benchmarkfcns.multiobjective.viennet3

benchmarkfcns.multiobjective.viennet3(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 3 multi-objective benchmark function. SCORES = multiobjective.viennet3(X) computes the value of the Viennet 3 function at point X. multiobjective.viennet3 accepts a matrix of size M-by-2 and returns a matrix SCORES of size M-by-3. Properties:

• Recommended domain: [-3, 3]^2

• Pareto front: Convoluted

Mathematical Definition

\[\begin{split}f_1(x_1, x_2) = 0.5(x_1^2 + x_2^2) + \sin(x_1^2 + x_2^2) \\\end{split}\]

f_2(x_1, x_2) = frac{(3x_1 - 2x_2 + 4)^2}{8} + frac{(x_1 - x_2 + 1)^2}{27} + 15 \ f_3(x_1, x_2) = frac{1}{x_1^2 + x_2^2 + 1} - 1.1 exp(-(x_1^2 + x_2^2))

Visualization

No visualization available for this function.