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

\[\begin{split}f_1(\mathbf{x}) = 1 - \exp\left(-\sum_{i=1}^n \left(x_i - \frac{1}{\sqrt{n}}\right)^2\right) \\\end{split}\]

f_2(mathbf{x}) = 1 - expleft(-sum_{i=1}^n left(x_i + frac{1}{sqrt{n}}right)^2right)

Visualization

No visualization available for this function.