benchmarkfcns.multiobjective.mop5

benchmarkfcns.multiobjective.mop5(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 MOP5 (Viennet1 alias) multi-objective benchmark function. SCORES = multiobjective.mop5(X) computes the value of the MOP5 function at point X. multiobjective.mop5 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) &= x_1^2 + (x_2 - 1)^2 \ f_2(x_1, x_2) &= x_1^2 + (x_2 + 1)^2 + 1 \ f_3(x_1, x_2) &= (x_1 - 1)^2 + x_2^2 + 2 end{aligned}

Visualization

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