benchmarkfcns.multiobjective.zdt4

benchmarkfcns.multiobjective.zdt4(arg0: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous']) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]']

Computes the value of the ZDT4 multi-objective benchmark function. SCORES = multiobjective.zdt4(X) computes the value of the ZDT4 function at point X. multiobjective.zdt4 accepts a matrix of size M-by-N and returns a matrix SCORES of size M-by-2. Properties:

  • Global Pareto front: f_2 = 1 - sqrt{f_1}

  • Number of dimensions: n (usually 10)

  • Recommended domain: x_1 ∈ [0, 1], x_i ∈ [-5, 5] for i > 1

  • Modality: Highly Multimodal (has 21^{n-1} local Pareto fronts)

For more information, please visit: benchmarkfcns.info/doc/zdt4fcn

Mathematical Definition

Visualization

zdt4 landscape