benchmarkfcns.judge

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

  • Global minimum: 16.0817

  • Location of global minimum: (0.8648, 1.2357)

  • Number of dimensions: 2

  • Recommended domain: [-10, 10]^2

  • Modality: multimodal

Mathematical Definition

\[f(x_1, x_2) = \sum_{i=1}^{20} \left[ (x_1 + B_i x_2 + C_i x_2^2) - A_i \right]^2\]

Visualization

../_images/judgefcn.png