benchmarkfcns.ackley

benchmarkfcns.ackley(arg0: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous']) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, 1]']

Computes the value of Ackley benchmark function. SCORES = ackley(X) computes the value of the Ackley function at point X. ackley accepts a matrix of size M-by-N and returns a vector SCORES of size M-by-1 in which each row contains the function value for each row of X. Properties:

• Global minimum: 0

• Location of global minimum: (0, 0, …, 0)

• Number of dimensions: N

• Recommended domain: [-35, 35]^N

• Number of local minima: many

• Number of global minima: 1

• Convexity: non-convex

• Separability: non-separable

• Modality: multimodal

• Symmetry: radial symmetry

For more information, please visit: benchmarkfcns.info/doc/ackleyfcn

Mathematical Definition

\[f(\textbf{x}) = f(x_1, ..., x_n)= -a.exp(-b\sqrt{\frac{1}{n}\sum_{i=1}^{n}x_i^2})-exp(\frac{1}{d}\sum_{i=1}^{n}cos(cx_i))+ a + exp(1)\]

Visualization