benchmarkfcns.multiobjective.uf2

benchmarkfcns.multiobjective.uf2(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 UF2 multi-objective benchmark function. SCORES = multiobjective.uf2(X) computes the value of the UF2 function at point X. multiobjective.uf2 accepts a matrix of size M-by-N and returns a matrix SCORES of size M-by-2. Properties:

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

Mathematical Definition

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

f_2 = 1 - sqrt{x_1} + frac{2}{|J_2|} sum_{j in J_2} y_j^2 \ y_j = begin{cases} x_j - [0.3x_1^2 cos(24pi x_1 + frac{4jpi}{n}) + 0.6x_1] cos(6pi x_1 + frac{jpi}{n}) & j in J_1 \ x_j - [0.3x_1^2 cos(24pi x_1 + frac{4jpi}{n}) + 0.6x_1] sin(6pi x_1 + frac{jpi}{n}) & j in J_2 end{cases} \ J_1 = {j | j text{ is odd and } 2 le j le n}, J_2 = {j | j text{ is even and } 2 le j le n}

Visualization

No visualization available for this function.