rl-opt

Library for relaxed lexicographic optimizaton (lexicographic semiorders) in Python

The library was developed with the following objectives in mind

• investigate the dependency of the EBO decision and the optimal solutions given a lexicographic semiorder,
• examine how the different parameters affect the size of the candidate set and the total number of comparisons made and
• create visualization to help understand lexicographic semiorders as preference structures.

Lexicographic Semiorder

A lexicographic semiorder compares elements of a Cartesian Product of several sets lexicographically. A element x is said to be smaller than another element y if there exists an index where x_i is better than y_i by a threshold sigma.

Visualizations

See Chapters 4.5 and 6.2 in Multi-objective Optimization using Preference Structures for the explanation of the visualizations and the outline of the simulations.

Optimal solutions

Minimum optimal set size vs. threshold size (two objectives)

Average optimal set size vs. threshold size (two objectives)

Maximum optimal set size vs. threshold size (two objectives)

Frequnency of and being non-empty.

Optimal set size vs. threshold size (three objectives)

EBO procedure

2D EBO procedure

3D EBO procedure

Candidate set size vs. threshold size (3 objectives)

Total number of comparisons vs. threshold size (3 objectives)

Candidate set size vs. sample size (3 objectives)

Total number of comparisons vs. sample size (3 objectives)

Contributors

André Stoll

References

• Multi-objective Optimization using Preference Structures by André Stoll

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