benchmarkfcns.multiobjective.wfg9

benchmarkfcns.multiobjective.wfg9(x: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous'], num_objectives: SupportsInt | SupportsIndex = 3, k: SupportsInt | SupportsIndex = 4) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]']

Computes the value of the WFG9 multi-objective benchmark function. SCORES = multiobjective.wfg9(X, num_objectives, k) computes the value of the WFG9 function at point X. multiobjective.wfg9 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:

• Domain: x_i in [0, 2i]

• Shape: concave

Mathematical Definition

\[f_m(\mathbf{x}) = x_M + 2m \cdot h_m(x_1, \dots, x_{M-1})\]

text{ where } h_{1 dots M-1} text{ are concave}.

Visualization

No visualization available for this function.