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. 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.

For $d$ dimensions, is defined as
: $f(x) = -a \exp \left( -b \sqrt \right) - \exp \left( \frac \sum_{i=1}^d \cos(c x_i) \right) + a + \exp(1)$
Recommended variable values are $a = 20$, $b = 0.2$, and $c = 2\pi$.

The global minimum is $f(x^*) = 0$ at $x^* = 0$.

See also

* Test functions for optimization

Notes

Test functions for optimization