Ackley function
From HandWiki
Short description: Function used as a performance test problem for optimization algorithms
Ackley function of two variables
Contour surfaces of Ackley's function in 3D
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]
On a 2-dimensional domain it is defined by:
- [math]\displaystyle{ \begin{align} f(x,y) = -20&{}\exp\left[-0.2\sqrt{0.5(x^2+y^2)}\,\right] \\ & {} -\exp\left[0.5\left(\cos 2\pi x + \cos 2\pi y \right)\right] + e + 20 \end{align} }[/math][2]
Its global optimum point is
- [math]\displaystyle{ f(0,0) = 0. }[/math]
See also
Notes
- ↑ Ackley, D. H. (1987) "A connectionist machine for genetic hillclimbing", Kluwer Academic Publishers, Boston MA.
- ↑ Bäck, Thomas (1996-02-15). "Artificial Landscapes". Evolutionary Algorithms in Theory and Practice. Oxford University Press. p. 142. doi:10.1093/oso/9780195099713.003.0008. ISBN 978-0-19-509971-3.
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