benchmarkfcns.alpinen2

benchmarkfcns.alpinen2(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 Alpine N. 2 function. SCORES = alpinen2(X) computes the value of the Alpine N. 2 function at point X. alpinen2 accepts a matrix of size M-by-N 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: Not typically defined as a single value across all n. Instead,

    the function is often used to find the Global Maximum.

  • Global Maximum Value: approx 2.808^n

  • Location of Global Maximum: approx (7.917, 7.917, …, 7.917)

  • Number of dimensions: n (Scalable)

  • Recommended domain: x_i ∈ [0, 10] (The function is usually restricted to

    positive values due to the square root).

  • Number of local minima/maxima: Numerous (The sine waves create a grid of peaks).

  • Number of global minima/maxima: 1 (within the [0, 10] range).

  • Convexity: Non-convex

  • Separability: Separable (Despite being a product, it can be transformed into a

    sum of logs, making it technically separable in optimization terms).

  • Modality: Multimodal

  • Symmetry: Symmetric

  • Differentiable: Yes

For more information, please visit: benchmarkfcns.info/doc/alpinen2fcn

Mathematical Definition

Visualization

alpinen2 landscape