benchmarkfcns.ishigami

benchmarkfcns.ishigami(x: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous'], a: SupportsFloat | SupportsIndex = 7.0, b: SupportsFloat | SupportsIndex = 0.1) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, 1]']

Computes the value of the Ishigami benchmark function. SCORES = ishigami(X) computes the value of the Ishigami function at point X. ishigami accepts a matrix of size M-by-3 and returns a vector SCORES of size M-by-1 in which each row contains the function value for the corresponding row of X. SCORES = ishigami(X, a=A, b=B) specifies the ‘a’ and ‘b’ parameters. Properties:

  • Global minimum: depends on a and b

  • Number of dimensions: 3

  • Recommended domain: [-π, π]^3

  • Number of local minima: many

  • Number of global minima: 1

  • Convexity: non-convex

  • Separability: non-separable (strong interaction between x1 and x3)

  • Modality: multimodal

Mathematical Definition

Visualization

ishigami landscape