benchmarkfcns.testtubeholder

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

  • Global minimum: -10.8723

  • Location of global minimum: (+/- pi/2, 0)

  • Number of dimensions: 2

  • Recommended domain: [-10, 10]^2

  • Modality: multimodal

Mathematical Definition

\[f(x_1, x_2) = -4 | \sin(x_1) \cos(x_2) \exp(| \cos(\frac{x_1^2 + x_2^2}{200}) |) |\]

Visualization

../_images/testtubeholderfcn.png