benchmarkfcns.multiobjective.mop3

benchmarkfcns.multiobjective.mop3(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 MOP3 (Poloni alias) multi-objective benchmark function. SCORES = multiobjective.mop3(X) computes the value of the MOP3 function at point X. multiobjective.mop3 accepts a matrix of size M-by-N and returns a matrix SCORES of size M-by-2.

Mathematical Definition

\[\begin{aligned}\]

f_1(x_1, x_2) &= 1 + (A_1 - B_1)^2 + (A_2 - B_2)^2 \ f_2(x_1, x_2) &= (x_1 + 3)^2 + (x_2 + 1)^2 \ A_1 &= 0.5 sin(1) - 2 cos(1) + sin(2) - 1.5 cos(2) \ A_2 &= 1.5 sin(1) - cos(1) + 2 sin(2) - 0.5 cos(2) \ B_1 &= 0.5 sin(x_1) - 2 cos(x_1) + sin(x_2) - 1.5 cos(x_2) \ B_2 &= 1.5 sin(x_1) - cos(x_1) + 2 sin(x_2) - 0.5 cos(x_2) end{aligned}

Visualization

No visualization available for this function.