benchmarkfcns.multiobjective.maf6

benchmarkfcns.multiobjective.maf6(x: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous'], num_objectives: SupportsInt | SupportsIndex = 3) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]']

Computes the value of the MaF6 multi-objective benchmark function. maf6 is a degenerate DTLZ5 variant.

Mathematical Definition

\[\begin{aligned}\]

f_i(textbf{x}) &= (1 + g(textbf{x}_M)) prod_{j=1}^{M-i} cos(theta_j) times begin{cases} sin(theta_{M-i+1}) & text{if } i > 1 \ 1 & text{if } i = 1 end{cases} \ theta_j &= begin{cases} frac{pi}{2}x_j & text{if } j < 2 \ frac{pi}{4(1+g)} (1 + 2gx_j) & text{if } j ge 2 end{cases} \ g(textbf{x}_M) &= sum_{x_j in textbf{x}_M} (x_j - 0.5)^2 end{aligned}

Visualization

No visualization available for this function.