benchmarkfcns.colville

benchmarkfcns.colville(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 Colville benchmark function. SCORES = colville(X) computes the value of the Colville function at point X. colville accepts a matrix of size M-by-4 and returns a vector SCORES of size M-by-1. Properties:

  • Global minimum: 0

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

  • Number of dimensions: 4

  • Recommended domain: [-10, 10]^4

  • Modality: unimodal

Mathematical Definition

\[f(\mathbf{x}) = 100(x_1^2-x_2)^2 + (x_1-1)^2 + (x_3-1)^2 + 90(x_3^2-x_4)^2 + 10.1((x_2-1)^2 + (x_4-1)^2) + 19.8(x_2-1)(x_4-1)\]

Visualization

No visualization available for this function.