benchmarkfcns.crosslegintray

benchmarkfcns.crosslegintray(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 Cross-Leg-in-Tray (Cross-Leg-Table) benchmark function. SCORES = crosslegintray(X) computes the value of the function at point X. crosslegintray accepts a matrix of size M-by-2 and returns a vector SCORES of size M-by-1. Properties:

  • Global minimum: -1

  • Location of global minimum: along x=0 or y=0 axes

  • Number of dimensions: 2

  • Recommended domain: [-10, 10]^2

  • Modality: multimodal

Mathematical Definition

\[f(x, y) = - \left[ \left| \sin(x) \sin(y) \exp \left( \left| 100 - \frac{\sqrt{x^2+y^2}}{\pi} \right| \right) \right| + 1 \right]^{-0.1}\]

Visualization

../_images/crosslegintrayfcn.png