benchmarkfcns.discus

benchmarkfcns.discus(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 Discus benchmark function. SCORES = discus(X) computes the value of the Discus function at point X. discus accepts a matrix of size M-by-N and returns a vetor 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: (0, 0, …, 0)

  • Number of dimensions: n

  • Recommended domain: [-100, 100]^n

  • Modality: unimodal

  • Characteristic: High conditioning (one sensitive direction).

Mathematical Definition

\[f(\mathbf{x}) = 10^6 x_1^2 + \sum_{i=2}^n x_i^2\]

Visualization

../_images/discusfcn.png