benchmarkfcns.langermannn2

benchmarkfcns.langermannn2(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 Langermann N. 2 benchmark function. langermannn2 is an alias for langermann. Properties:

  • Global minimum: -5.1621

  • Location of global minimum: (2.0029, 1.0060)

  • Number of dimensions: 2

  • Recommended domain: [0, 10]^2

  • Modality: multimodal

Mathematical Definition

\[f(\textbf{x}) = -\sum_{i=1}^{5} c_i \exp(-\frac{1}{\pi} \sum_{j=1}^{2} (x_j - A_{ij})^2) \cos(\pi \sum_{j=1}^{2} (x_j - A_{ij})^2)\]

Visualization

../_images/langermannn2fcn.png