benchmarkfcns.multiobjective.kita

benchmarkfcns.multiobjective.kita(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 KITA bi-objective benchmark function. SCORES = multiobjective.kita(X) computes the value of the KITA function at point X. multiobjective.kita 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-5 matrix where the last three columns contain the constraint violations (values > 0 are violations). Properties:

• Recommended domain: x1, x2 in [0, 7]

Mathematical Definition

\[\begin{aligned}\]

text{Maximize: } & f_1(x_1, x_2) = -x_1^2 + x_2 \ & f_2(x_1, x_2) = 0.5x_1 + x_2 + 1 \ text{Subject to: } & frac{1}{6}x_1 + x_2 le 6.5 \ & frac{1}{2}x_1 + x_2 le 7.5 \ & 5x_1 + x_2 le 30 \ & x_1, x_2 ge 0 end{aligned}

Visualization

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