benchmarkfcns.freudensteinroth

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

  • Global minimum: 0

  • Location of global minimum: (5, 4)

  • Number of dimensions: 2

  • Recommended domain: [-10, 10]^2

  • Modality: multimodal

Mathematical Definition

\[f(x_1, x_2) = \left[ x_1 - 13 + ((5 - x_2)x_2 - 2)x_2 \right]^2 + \left[ x_1 - 29 + ((x_2 + 1)x_2 - 14)x_2 \right]^2\]

Visualization

../_images/freudensteinrothfcn.png