benchmarkfcns.chenbird

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

  • Global minimum: -2000

  • Location of global minimum: (7/18, 13/18)

  • Number of dimensions: 2

  • Recommended domain: [-500, 500]^2

  • Modality: multimodal

Mathematical Definition

\[f(x_1, x_2) = -\frac{0.001}{0.001^2 + (x_1 - 0.4x_2 - 0.1)^2} - \frac{0.001}{0.001^2 + (2x_1 + x_2 - 1.5)^2}\]

Visualization

../_images/chenbirdfcn.png