Solving the Air Conflict Resolution Problem Under Uncertainty Using an Iterative Biobjective Mixed Integer Programming Approach
Bibliographic record
Abstract
In this paper, we tackle the aircraft conflict resolution problem under uncertainties. We consider errors due to the wind effect, the imprecision of aircraft speed prediction, and the delay in the execution of maneuvers. Using a geometrical approach, we derive an analytical expression for the minimum distance between aircraft, along with the corresponding probability of conflict. These expressions are incorporated into an existing deterministic model for conflict resolution. This model solves the problem as a maximum clique of minimum weight in a graph whose vertices represent possible maneuvers and where edges link conflict-free maneuvers of different aircraft. We then present a solution procedure focusing on two criteria, namely, fuel efficiency and the probability of reissuing maneuvers in the future: we iteratively generate Pareto front solutions to provide the controller with a set of possible solutions where she can choose the one corresponding the most to her preferences. Intensive Monte Carlo simulations validate the expressions derived for the minimum distance and the probability of conflict. Computational results highlight that up to 10 different solutions for instances involving up to 35 aircraft are generated within 3 minutes.
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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 | 0.003 | 0.005 |
| Meta-epidemiology (narrow) | 0.002 | 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 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".