benchmarkfcns.multiobjective.viennet2

benchmarkfcns.multiobjective.viennet2(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 Viennet 2 multi-objective benchmark function. SCORES = multiobjective.viennet2(X) computes the value of the Viennet 2 function at point X. multiobjective.viennet2 accepts a matrix of size M-by-2 and returns a matrix SCORES of size M-by-3. Properties:

• Recommended domain: [-4, 4]^2

• Pareto front: Curved

Mathematical Definition

\[\begin{split}f_1(x_1, x_2) = \frac{(x_1 - 2)^2}{2} + \frac{(x_2 + 1)^2}{13} + 3 \\\end{split}\]

f_2(x_1, x_2) = frac{(x_1 + x_2 - 3)^2}{36} + frac{(-x_1 + x_2 + 2)^2}{8} - 17 \ f_3(x_1, x_2) = frac{(x_1 + 2x_2 - 1)^2}{175} + frac{(2x_1 - x_2)^2}{17} - 13

Visualization

No visualization available for this function.