benchmarkfcns.ackley6

benchmarkfcns.ackley6(arg0: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous']) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, 1]']

Computes the value of the Ackley N. 6 benchmark function. SCORES = ackley6(X) computes the value of the function at point X. ackley6 accepts a matrix of size M-by-N and returns a vector SCORES of size M-by-1. Properties:

  • Global minimum: 0

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

  • Number of dimensions: n

  • Recommended domain: [-32, 32]^n

  • Modality: multimodal

Mathematical Definition

\[f(\textbf{x}) = 1 + \sum_{i=1}^{n-1} \left[ 1 - \cos(2\pi \sqrt{x_i^2 + x_{i+1}^2}) \right]\]

Visualization

../_images/ackley6fcn.png