benchmarkfcns.multiobjective.mop7

benchmarkfcns.multiobjective.mop7(x: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous']) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]']

Computes the value of the MOP7 (Viennet3 alias) multi-objective benchmark function. SCORES = multiobjective.mop7(X) computes the value of the MOP7 function at point X. multiobjective.mop7 accepts a matrix of size M-by-N and returns a matrix SCORES of size M-by-3.

Mathematical Definition

\[\begin{aligned}\]

f_1(x_1, x_2) &= 0.5(x_1^2 + x_2^2) + sin(x_1^2 + x_2^2) \ f_2(x_1, x_2) &= frac{(3x_1 - 2x_2 + 4)^2}{8} + frac{(x_1 - x_2 + 1)^2}{27} + 15 \ f_3(x_1, x_2) &= frac{1}{x_1^2 + x_2^2 + 1} - 1.1 exp(-(x_1^2 + x_2^2)) end{aligned}

Visualization

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