benchmarkfcns.multiobjective.uf9

benchmarkfcns.multiobjective.uf9(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 UF9 multi-objective benchmark function. SCORES = multiobjective.uf9(X) computes the value of the UF9 function at point X. multiobjective.uf9 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

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

f_2 = 0.5 [ E(x_1) + 2x_1 ] (1-x_2) + frac{2}{|J_2|} sum_{j in J_2} y_j^2 \ f_3 = 1 - x_1 + frac{2}{|J_3|} sum_{j in J_3} y_j^2 \ E(x_1) = max(0, 1.1(1-4(2x_1-1)^2)) \ 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.