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.
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.
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.
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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) |
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Frequnency of |
Optimal set size vs. threshold size (three objectives) |
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2D EBO procedure |
3D EBO procedure |
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Candidate set size vs. threshold size (3 objectives) |
Total number of comparisons vs. threshold size (3 objectives) |
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Candidate set size vs. sample size (3 objectives) |
Total number of comparisons vs. sample size (3 objectives) |
André Stoll
- Multi-objective Optimization using Preference Structures by André Stoll