benchmarkfcns.pathological

benchmarkfcns.pathological(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 Pathological function. SCORES = pathological(X) computes the value of the function at point X. pathological 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: Any

  • Recommended domain: [-100, 100]^N

  • Modality: Multimodal

Mathematical Definition

\[f(\mathbf{x}) = \sum_{i=1}^{n-1} \left[ 0.5 + \frac{\sin^2\left(\sqrt{100x_i^2 + x_{i+1}^2}\right) - 0.5}{1 + 0.001(x_i^2 - 2x_ix_{i+1} + x_{i+1}^2)^2} \right]\]

Visualization

../_images/pathologicalfcn.png