Branch & Bound-Based Algorithm for Aircraft VNAV Profile Reference Trajectory Optimization
Bibliographic record
Abstract
Computing the vertical navigation reference trajectory is investigated as a way to reduce fuel consumption. Future Air Traffic Management functions might be able to allow aircraft to fly at their most economical profiles allowing fuel consumption reduction. The vertical navigation reference trajectory solution is a combination of the possible Indicated Air Speed, Mach number and altitude of the different flight phases. This paper considers these speeds and altitudes as discrete values, which area available in a Performance Database. The possible combinations are modeled as a tree-like graph. The graph was browsed using a mixture of Best-First Search and Depth-First Search method. A Branch & Bound based algorithm was implemented to reduce the number of computations required to find the optimal combination. A bounding function to estimate the cost at each node was developed and a parameter defined as the Optimism Coefficient was introduced to vary the accuracy of the bounding function. Comparing the experimental results to an exhaustive search algorithm proved the optimal solution and the fuel reduction potential of this algorithm. This algorithm tries to calculate the least possible combinations making it a good choice in low processing power devices such as the Flight Management System.
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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 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 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".