benchmarkfcns.multiobjective.maf4

benchmarkfcns.multiobjective.maf4(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 MaF4 multi-objective benchmark function. maf4 is an inverted DTLZ3 variant.

Mathematical Definition

\[\begin{aligned}\]

f_i(textbf{x}) &= 10^{i-1} (1 + g(textbf{x}_M)) [ 1 - prod_{j=1}^{M-i} cos(frac{pi}{2}x_j) times begin{cases} sin(frac{pi}{2}x_{M-i+1}) & text{if } i > 1 \ 1 & text{if } i = 1 end{cases} ] \ g(textbf{x}_M) &= 100 left[ k + sum_{x_j in textbf{x}_M} ((x_j - 0.5)^2 - cos(20pi(x_j - 0.5))) right] end{aligned}

Visualization

No visualization available for this function.