saealib.TchebycheffDecomposition

class saealib.TchebycheffDecomposition

Bases: Decomposition

Tchebycheff (Chebyshev) scalarization.

score_i = max_{j} { w_j * |f_{ij} - z_j*| }

where z* is the ideal point. Unlike the weighted sum, this scalarization can reach any point on the Pareto front, including parts of non-convex fronts, by varying the weight vector.

Zero weights are replaced by 1e-6 to avoid degenerate sub-problems (a convention from Zhang & Li 2007, Appendix A).

References

[9]: Zhang, Q., & Li, H. (2007). MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Transactions on Evolutionary Computation, 11(6), 712-731.

Methods

__init__
aggregate	Compute the Tchebycheff scalar score.
contract	Return the decomposition contract.

Method Details

TchebycheffDecomposition.__init__()

TchebycheffDecomposition.aggregate(f, weights, ideal_point)

Compute the Tchebycheff scalar score.

Parameters:

• f (np.ndarray) – Objective matrix, shape (N, n_obj).

• weights (np.ndarray) – Non-negative weight vector, shape (n_obj,). Zero entries are internally replaced by 1e-6.

• ideal_point (np.ndarray) – Ideal (reference minimum) point, shape (n_obj,).

Returns:

Scores, shape (N,). Lower is better.

Return type:

np.ndarray

TchebycheffDecomposition.contract()

Return the decomposition contract.

Return type:

ComponentContract