函数名

数学表达式

取值范围

类型

Rosenbrock

$f_1\left(x\right)={\displaystyle \sum _{i=1}^{n-1}\left[100{\left(x_{i+1}-x_i^2\right)}^2+{\left(x_i-1\right)}^2\right]}$

$x_i\in \left[-30,30\right]$

单峰病态

Rastrigrin

$f_2\left(x\right)={\displaystyle \sum _{i=1}^n\left(x_i^2-10\cos \left(2\pi x_i\right)+10\right)}$

$x_i\in \left[-5.12,5.12\right]$

多峰

Griewank

$f_3\left(x\right)=\frac{1}{4000}{\displaystyle \sum _{i=1}^n{x}_i^2}-{\displaystyle \prod _{i=1}^n\cos \left(\frac{x_i}{\sqrt{i}}\right)}+1$

$x_i\in \left[-100,100\right]$

多峰

Levy

$\begin{array}{l}{f}_4\left(x\right)={\sin }^{\text{2}}\left(\pi {\omega }_1\right)+{\displaystyle \sum _{i=1}^{d-1}{\left({\omega }_i-1\right)}^2\left[1+10{\sin }^2\left(2\pi {\omega }_d\right)\right]}\\ +{\left({\omega }_d-1\right)}^2\left[1+{\sin }^2\left(2\pi {\omega }_d\right)\right]\end{array}$

$x_i\in \left[-\text{10},\text{10}\right]$

多峰