benchmarkfcns.schafferf6

benchmarkfcns.schafferf6(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 Schaffer F6 function. SCORES = schafferf6(X) computes the value of the Schaffer F6 function at point X. schafferf6 accepts a matrix of size M-by-2 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)

  • Number of dimensions: 2

  • Recommended domain: [-100, 100]^2

  • Number of local minima: many

  • Number of global minima: 1

  • Convexity: non-convex

  • Separability: non-separable

  • Modality: multimodal

Mathematical Definition

\[f(x, y) = 0.5 + \frac{\sin^2(\sqrt{x^2 + y^2}) - 0.5}{(1 + 0.001(x^2 + y^2))^2}\]

Visualization

../_images/schafferf6fcn.png