Ackley function
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] The function is commonly used as a minimization function with global minimum value 0 at 0,.., 0 in the form due to Thomas Bäck. While Ackley gives the function as an example of "fine-textured broadly unimodal space" his thesis does not actually use the function as a test.
On a 2-dimensional domain it is defined by:
![{\displaystyle {\begin{aligned}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{aligned}}}](https://backend.710302.xyz/https/wikimedia.org/api/rest_v1/media/math/render/svg/e39a626ac0fb6c0e2a1f26c0883cb7e3f5be6fc0)
Its global optimum point is
See also
[edit]Notes
[edit]- ^ Ackley, D. H. (1987) "A connectionist machine for genetic hillclimbing", Kluwer Academic Publishers, Boston MA. p. 13-14
- ^ 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.