benchmarkfcns.levyn2

benchmarkfcns.levyn2(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 Levy N. 2 benchmark function. levyn2 is an alias for levy for n=2. Properties:

  • Global minimum: 0

  • Location of global minimum: (1, 1)

  • Number of dimensions: 2

  • Recommended domain: [-10, 10]^2

  • Modality: multimodal

Mathematical Definition

\[f(\textbf{x}) = \sin^2(\pi w_1) + \sum_{i=1}^{n-1} (w_i-1)^2 [1 + 10\sin^2(\pi w_i + 1)] + (w_n-1)^2 [1 + \sin^2(2\pi w_n)], \quad w_i = 1 + \frac{x_i-1}{4}\]

Visualization

../_images/levyn2fcn.png