benchmarkfcns.qingn2

benchmarkfcns.qingn2(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 Qing N. 2 benchmark function. SCORES = qingn2(X) computes the value of the function at point X. qingn2 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: [-500, 500]^n

  • Modality: multimodal

Mathematical Definition

\[f(\textbf{x}) = \sum_{i=1}^{n} \sin^2(x_i) + \sum_{i=1}^{n} \frac{x_i^2}{4000} - \prod_{i=1}^{n} \cos(\frac{x_i}{\sqrt{i}}) + 1\]

Visualization

../_images/qingn2fcn.png