benchmarkfcns.hansen

benchmarkfcns.hansen(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 Hansen benchmark function. SCORES = hansen(X) computes the value of the Hansen function at point X. hansen accepts a matrix of size M-by-2 and returns a vector SCORES of size M-by-1. Properties:

  • Global minimum: -176.541793

  • Location of global minimum: 9 global minima in [-10, 10]^2

  • Number of dimensions: 2

  • Recommended domain: [-10, 10]^2

  • Modality: multimodal

Mathematical Definition

\[f(x_1, x_2) = \left( \sum_{i=1}^5 i \cos((i-1)x_1 + i) \right) \left( \sum_{j=1}^5 j \cos((j+1)x_2 + j) \right)\]

Visualization

../_images/hansenfcn.png