benchmarkfcns.mishran11

benchmarkfcns.mishran11(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 Mishra’s Function No. 11 benchmark function. SCORES = mishran11(X) computes the value of the function at point X. mishran11 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: x1 = x2 = … = xn

  • Number of dimensions: Any

  • Recommended domain: [0, 10]^N

  • Modality: Multimodal

Mathematical Definition

\[f(\mathbf{x}) = \left[ \frac{1}{n} \sum_{i=1}^{n} |x_i| - \left( \prod_{i=1}^{n} |x_i| \right)^{1/n} \right]^2\]

Visualization

../_images/mishran11fcn.png