benchmarkfcns.multiobjective.uf6

benchmarkfcns.multiobjective.uf6(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 UF6 multi-objective benchmark function. SCORES = multiobjective.uf6(X) computes the value of the UF6 function at point X. multiobjective.uf6 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

• Pareto front: Disconnected

Mathematical Definition

\[\begin{split}f_1 = x_1 + \max(0, 2(\frac{1}{4} + 0.1) \sin(4\pi x_1)) + \frac{2}{|J_1|} g(y, J_1) \\\end{split}\]

f_2 = 1 - x_1 + max(0, 2(frac{1}{4} + 0.1) sin(4pi x_1)) + frac{2}{|J_2|} g(y, J_2) \ g(y, J) = 4 sum_{j in J} y_j^2 - 2 prod_{j in J} cosleft(frac{20y_jpi}{sqrt{j}}right) + 2 \ y_j = x_j - sin(6pi x_1 + frac{jpi}{n}) \ 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.