benchmarkfcns.mishran6

benchmarkfcns.mishran6(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. 6 benchmark function. SCORES = mishran6(X) computes the value of the function at point X. mishran6 accepts a matrix of size M-by-2 and returns a vector SCORES of size M-by-1. Properties:

  • Global minimum: ~-2.28395

  • Location of global minimum: (2.88631, 1.82326)

  • Number of dimensions: 2

  • Recommended domain: [-10, 10]^2

  • Modality: Multimodal

Mathematical Definition

\[f(x_1, x_2) = -\ln \left[ \left( \sin^2([\cos x_1 + \cos x_2]^2) - \cos^2([\sin x_1 + \sin x_2]^2) + x_1 \right)^2 \right] + 0.1 \left[ (x_1 - 1)^2 + (x_2 - 1)^2 \right]\]

Visualization

../_images/mishran6fcn.png