benchmarkfcns.hosaki

benchmarkfcns.hosaki(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 Hosaki benchmark function. SCORES = hosaki(X) computes the value of the Hosaki function at point X. hosaki 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: -2.3458 (approximately)

  • Location of global minimum: (0.803, 9.126)

  • Number of dimensions: 2

  • Recommended domain: x ∈ [0, 5], y ∈ [0, 10]

  • Number of local minima: 2 (The global minimum and one local minimum)

  • Number of global minima: 1

  • Convexity: Non-convex

  • Separability: Non-separable (The exponential term couples x and y)

  • Modality: Bimodal

  • Symmetry: Non-symmetric

  • Differentiable: Yes

Mathematical Definition

Visualization

hosaki landscape