Ackley function

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 Dissertation.[1]

Ackley function of two variables

Animation of Ackley's function of three variables with time the 3rd variable.

On a 2-dimensional domain it is defined by:

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

Its global optimum point is:

${\displaystyle f(0,0)=0}$

See also

• Test functions for optimization

Notes

1. Ackley, D. H. (1987) "A connectionist machine for genetic hillclimbing", Kluwer Academic Publishers, Boston MA.