benchmarkfcns.himmelblau

benchmarkfcns.himmelblau(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 Himmelblau’s benchmark function. SCORES = himmelblau(X) computes the value of the Himmelblau’s function at point X. himmelblau 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

  • Location of global minima: There are 4 global minima: (3.0, 2.0),

    (-2.805118, 3.131312), (-3.779310, -3.283186), (3.584428, -1.848126)

  • Number of dimensions: 2

  • Recommended domain: x, y ∈ [-5, 5]

  • Number of local minima: 0 (Every “valley” leads to a global minimum)

  • Number of global minima: 4

  • Convexity: Non-convex

  • Separability: Non-separable

  • Modality: Multimodal (Quadrimodal)

  • Symmetry: Non-symmetric (The locations are not mirror images)

  • Differentiable: Yes

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

Mathematical Definition

Visualization

himmelblau landscape