benchmarkfcns.multiobjective.kursawe

benchmarkfcns.multiobjective.kursawe(arg0: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous']) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]']

Computes the value of the Kursawe multi-objective benchmark function. SCORES = multiobjective.kursawe(X) computes the value of the Kursawe function at point X. multiobjective.kursawe accepts a matrix of size M-by-N and returns a matrix SCORES of size M-by-2. Properties:

• Global Pareto front: Disconnected and non-convex

• Number of dimensions: n (usually 3)

• Recommended domain: [-5, 5]^n

• Modality: multimodal

For more information, please visit: benchmarkfcns.info/doc/kursafcn

Mathematical Definition

\[\begin{split}f_1(\textbf{x}) = \sum_{i=1}^{n-1} -10 \exp \left( -0.2 \sqrt{x_i^2 + x_{i+1}^2} \right) \\\end{split}\]

f_2(textbf{x}) = sum_{i=1}^{n} left( |x_i|^{0.8} + 5 sin(x_i^3) right)

Visualization

No visualization available for this function.