benchmarkfcns.damavandi

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

  • Global minimum: 0

  • Location of global minimum: (2, 2)

  • Number of dimensions: 2

  • Recommended domain: [0, 14]^2

  • Modality: multimodal

Mathematical Definition

\[f(x_1, x_2) = \left[ 1 - \left| \frac{\sin(\pi(x_1-2))\sin(\pi(x_2-2))}{\pi^2(x_1-2)(x_2-2)} \right|^5 \right] \left[ 2 + (x_1-7)^2 + 2(x_2-7)^2 \right]\]

Visualization

../_images/damavandifcn.png