benchmarkfcns.sineenvelopesinewave

benchmarkfcns.sineenvelopesinewave(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 Sine Envelope Sine Wave (Schaffer F6 scalable) benchmark function. SCORES = sineenvelopesinewave(X) computes the value of the function at point X. sineenvelopesinewave 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: [-100, 100]^n

  • Modality: multimodal

Mathematical Definition

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

Visualization

../_images/sineenvelopesinewavefcn.png