benchmarkfcns.trigonometricn2

benchmarkfcns.trigonometricn2(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 Trigonometric N. 2 benchmark function. SCORES = trigonometricn2(X) computes the value of the function at point X. trigonometricn2 accepts a matrix of size M-by-N and returns a vector SCORES of size M-by-1. Properties:

  • Global minimum: 1

  • Location of global minimum: (0.9, 0.9, …, 0.9)

  • Number of dimensions: n

  • Recommended domain: [-500, 500]^n

  • Modality: multimodal

Mathematical Definition

\[f(\textbf{x}) = 1 + \sum_{i=1}^{n} \left[ 8 \sin^2(7(x_i - 0.9)^2) + 6 \sin^2(14(x_i - 0.9)^2) + (x_i - 0.9)^2 \right]\]

Visualization

../_images/trigonometricn2fcn.png