Solving LBBD Master Problems with Constraint Programming and Domain-Independent Dynamic Programming
Why this work is in the frame
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Bibliographic record
Abstract
We investigate using Constraint Programming (CP) and Domain-Independent Dynamic Programming (DIDP) to solve the master problem in Logic-based Benders Decomposition (LBBD) models, in particular addressing the challenge of feasibility cut formulation. For CP, we exploit key variable manipulation, constraint-based expressions, and global constraints to construct three combinatorial cut encodings. For the state-based DIDP model, we propose two cut encoding approaches: using additional preconditions of state transitions or adding state constraints. Each of these approaches can be modeled using integer numeric variables or set variables, resulting in four novel encodings. We apply the three CP variants and four DIDP variants to simple assembly line balancing problems with sequence-dependent setup times type-1 (SUALBP-1). Experimental results show all approaches outperform a mixed-integer programming (MIP) based master problem and the state-of-the-art monolithic MIP model, with the three CP variants being superior to all of the DIDP approaches.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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