benchmarkfcns.schwefel225

benchmarkfcns.schwefel225(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 Schwefel 2.25 benchmark function. SCORES = schwefel225(X) computes the value of the Schwefel 2.25 function at point X. schwefel225 accepts a matrix of size M-by-N and returns a vector SCORES of size M-by-1. Properties:

  • Global minimum: 0

  • Location of global minimum: (1, 1, …, 1)

  • Number of dimensions: n

  • Recommended domain: [0, 10]^n

  • Modality: multimodal

Mathematical Definition

\[f(\textbf{x}) = \sum_{i=2}^{n} \left[ (x_i - 1)^2 + (x_1 - x_i^2)^2 \right]\]

Visualization

../_images/schwefel225fcn.png