ackley_func: Ackley Function

In EmiR: Evolutionary Minimizer for R

Ackley Function

Description

\loadmathjax

Implementation of n-dimensional Ackley function, with \mjeqna=20a=20, \mjeqnb=0.2b=0.2 and \mjeqnc=2\pic=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

\mjdeqn

f(\vecx) = -a\exp\left(-b \sqrt\frac1n\sum_i=1^n x_i^2 \right) -\exp\left(\frac1n\sum_i=1^n \cos(cx_i) \right) + a + \exp(1),-aexp(-bsqrt(1/nsum_1^n (x_i^2)) -exp(1/nsum_1^n (\cos(c*x_i)) + a + exp(1), and is usually evaluated on \mjeqnx_i \in [ -32.768, 32.768 ]x_i in [-32.768, 32.768], for all \mjeqni=1,...,ni=1,...,n. The function has one global minimum at \mjeqnf(\vecx)=0f(x)=0 for \mjeqnx_i=0x_i=0 for all \mjeqni=1,...,ni=1,...,n.

Value

The value of the function.

References

\insertRef

Ackley1987EmiR

EmiR documentation built on Dec. 10, 2022, 1:12 a.m.