A line decomposition algorithm for multiobjective optimization
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Bibliographic record
Abstract
Decomposition techniques are proven highly effective in addressing complexity of optimization problems.For multiobjective optimization problems (MOPs), a variety of objective-space decomposition approaches are developed and applied in practice, while decision-space decomposition remains rather underexplored.We develop a line-decomposition algorithm for computing an approximation of the efficient set of strictly convex MOPs.The feasible region is decomposed into lines whose efficient sets are used to reconstruct the overall efficient set.Because the algorithm relies on solving a collection of single objective line search problems, it is immediately applicable to single-objective optimization with no modifications.We prove the algorithm convergence and provide a preliminary error analysis.The algorithm is implemented in Python and tested on biobjective and single objective problems with bounded variables.Numerical results are also included.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it