benchmarkfcns.ursemn4

benchmarkfcns.ursemn4(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 Ursem N. 4 benchmark function. SCORES = ursemn4(X) computes the value of the function at point X. ursemn4 accepts a matrix of size M-by-2 and returns a vector SCORES of size M-by-1. Properties:

  • Global minimum: -3

  • Location of global minimum: (0, 0)

  • Number of dimensions: 2

  • Recommended domain: [-2, 2]^2

  • Modality: multimodal

Mathematical Definition

\[f(x_1, x_2) = -3\sin(0.5\pi x_1 + 0.5\pi) \frac{2 - \sqrt{x_1^2 + x_2^2}}{2}\]

Visualization

../_images/ursemn4fcn.png