benchmarkfcns.multiobjective.tanaka

benchmarkfcns.multiobjective.tanaka(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 Tanaka multi-objective benchmark function. SCORES = multiobjective.tanaka(X) computes the value of the Tanaka function at point X. multiobjective.tanaka 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:

  • Number of dimensions: 2

  • Recommended domain: [0, Pi]^2

  • Constraints: 2 nonlinear constraints (one “ripple” constraint)

  • Pareto front: Disconnected

Mathematical Definition

\[\begin{split}f_1(x_1, x_2) = x_1 \\\end{split}\]

f_2(x_1, x_2) = x_2 \ C_1(mathbf{x}): x_1^2 + x_2^2 - 1 - 0.1 cos(16 arctan(x_1, x_2)) ge 0 \ C_2(mathbf{x}): (x_1 - 0.5)^2 + (x_2 - 0.5)^2 le 0.5

Visualization

No visualization available for this function.