benchmarkfcns.multiobjective.zdt3

benchmarkfcns.multiobjective.zdt3(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 ZDT3 multi-objective benchmark function. SCORES = multiobjective.zdt3(X) computes the value of the ZDT3 function at point X. multiobjective.zdt3 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} - f_1 sin(10π 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

  • Convexity: disconnected (Pareto front)

  • Modality: multimodal

For more information, please visit: benchmarkfcns.info/doc/zdt3fcn

Mathematical Definition

Visualization

zdt3 landscape