benchmarkfcns.gallagher101

benchmarkfcns.gallagher101(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 Gallagher’s Gaussian 101-me Peaks benchmark function. SCORES = gallagher101(X) computes the value of the Gallagher’s 101-me Peaks function at point X. gallagher101 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: randomized (seeded)

  • Number of dimensions: n

  • Recommended domain: [-5, 5]^n

  • Modality: highly multimodal (101 Gaussian peaks)

Mathematical Definition

\[f(\mathbf{x}) = 10 - \max_{i=1, \dots, 101} \{ w_i \exp( -\frac{1}{2n} (\mathbf{x} - \mathbf{y}_i)^T \mathbf{C}_i (\mathbf{x} - \mathbf{y}_i) ) \}\]

Visualization

../_images/gallagher101fcn.png