benchmarkfcns.multiobjective.zdt1

benchmarkfcns.multiobjective.zdt1(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 ZDT1 multi-objective benchmark function. SCORES = multiobjective.zdt1(X) computes the value of the ZDT1 function at point X. multiobjective.zdt1 accepts a matrix of size M-by-N and returns a matrix SCORES of size M-by-2 in which each row contains the function value for the corresponding row of X and each column corresponds to an objective. Properties:

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

  • Location of global Pareto front: x_1 ∈ [0, 1], x_i = 0 for i = 2, …, n

  • Number of dimensions: n (usually 30)

  • Recommended domain: [0, 1]^n

  • Number of local fronts: 0

  • Number of global fronts: 1

  • Convexity: convex (Pareto front)

  • Modality: unimodal

  • Separability: non-separable

  • Differentiable: Yes

For more information, please visit: benchmarkfcns.info/doc/zdt1fcn

Mathematical Definition

Visualization

zdt1 landscape