Modified Orbital Branching with Applications to Orbitopes and to Unit Commitment
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Bibliographic record
Abstract
The past decade has seen advances in general methods for symmetry breaking in mixed-integer linear programming. These methods are advantageous for general problems with general symmetry groups. Some important classes of MILP problems, such as bin packing and graph coloring, contain highly structured symmetry groups. This observation has motivated the development of problem-specific techniques. In this paper we show how to strengthen orbital branching in order to exploit special structures in a problem’s symmetry group. The proposed technique, to which we refer as modified orbital branching, is able to solve problems with structured symmetry groups more efficiently. One class of problems for which this technique is effective is when the solution variables can be expressed as orbitopes, as this technique extends the classes of orbitopes where symmetry can be efficiently removed. We use the unit commitment problem, an important problem in power systems, to demonstrate the strength of modified orbital branching.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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