benchmarkfcns.multiobjective.fonsecafleming

benchmarkfcns.multiobjective.fonsecafleming(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 Fonseca-Fleming multi-objective benchmark function. SCORES = multiobjective.fonsecafleming(X) computes the value of the Fonseca-Fleming function at point X. multiobjective.fonsecafleming accepts a matrix of size M-by-N and returns a matrix SCORES of size M-by-2 containing the function values for each objective. Properties:

  • Number of dimensions: n (typically 2 or 3)

  • Recommended domain: [-4, 4]^n

  • Pareto front: Concave

  • Separability: Non-separable

  • Modality: Unimodal (in terms of single objective components)

Mathematical Definition

Visualization

fonsecafleming landscape