benchmarkfcns.multiobjective.dtlz5

benchmarkfcns.multiobjective.dtlz5(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 DTLZ5 multi-objective benchmark function. SCORES = multiobjective.dtlz5(X, num_objectives) computes the value of the DTLZ5 function at point X. multiobjective.dtlz5 accepts a matrix of size M-by-N and returns a matrix SCORES of size M-by-K where K is the number of objectives. Properties:

  • Global Pareto front: Degenerate (Curve)

  • Number of dimensions: n (usually 10)

  • Recommended domain: [0, 1]^n

  • Modality: unimodal

  • Characteristic: Tests ability to converge to a lower-dimensional Pareto front.

Mathematical Definition

Visualization

dtlz5 landscape