benchmarkfcns.shubert

benchmarkfcns.shubert(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 Shubert function. SCORES = shubert(X) computes the value of the Shubert function at point X. shubert 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: approx -186.7309 (for n=2)

• Location of global minimum: multiple

• Number of dimensions: n

• Recommended domain: [-10, 10]^n

• Number of local minima: many

• Number of global minima: multiple

• Convexity: non-convex

• Separability: non-separable

• Modality: multimodal

• Symmetry: symmetric

• Differentiable: Yes

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

Mathematical Definition

\[f(\mathbf{x})=f(x_1, ...,x_n)=\prod_{i=1}^{n}{\left(\sum_{j=1}^5{ cos((j+1)x_i+j)}\right)}\]

Visualization