benchmarkfcns.braninn1

benchmarkfcns.braninn1(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 Branin N. 1 benchmark function. SCORES = braninn01(X) computes the value of the Branin N. 1 function at point X. braninn01 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: 0.397887

  • Location of global minimum: (-π, 12.275), (π, 2.275), (9.42478, 2.475)

  • Number of dimensions: 2

  • Recommended domain: [-5, 15] for x1, [0, 15] for x2

  • Number of local minima: no local minima other than the three global ones

  • Number of global minima: 3

  • Convexity: non-convex

  • Separability: non-separable

  • Modality: multimodal

  • Symmetry: Non-symmetric

  • Differentiable: Yes

For more information, please visit: benchmarkfcns.info/doc/braninn1fcn

Mathematical Definition

Visualization

braninn1 landscape