benchmarkfcns.kowalik

benchmarkfcns.kowalik(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 Kowalik benchmark function. SCORES = kowalik(X) computes the value of the function at point X. kowalik accepts a matrix of size M-by-4 and returns a vector SCORES of size M-by-1. Properties:

• Global minimum: 0.0003075

• Location of global minimum: (0.1928, 0.1928, 0.1231, 0.1358)

• Number of dimensions: 4

• Recommended domain: [-5, 5]^4

• Modality: multimodal

Mathematical Definition

\[f(\mathbf{x}) = \sum_{i=1}^{11} \left[ a_i - \frac{x_1(b_i^2 + b_i x_2)}{b_i^2 + b_i x_3 + x_4} \right]^2\]

Visualization

No visualization available for this function.