benchmarkfcns.multiobjective.oka1

benchmarkfcns.multiobjective.oka1(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 OKA1 bi-objective benchmark function. SCORES = multiobjective.oka1(X) computes the value of the OKA1 function at point X. multiobjective.oka1 accepts a matrix of size M-by-2 and returns a matrix SCORES of size M-by-2. Properties:

• Recommended domain: x1 in [6*sin(pi/12), 6*sin(pi/12) + 2*pi*cos(pi/12)], x2 in [-2*pi*sin(pi/12), 6*cos(pi/12)]

Mathematical Definition

\[\begin{aligned}\]

x_1’ &= x_1 cos(frac{pi}{12}) - x_2 sin(frac{pi}{12}) \ x_2’ &= x_1 sin(frac{pi}{12}) + x_2 cos(frac{pi}{12}) \ f_1(x) &= x_1’ \ f_2(x) &= sqrt{2pi} - sqrt{|x_1'|} + 2|x_2’ - 3 cos(x_1’) - 3|^{1/3} end{aligned}

Visualization

No visualization available for this function.