benchmarkfcns.trigonometricn1

benchmarkfcns.trigonometricn1(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. 1 benchmark function. SCORES = trigonometricn1(X) computes the value of the function at point X. trigonometricn1 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: (0, 0, …, 0)

  • Number of dimensions: n

  • Recommended domain: [0, pi]^n

  • Modality: multimodal

Mathematical Definition

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

Visualization

../_images/trigonometricn1fcn.png