An Improved Integral Column Generation Algorithm Using Machine Learning for Aircrew Pairing
Bibliographic record
Abstract
The crew-pairing problem (CPP) is solved in the first step of the crew-scheduling process. It consists of creating a set of pairings (sequence of flights, connections, and rests forming one or multiple days of work for an anonymous crew member) that covers a given set of flights at minimum cost. Those pairings are assigned to crew members in a subsequent crew-rostering step. In this paper, we propose a new integral column-generation algorithm for the CPP, called improved integral column generation with prediction ([Formula: see text]), which leaps from one integer solution to another until a near-optimal solution is found. Our algorithm improves on previous integral column-generation algorithms by introducing a set of reduced subproblems. Those subproblems only contain flight connections that have a high probability of being selected in a near-optimal solution and are, therefore, solved faster. We predict flight-connection probabilities using a deep neural network trained in a supervised framework. We test [Formula: see text] on several real-life instances and show that it outperforms a state-of-the-art integral column-generation algorithm as well as a branch-and-price heuristic commonly used in commercial airline planning software, in terms of both solution costs and computing times. We highlight the contributions of the neural network to [Formula: see text].
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".