Name

function

search Range

optimal value

function type

Sum square

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

[−10, 10]

0

unimodal

Exponential

$f\left(x\right)=-\exp \left(-0.5{\displaystyle \sum _{i=1}^n}{x}_i^2\right)$

[−1, 1]

−1

unimodal

Rastrigin

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

[−5.12, 5.12]

0

multimodal

Schaffer

$f\left(x\right)=\frac{{\sin }^2\left(\sqrt{{\displaystyle \sum _{i=1}^n}{x}_i^2}\right)-0.5}{{\left(1+0.001\left({\displaystyle \sum _{i=1}^n}{x}_i^2\right)\right)}^2}+0.5$

[−100, 100]

0

multimodal

Griewank

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

[−600, 600]

0

multimodal

Ackley

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

[−32, 32]

0

multimodal