benchmarkfcns.pinter

benchmarkfcns.pinter(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 Pinter benchmark function. SCORES = pinter(X) computes the value of the Pinter function at point X. pinter 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: [-10, 10]^N

  • Modality: Multimodal

Mathematical Definition

\[\begin{split}f(\mathbf{x}) = \sum_{i=1}^n i x_i^2 + \sum_{i=1}^n 20i \sin^2(A_i) + \sum_{i=1}^n i \log_{10}(1 + i B_i^2) \\\end{split}\]

text{where: } \ A_i = (x_{i-1} sin(x_i) + sin(x_{i+1})) \ B_i = (x_{i-1}^2 - 2x_i + 3x_{i+1} - cos(x_i) + 1)

Visualization

../_images/pinterfcn.png