benchmarkfcns.multiobjective.uf3

benchmarkfcns.multiobjective.uf3(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 UF3 multi-objective benchmark function. SCORES = multiobjective.uf3(X) computes the value of the UF3 function at point X. multiobjective.uf3 accepts a matrix of size M-by-N and returns a matrix SCORES of size M-by-2. Properties:

• Recommended domain: x in [0, 1]^N

Mathematical Definition

\[\begin{split}f_1 = x_1 + \frac{2}{|J_1|} \left[ 4 \sum_{j \in J_1} y_j^2 - 2 \prod_{j \in J_1} \cos\left(\frac{20y_j\pi}{\sqrt{j}}\right) + 2 \right] \\\end{split}\]

f_2 = 1 - sqrt{x_1} + frac{2}{|J_2|} left[ 4 sum_{j in J_2} y_j^2 - 2 prod_{j in J_2} cosleft(frac{20y_jpi}{sqrt{j}}right) + 2 right] \ y_j = x_j - x_1^{0.5(1 + frac{3(j-2)}{n-2})} \ 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.