benchmarkfcns.mishran5

benchmarkfcns.mishran5(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. 5 benchmark function. SCORES = mishran5(X) computes the value of the function at point X. mishran5 accepts a matrix of size M-by-2 and returns a vector SCORES of size M-by-1. Properties:

  • Global minimum: ~-1.01983

  • Location of global minimum: (-1.9868, -10)

  • Number of dimensions: 2

  • Recommended domain: [-10, 10]^2

  • Modality: Multimodal

Mathematical Definition

\[f(x_1, x_2) = [\sin^2((\cos x_1 + \cos x_2)^2) + \cos^2((\sin x_1 + \sin x_2)^2) + x_1]^2 + 0.01x_1 + 0.1x_2\]

Visualization

../_images/mishran5fcn.png