benchmarkfcns.gramacylee

benchmarkfcns.gramacylee(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 Gramacy & Lee benchmark function. SCORES = gramacylee(X) computes the value of the Gramacy & Lee function at point X. gramacylee 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: -0.869 (approximately)

  • Location of global minimum: x ≈ 0.5485

  • Number of dimensions: 1 (x)

  • Recommended domain: x ∈ [0.5, 2.5]

  • Number of local minima: Numerous (Highly oscillatory)

  • Number of global minima: 1

  • Convexity: Non-convex

  • Separability: N/A (1D function)

  • Modality: Highly Multimodal

  • Symmetry: Non-symmetric

  • Differentiable: Yes

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

Mathematical Definition

Visualization

gramacylee landscape