benchmarkfcns.multiobjective.viennet1

benchmarkfcns.multiobjective.viennet1(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 1 multi-objective benchmark function. SCORES = multiobjective.viennet1(X) computes the value of the Viennet 1 function at point X. multiobjective.viennet1 accepts a matrix of size M-by-2 and returns a matrix SCORES of size M-by-3. Properties:

• Recommended domain: [-2, 2]^2

• Pareto front: Disconnected

Mathematical Definition

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

f_2(x_1, x_2) = x_1^2 + (x_2 + 1)^2 + 1 \ f_3(x_1, x_2) = (x_1 - 1)^2 + x_2^2 + 2

Visualization

No visualization available for this function.