benchmarkfcns.mishran9

benchmarkfcns.mishran9(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. 9 benchmark function. SCORES = mishran9(X) computes the value of the function at point X. mishran9 accepts a matrix of size M-by-3 and returns a vector SCORES of size M-by-1. Properties:

• Global minimum: 0

• Location of global minimum: (1, 2, 3)

• Number of dimensions: 3

• Recommended domain: [-10, 10]^3

• Modality: Multimodal

Mathematical Definition

\[\begin{split}f(\mathbf{x}) = \left[ f_1 f_2^2 f_3 + f_1 f_2 f_3^2 + f_2^2 + (x_1 + x_2 - x_3)^2 \right]^2 \\\end{split}\]

text{where: } \ f_1 = 2x_1^3 + 5x_1x_2 + 4x_3 - 2x_1^2x_3 - 18 \ f_2 = x_1 + x_3^2 + x_1x_2^2 + x_1x_2^3 - 22 \ f_3 = 8x_1^2 + 2x_2x_3 + 2x_2^2 + 3x_3^2 - 52

Visualization

No visualization available for this function.