benchmarkfcns.mishran12

benchmarkfcns.mishran12(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. 12 benchmark function. SCORES = mishran12(X) computes the value of the function at point X. mishran12 accepts a matrix of size M-by-2 and returns a vector SCORES of size M-by-1. Properties:

  • Global minimum: -106.764537

  • Location of global minimum: (4.70104, 3.15294) or (-1.58214, -3.13024)

  • Number of dimensions: 2

  • Recommended domain: [-10, 10]^2

  • Modality: Multimodal

Mathematical Definition

\[f(x, y) = \sin(x) e^{(1-\cos(y))^2} + \cos(y) e^{(1-\sin(x))^2} + (x-y)^2\]

Visualization

../_images/mishran12fcn.png