benchmarkfcns.multiobjective.cf6

benchmarkfcns.multiobjective.cf6(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 CEC 2009 CF6 constrained multi-objective benchmark function. SCORES = multiobjective.cf6(X) computes the value of the CF6 function at point X. multiobjective.cf6 accepts a matrix of size M-by-N 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, 1], xj in [-2, 2] for j=2..N

Mathematical Definition

\[\begin{aligned}\]

f_1(textbf{x}) &= x_1 + frac{2}{|J_1|} sum_{j in J_1} y_j^2 \ f_2(textbf{x}) &= (1 - x_1)^2 + frac{2}{|J_2|} sum_{j in J_2} y_j^2 \ y_j &= begin{cases} x_j - 0.8x_1 cos(6pi x_1 + frac{jpi}{n}) & j in J_1 \ x_j - 0.8x_1 sin(6pi x_1 + frac{jpi}{n}) & j in J_2 end{cases} \ text{Subject to: } & x_2 - 0.8x_1 sin(6pi x_1 + frac{2pi}{n}) - 0.5x_1 + 0.25 ge 0 \ & x_4 - 0.8x_1 sin(6pi x_1 + frac{4pi}{n}) - 0.5x_1 + 0.25 ge 0 \ & x_1 in [0, 1], x_j in [-2, 2] end{aligned}

Visualization

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