{\sqrt{i}}+1$

30

[−600, 600]

0

Generalized Penalized Function

$\begin{array}{c}{F}_8\left(x\right)=\frac{\pi }{n}\left\{10{\sin }^2\left(\pi y_i\right)+{\displaystyle \sum }_{i=1}^{n-1}{\left(y_i-1\right)}^2\cdot \left[1+10{\sin }^2\left(\pi y_{i+1}\right)\right]+{\left(y_n-1\right)}^2\right\}\\ +{\displaystyle \sum }_{i=1}^{n}u\left(x_i,10,100,4\right)\end{array}$

30

[−50, 50]

0

Kowalik’s Function

$F_9\left(x\right)={\displaystyle \sum }_{i=1}^{11}{\left[a_i-\frac{x_i\left(b_i^2+b_i{x}_2\right)}{b_i^2+b_i{x}_3+x_4}\right]}^2$

4

[−5, 5]

3.07E−04

Branin Function

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

2

[−5, 5]

0.398