benchmarkfcns.stretchedvsine

benchmarkfcns.stretchedvsine(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 Stretched V Sine benchmark function. SCORES = stretchedvsine(X) computes the value of the Stretched V Sine function at point X. stretchedvsine accepts a matrix of size M-by-N and returns a vector SCORES of size M-by-1 in which each row contains the function value for the corresponding row of X. Properties:

  • Global minimum: 0

  • Location of global minimum: (0, 0, …, 0)

  • Number of dimensions: n

  • Recommended domain: [-10, 10]^n

  • Number of local minima: many

  • Number of global minima: 1

  • Convexity: non-convex

  • Separability: non-separable

  • Modality: multimodal

  • Symmetry: symmetric

  • Differentiable: Yes

For more information, please visit: benchmarkfcns.info/doc/stretchedvsinefcn

Mathematical Definition

\[f(\textbf{x}) = \sum_{i=1}^{n-1} \left( (x_i^2 + x_{i+1}^2)^{0.25} \left( \sin^2\left( 50 (x_i^2 + x_{i+1}^2)^{0.1} \right) + 0.1 \right) \right)\]

Visualization

../_images/stretchedvsinefcn.png