benchmarkfcns.multiobjective.uf1

benchmarkfcns.multiobjective.uf1(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 UF1 multi-objective benchmark function. SCORES = multiobjective.uf1(X) computes the value of the UF1 function at point X. multiobjective.uf1 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: Convex

Mathematical Definition

\[\begin{split}f_1 = x_1 + \frac{2}{|J_1|} \sum_{j \in J_1} (x_j - \sin(6\pi x_1 + \frac{j\pi}{n}))^2 \\\end{split}\]

f_2 = 1 - sqrt{x_1} + frac{2}{|J_2|} sum_{j in J_2} (x_j - sin(6pi x_1 + frac{jpi}{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.