benchmarkfcns.eggholder

benchmarkfcns.eggholder(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 Eggholder benchmark function. SCORES = eggholder(X) computes the value of the Eggholder function at point X. eggholder 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: -959.6407

  • Location of global minimum: (512, 404.2319)

  • Number of dimensions: 2

  • Recommended domain: [-512, 512]^2

  • Number of local minima: many

  • Number of global minima: 1

  • Convexity: non-convex

  • Separability: non-separable

  • Modality: multimodal

  • Differentiable: Yes

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

Mathematical Definition

\[\begin{aligned}\]

f_{hf}(mathbf{x}) &= -(x_2+47)sinleft(sqrt{|x_1/2 + x_2 + 47|}right) - x_1sinleft(sqrt{|x_1 - (x_2 + 47)|}right) f_{lf}(mathbf{x}) &= 0.5 f_{hf}(mathbf{x}) + 0.1 (x_1 + x_2) end{aligned}

Visualization

../_images/eggholderfcn.png