Ackley function

Ackley function of two variables

Animation of Ackley's function of three variables.

In mathematical optimization, the Ackley function is a non-convex function used as a performance test problem for optimization algorithms. It was proposed by David Ackley in his 1987 PhD Disertation .

On an n-dimensional domain it is defined by:

${\begin{aligned}f(x,y)={}&-20\exp \left[-0.2{\sqrt {0.5\left(x^{2}+y^{2}\right)}}\right]&{}-\exp \left[0.5\left(\cos 2\pi x+\cos 2\pi y\right)\right]+e+20\end{aligned}}$

Its global optimum point is:

$f(0,0)=0$

See also

• Test functions for optimization