benchmarkfcns.multiobjective.maf1

benchmarkfcns.multiobjective.maf1(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 MaF1 multi-objective benchmark function. SCORES = multiobjective.maf1(X) computes the value of the function at point X. maf1 is an inverted version of DTLZ1.

Mathematical Definition

\[\begin{aligned}\]

f_i(textbf{x}) &= 0.5(1 + g(textbf{x}_M)) [ 1 - prod_{j=1}^{M-i} x_j times begin{cases} 1 - x_{M-i+1} & text{if } i > 1 \ 1 & text{if } i = 1 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.