benchmarkfcns.mishran1

benchmarkfcns.mishran1(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. 1 benchmark function. SCORES = mishran1(X) computes the value of the function at point X. mishran1 accepts a matrix of size M-by-N and returns a vector SCORES of size M-by-1. Properties:

  • Global minimum: 2

  • Location of global minimum: (1, …, 1)

  • Number of dimensions: Any

  • Recommended domain: [0, 1]^N

  • Modality: Multimodal

Mathematical Definition

\[f(\mathbf{x}) = (1 + g_n)^{g_n} \text{ where } g_n = n - \sum_{i=1}^{n-1} x_i\]

Visualization

../_images/mishran1fcn.png