benchmarkfcns.multiobjective.dtlz7

benchmarkfcns.multiobjective.dtlz7(x: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous'], num_objectives: SupportsInt | SupportsIndex = 3) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]']

Computes the value of the DTLZ7 multi-objective benchmark function. SCORES = multiobjective.dtlz7(X, num_objectives) computes the value of the DTLZ7 function at point X. multiobjective.dtlz7 accepts a matrix of size M-by-N and returns a matrix SCORES of size M-by-K where K is the number of objectives. Properties:

  • Global Pareto front: Disconnected (2^(M-1) regions)

  • Number of dimensions: n (usually 20)

  • Recommended domain: [0, 1]^n

  • Modality: multimodal (disconnected front)

For more information, please visit: benchmarkfcns.info/doc/dtlz7fcn

Mathematical Definition

\[\begin{split}f_i(\textbf{x}) = x_i, \quad i = 1, \dots, M-1 \\\end{split}\]

f_M(textbf{x}) = (1 + g(textbf{x})) h(f_1, dots, f_{M-1}, g) \ g(textbf{x}) = 1 + frac{9}{k} sum_{i=n-k+1}^n x_i \ h(f_1, dots, f_{M-1}, g) = M - sum_{i=1}^{M-1} left[ frac{f_i}{1+g} (1 + sin(3 pi f_i)) right]

Visualization

No visualization available for this function.