Neural Sequence Generation with Constraints via Beam Search with Cuts: A Case Study on VRP
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
In recent years, neural sequence models have been applied successfully to solve combinatorial optimization problems. Solutions, encoded as sequences, are typically generated from trained models via beam search, a search algorithm that generates sequences token-by-token while keeping a fixed number of promising partial solutions at each step. In this paper, we explore the problem of augmenting beam search generation with the enforcement of requirements---hard constraints that any generated solution must adhere to. We propose a hybrid approach, by encoding the requirements in the form of a constraint satisfaction problem (CSP) and iteratively solving the CSP to cut any partial solution within the beam search that is incapable of satisfying the requirements. We study this problem in the context of vehicle routing problems (VRP) further augmented with capacity-related or temporal requirements. We experimentally show that cuts often allow us to satisfy the requirements with negligible impact on solution quality. Without the use of cuts, beam search is shown to be exponentially less likely to satisfy the requirements as the length of the solution increases and/or the requirements are strengthened.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 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