benchmarkfcns.braninn2

benchmarkfcns.braninn2(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. 2 benchmark function. SCORES = braninn02(X) computes the value of the Branin N. 2 function at point X. braninn02 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: 5.55903732

  • Location of global minimum: [-3.2, 12.53]

  • Number of dimensions: 2

  • Recommended domain: [-5, 15]^2

  • Number of local minima: Dependent on the specific bounds, but typically includes

    several local traps.

  • 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/braninn2fcn

Mathematical Definition

\[f(x, y) = \left(-1.275 \frac{x^2}{\pi^2} + 5 \frac{x}{\pi} + y - 6\right)^2 + \left(10 - \frac{5}{4\pi} \right)\cos(x)\cos(y) + \log(x^2 + y^2 + 1) + 10\]

Visualization

../_images/braninn2fcn.png