Ackley

../../_images/Ackley.png
class gob.benchmarks.ackley.Ackley(a=20, b=0.2, c=1)

Bases: Benchmark

The Ackley function.

\(f(x) = -a\exp\left(-b \sqrt{\frac{1}{d} \sum_{i=1}^d x_i^2} \right) - \exp\left( \frac{1}{d} \sum_{i=1}^d \cos(c x_i) \right) + a + \exp(1)\). By default, hyper-parameters are set to \(a = 20, b = 0.2, c = 1\).

Its minimum is \(0\) achieved at \(x = 0\).

expr(x)

The expression of the function.

Parameters:

x (array-like) – The point at which to evaluate the function.

Returns:

The value of the function at x.

Return type:

float