benchmarkfcns.multiobjective.cf1

benchmarkfcns.multiobjective.cf1(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 CF1 constrained multi-objective benchmark function. SCORES = multiobjective.cf1(X) computes the value of the CF1 function at point X. multiobjective.cf1 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-3 matrix where the last column contains the constraint violation (values > 0 are violations). Properties:

• Recommended domain: x1 in [0, 1], xj in [-1, 1] for j=2..N

Mathematical Definition

\[\begin{aligned}\]

f_1(textbf{x}) &= x_1 + frac{2}{|J_1|} sum_{j in J_1} [x_j - x_1^{0.5(1.0 + frac{3(j-2)}{n-2})}]^2 \ f_2(textbf{x}) &= 1 - x_1 + frac{2}{|J_2|} sum_{j in J_2} [x_j - x_1^{0.5(1.0 + frac{3(j-2)}{n-2})}]^2 \ text{Subject to: } & f_1 + f_2 - a |\sin(N\pi(f_1 - f_2 + 1))| - 1 ge 0 \ & x_i in [0, 1], quad N=10, a=1 end{aligned}

Visualization

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