benchmarkfcns.whitley

benchmarkfcns.whitley(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 Whitley benchmark function. SCORES = whitley(X) computes the value of the Whitley function at point X. whitley 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 the corresponding row of X. Properties:

  • Global minimum: 0

  • Location of global minimum: (1, 1, …, 1)

  • Number of dimensions: n

  • Recommended domain: [-10.24, 10.24]^n

  • Modality: multimodal

  • Separability: non-separable

Mathematical Definition

\[f(\mathbf{x}) = \sum_{i=1}^{n} \sum_{j=1}^{n} \left[ \frac{(100(x_i^2 - x_j)^2 + (1 - x_j)^2)^2}{4000} - \cos(100(x_i^2 - x_j)^2 + (1 - x_j)^2) + 1 \right]\]

Visualization

../_images/whitleyfcn.png