benchmarkfcns.multiobjective.poloni

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

• Recommended domain: [-pi, pi]^2

• Pareto front: Non-convex and disconnected

Mathematical Definition

\[\begin{split}A_1 = 0.5 \sin(1) - 2 \cos(1) + \sin(2) - 1.5 \cos(2) \\\end{split}\]

A_2 = 1.5 sin(1) - cos(1) + 2 sin(2) - 0.5 cos(2) \ B_1 = 0.5 sin(x_1) - 2 cos(x_1) + sin(x_2) - 1.5 cos(x_2) \ B_2 = 1.5 sin(x_1) - cos(x_1) + 2 sin(x_2) - 0.5 cos(x_2) \ f_1(x_1, x_2) = 1 + (A_1 - B_1)^2 + (A_2 - B_2)^2 \ f_2(x_1, x_2) = (x_1 + 3)^2 + (x_2 + 1)^2

Visualization

No visualization available for this function.