benchmarkfcns.bohachevskyn4

benchmarkfcns.bohachevskyn4(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 Bohachevsky N. 4 benchmark function. SCORES = bohachevskyn4(X) computes the value of the function at point X. bohachevskyn4 accepts a matrix of size M-by-N and returns a vector SCORES of size M-by-1. Properties:

  • Global minimum: 0

  • Location of global minimum: (0, 0, …, 0)

  • Number of dimensions: n

  • Recommended domain: [-100, 100]^n

  • Modality: multimodal

Mathematical Definition

\[f(\textbf{x}) = \sum_{i=1}^{n-1} \left[ x_i^2 + 2x_{i+1}^2 - 0.3\cos(3\pi x_i) - 0.4\cos(4\pi x_{i+1}) + 0.7 \right]\]

Visualization

../_images/bohachevskyn4fcn.png