benchmarkfcns.crownedcross

benchmarkfcns.crownedcross(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 Crowned Cross benchmark function. SCORES = crownedcross(X) computes the value of the Crowned Cross function at point X. crownedcross 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: 0.0001

  • Location of global minimum: (0, 0)

  • Number of dimensions: 2

  • Recommended domain: [-10, 10]^2

  • Number of local minima: many

  • Number of global minima: 1

  • Convexity: non-convex

  • Separability: non-separable

  • Modality: multimodal

  • Symmetry: symmetric

Mathematical Definition

\[f(x, y) = 0.0001 \left( \left| e^ { \left| 100 - \frac{\sqrt{x^2 + y^2}}{\pi} \right| } \sin(x) \sin(y) \right| + 1\right) ^{0.1}\]

Visualization

../_images/crownedcrossfcn.png