benchmarkfcns.multiobjective.uf10

benchmarkfcns.multiobjective.uf10(x: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous']) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]']

Computes the value of the CEC 2009 UF10 multi-objective benchmark function. SCORES = multiobjective.uf10(X) computes the value of the UF10 function at point X. multiobjective.uf10 accepts a matrix of size M-by-N and returns a matrix SCORES of size M-by-3. Properties:

• Recommended domain: x1, x2 in [0, 1], xj in [-2, 2] for j=3..N

Mathematical Definition

\[\begin{split}f_1 = \cos(0.5\pi x_1) \cos(0.5\pi x_2) + \frac{2}{|J_1|} \sum_{j \in J_1} (4y_j^2 - \cos(8\pi y_j) + 1) \\\end{split}\]

f_2 = cos(0.5pi x_1) sin(0.5pi x_2) + frac{2}{|J_2|} sum_{j in J_2} (4y_j^2 - cos(8pi y_j) + 1) \ f_3 = sin(0.5pi x_1) + frac{2}{|J_3|} sum_{j in J_3} (4y_j^2 - cos(8pi y_j) + 1) \ y_j = x_j - 2x_2 sin(2pi x_1 + frac{jpi}{n}) \ J_1, J_2, J_3 text{ same as UF8}

Visualization

No visualization available for this function.