benchmarkfcns.multiobjective.uf8

benchmarkfcns.multiobjective.uf8(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 UF8 multi-objective benchmark function. SCORES = multiobjective.uf8(X) computes the value of the UF8 function at point X. multiobjective.uf8 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

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

f_2 = cos(0.5pi x_1) sin(0.5pi x_2) + frac{2}{|J_2|} sum_{j in J_2} y_j^2 \ f_3 = sin(0.5pi x_1) + frac{2}{|J_3|} sum_{j in J_3} y_j^2 \ y_j = x_j - 2x_2 sin(2pi x_1 + frac{jpi}{n}) \ J_1 = {j | 3 le j le n, j-1 text{ is multiple of } 3} \ J_2 = {j | 3 le j le n, j-2 text{ is multiple of } 3} \ J_3 = {j | 3 le j le n, j text{ is multiple of } 3}

Visualization

No visualization available for this function.