benchmarkfcns.multiobjective.dtlz1

benchmarkfcns.multiobjective.dtlz1(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 DTLZ1 multi-objective benchmark function. SCORES = multiobjective.dtlz1(X, num_objectives) computes the value of the DTLZ1 function at point X. multiobjective.dtlz1 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: Linear hyperplane (sum f_i = 0.5)

  • Number of dimensions: n (usually k + num_objectives - 1, k=5)

  • Recommended domain: [0, 1]^n

  • Convexity: linear hyperplane

  • Modality: multimodal

For more information, please visit: benchmarkfcns.info/doc/dtlz1fcn

Mathematical Definition

Visualization

dtlz1 landscape