benchmarkfcns.multiobjective.bnh

benchmarkfcns.multiobjective.bnh(x: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous'], return_constraints: bool = False) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]']

Computes the value of the BNH (Binh and Korn) multi-objective benchmark function. SCORES = multiobjective.bnh(X) computes the value of the BNH function at point X. multiobjective.bnh accepts a matrix of size M-by-2 and returns a matrix SCORES of size M-by-2. If return_constraints is True, returns an M-by-4 matrix where the last two columns contain the constraint violations (values > 0 are violations). Properties:

• Recommended domain: x1 in [0, 5], x2 in [0, 3]

Mathematical Definition

\[\begin{split}f_1(x_1, x_2) = 4x_1^2 + 4x_2^2 \\\end{split}\]

f_2(x_1, x_2) = (x_1 - 5)^2 + (x_2 - 5)^2

Visualization

No visualization available for this function.