ackley_func {EmiR}

Ackley Function

Description

Implementation of n-dimensional Ackley function, with \(a=20\), \(b=0.2\) and \(c=2\pi\) (see definition below).

Usage

ackley_func(x)

Arguments

x

numeric or complex vector.

Details

On an n-dimensional domain it is defined by

\[f(\vec{x}) = -a\exp\left(-b \sqrt{\frac{1}{n}\sum_{i=1}^n x_{i}^2} \right) -\exp\left(\frac{1}{n}\sum_{i=1}^n \cos(cx_{i}) \right) + a + \exp(1),\]

and is usually evaluated on \(x_{i} \in [ -32.768, 32.768 ]\), for all \(i=1,...,n\). The function has one global minimum at \(f(\vec{x})=0\) for \(x_{i}=0\) for all \(i=1,...,n\).

Value

The value of the function.

References

Ackley DH (1987). A Connectionist Machine for Genetic Hillclimbing. Springer US. doi:10.1007/978-1-4613-1997-9.