benchmarkfcns.multiobjective.zdt6

benchmarkfcns.multiobjective.zdt6(arg0: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous']) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]']

Computes the value of the ZDT6 multi-objective benchmark function. SCORES = multiobjective.zdt6(X) computes the value of the ZDT6 function at point X. multiobjective.zdt6 accepts a matrix of size M-by-N and returns a matrix SCORES of size M-by-2. Properties:

• Global Pareto front: f_2 = 1 - f_1^2

• Number of dimensions: n (usually 10)

• Recommended domain: [0, 1]^n

• Mapping: Tests Non-uniform mapping/density to the Pareto front

For more information, please visit: benchmarkfcns.info/doc/zdt6fcn

Mathematical Definition

\[\begin{split}f_1(\textbf{x}) = 1 - \exp(-4x_1) \sin^6(6\pi x_1) \\\end{split}\]

f_2(textbf{x}) = g(textbf{x}) h(f_1, g) \ g(textbf{x}) = 1 + 9 left( frac{sum_{i=2}^{n} x_i}{n-1} right)^{0.25} \ h(f_1, g) = 1 - left( frac{f_1}{g} right)^2

Visualization

No visualization available for this function.