benchmarkfcns.multiobjective.osyczkakundu

benchmarkfcns.multiobjective.osyczkakundu(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 Osyczka and Kundu multi-objective benchmark function. SCORES = multiobjective.osyczkakundu(X) computes the value of the Osyczka and Kundu function at point X. multiobjective.osyczkakundu accepts a matrix of size M-by-6 and returns a matrix SCORES of size M-by-2. If return_constraints is True, returns an M-by-8 matrix where the last six columns contain the constraint violations (values > 0 are violations). Properties:

  • Number of dimensions: 6

  • Recommended domain: x1, x2, x6 in [0, 10]; x3, x5 in [1, 5]; x4 in [0, 6]

  • Constraints: 6 complex non-linear constraints

Mathematical Definition

\[\begin{split}f_1(\mathbf{x}) = -(25(x_1 - 2)^2 + (x_2 - 2)^2 + (x_3 - 1)^2 + (x_4 - 4)^2 + (x_5 - 1)^2) \\\end{split}\]

f_2(mathbf{x}) = sum_{i=1}^6 x_i^2 \ C_1(mathbf{x}): x_1 + x_2 - 2 ge 0 \ C_2(mathbf{x}): 6 - x_1 - x_2 ge 0 \ C_3(mathbf{x}): 2 - x_2 + x_1 ge 0 \ C_4(mathbf{x}): 2 - x_1 + 3x_2 ge 0 \ C_5(mathbf{x}): 4 - (x_3 - 3)^2 - x_4 ge 0 \ C_6(mathbf{x}): (x_5 - 3)^2 + x_6 - 4 ge 0

Visualization

No visualization available for this function.