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Disjunctive linear separation conditions and mixed-integer formulations for aircraft conflict resolution [article]

Fernando H. C. Dias, Hassan Hijazi, David Rey
2020 arXiv   pre-print
We introduce new mixed-integer programming formulations for aircraft conflict resolution with speed, heading and altitude control which are based on disjunctive linear separation conditions.  ...  We show that the proposed disjunctive linear separation conditions are equivalent to the traditional nonlinear conditions for aircraft separation.  ...  Aircraft Conflict Resolution Formulations In this section, we present mixed-integer formulations for aircraft conflict resolution.  ... 
arXiv:1911.12997v3 fatcat:b5kthfkgqveqfim7r7lc5mqbni

Complex Number Formulation and Convex Relaxations for Aircraft Conflict Resolution [article]

David Rey, Hassan Hijazi
2017 arXiv   pre-print
As a side result, we present a new characterization of the conflict separation condition in the form of disjunctive linear constraints.  ...  We present a novel complex number formulation along with tight convex relaxations for the aircraft conflict resolution problem.  ...  In [4] , the authors propose a Mixed-Integer Linear Program (MILP) to find conflict-free aircraft trajectories in the horizontal space.  ... 
arXiv:1703.06708v2 fatcat:xjkptovqorhbnorkmbu6nccaxi

Geometric programming and mechanism design for air traffic conflict resolution

J Le Ny, G J Pappas
2010 Proceedings of the 2010 American Control Conference  
We develop certain extensions of optimizationbased conflict resolution methods in air traffic control.  ...  The problem considered concerns the scheduling of the crossing times of a set of aircraft through a metering fix, while maintaining aircraft separation.  ...  Modeling the disjunctions in the separation and scheduling constraints this way, we obtain a mixed integer geometric program. V.  ... 
doi:10.1109/acc.2010.5530432 fatcat:xeadaa3pd5gy3aom5thq5zu2ru

Joint Metering and Conflict Resolution in Air Traffic Control

Jerome Le Ny, George J. Pappas
2011 Journal of Guidance Control and Dynamics  
Moreover, the proposed methodology can account for some of the nonlinearities present in the formulations of conflict resolution problems, while incurring only a small penalty in computation time with  ...  Integer variables can be introduced to improve the quality of the solutions and to include combinatorial choices, for example, to optimize over aircraft sequences in merging streams.  ...  Recall [14, 28] the standard "big-M" formulation used to model a disjunction of linear constraints a T 1 x b 1 _ a T 2 x b 2 via mixed-integer linear programming.  ... 
doi:10.2514/1.53253 fatcat:e2rpb5225ragxkcazrvugbik2e

Aircraft Conflict Resolution with Trajectory Recovery Using Mixed-Integer Programming [article]

Fernando H. C. Dias, David Rey
2022 arXiv   pre-print
The avoidance stage extends existing mixed-integer programming formulations, and for the recovery stage, we propose a novel mixed-integer formulation.  ...  In this study, we address the aircraft conflict avoidance and trajectory recovery problem.  ...  In the proposed MIP (Mixed Integer Problem) formulation for conflict resolution with speed control, the authors derived linear pairwise aircraft separation constraints based on the geometric construction  ... 
arXiv:2203.11990v1 fatcat:uxpyzajiyncnnjzzgjtceu4blq

Chapter 22: Mixed-Integer Nonlinear Optimization in Air Traffic Management: Aircraft Conflict Avoidance [chapter]

Sonia Cafieri
2017 Advances and Trends in Optimization with Engineering Applications  
A mixed-integer linear model for conflict resolution by velocity and altitude changes is proposed in [2] .  ...  Interesting MINLP problems also come from mixed-integer optimal control models for conflict-free trajectories planning and conflicts resolution, where typical discretization steps lead to the solution  ... 
doi:10.1137/1.9781611974683.ch22 fatcat:ixcgb23p2zaqbf73hshytpbrza

MILP and NLP Techniques for centralized trajectory planning of multiple unmanned air vehicles

F. Borrelli, D. Subramanian, A.U. Raghunathan, L.T. Biegler
2006 2006 American Control Conference  
In the second approach the optimal control is converted to a finite dimensional Mixed Integer Linear Program (MILP) using Euler discretization and reformulating the disjunctions involved with the protected  ...  We consider the problem of optimal cooperative three-dimensional conflict resolution involving multiple Unmanned Air Vehicles (UAVs) using numerical trajectory optimization methods.  ...  INTRODUCTION The approaches to aircraft control for conflict resolution can differ on various criteria and objectives. A good review can be found in [20] , [12] , [13] .  ... 
doi:10.1109/acc.2006.1657644 fatcat:u52qnzlvwbe55nhi5lr4tewofq

A two-stage algorithm for aircraft conflict resolution with trajectory recovery [article]

Fernando H. C. Dias, Stephanie Rahme, David Rey
2020 arXiv   pre-print
For the trajectory recovery stage, we introduce a novel exact mixed-integer programming formulation as well as a greedy heuristic algorithm.  ...  We address the conflict resolution problem in air traffic control using a novel approach for aircraft collision avoidance with trajectory recovery.  ...  compromise between speed and angle change: minimize i∈A   w(1 − q i ) 2 + (1 − w) k∈Hi δ ik θ k 2   (8) 3) Disjunctive formulation: The proposed approach for conflict resolution via speed and discrete  ... 
arXiv:2002.06731v1 fatcat:3k3snirqcfg7dg723rh5xdmipe

Comparison of Mixed-Integer Linear Models for Fuel-Optimal Air Conflict Resolution With Recovery

Jeremy Omer
2015 IEEE transactions on intelligent transportation systems (Print)  
After describing the major modifications to existing models that are necessary to satisfy this definition of the problem, we compare three mixed integer linear programs.  ...  One of the tasks of air traffic management is to modify trajectories when necessary to maintain a sufficient separation between pairs of aircraft.  ...  For faster solution and guaranteed convergence, the nonlinear constraints and objective function of the NLP can be approximated with linear equations involving integer variables to obtain a mixed integer  ... 
doi:10.1109/tits.2015.2434942 fatcat:p3lgja63jrcepgkdd4ouxjd5hi

Formal testing for separation assurance

Dimitra Giannakopoulou, David H. Bushnell, Johann Schumann, Heinz Erzberger, Karen Heere
2011 Annals of Mathematics and Artificial Intelligence  
the aircraft to resolve this potential conflict.  ...  Separation assurance algorithms aim at predicting if two aircraft will get closer to each other than a minimum safe distance; if loss of separation is predicted, they also propose a change of course for  ...  We also gratefully acknowledge Peter Mehlitz for his help with JavaPathfinder, and Todd Farley and the NextGen program for funding this work.  ... 
doi:10.1007/s10472-011-9224-3 fatcat:ieqeswbnsjhm7ogcnomvgai22i

Optimization-Based Autonomous Air Traffic Control for Airspace Capacity Improvement

Baris Baspinar, Hamsa Balakrishnan, Emre Koyuncu
2020 IEEE Transactions on Aerospace and Electronic Systems  
ACKNOWLEDGMENT The authors disclosed that Barış Başpınar was supported by The Scientific and Technological Research Council of Turkey (TUBITAK) with International Doctoral Research Fellowship.  ...  The work [16] follows a similar approach that performs separation assurance via solving a quadratic program. The problem is also formulated as a mixed-integer programming in the study [17] .  ...  Then, we develop a mapping process based on discretization of the airspace to improve the performance of conflict detection and resolution and create an integer linear programming (ILP) that uses the sets  ... 
doi:10.1109/taes.2020.3003106 fatcat:egmpfmjw6nef3bjuwbgvkr7tgm

Review of real-time vehicle schedule recovery methods in transportation services

Monize Sâmara Visentini, Denis Borenstein, Jing-Quan Li, Pitu B. Mirchandani
2013 Journal of Scheduling  
For each class, a classification of the models is presented based on problem formulations and solution strategies.  ...  Real-time vehicle schedule recovery problems (RTVSRP) are classified into three classes: vehicle rescheduling, for road-based services, trainbased rescheduling, and airline schedule recovery problems.  ...  Acknowledgments We are indebted to the anonymous referees for very useful comments and criticism.  ... 
doi:10.1007/s10951-013-0339-8 fatcat:mnuq55wgorhddlj2bozz5xws5u

Optimal methods for resource allocation and scheduling: a cross-disciplinary survey

Michele Lombardi, Michela Milano
2012 Constraints  
and interactive fashion with a mix of CP and OR techniques, often reporting impressive speed-ups compared to pure CP and OR methods.  ...  Classical scheduling formulations typically assume static resource requirements and focus on deciding when to start the problem activities, so as to optimize some performance metric.  ...  We hope our effort will provide motivation to the research community for surveying the state of the art of heuristics for resource assignment and scheduling.  ... 
doi:10.1007/s10601-011-9115-6 fatcat:7mwr72aet5h63d4qm45h3c44fm

Constraints and AI Planning

A. Nareyek, E.C. Freuder, R. Fourer, E. Giunchiglia, R.P. Goldman, H. Kautz, J. Rintanen, A. Tate
2005 IEEE Intelligent Systems  
This article describes how planning techniques can be integrated with general constraintsolving frameworks, like SAT, IP and CP.  ...  Acknowledgments We would like to thank the reviewers for many improvement suggestions, as well as Kate Larson and Vincent Conitzer for a final check.  ...  The authors and their sponsors are authorized to reproduce and distribute reprints for their purposes notwithstanding any copyright annotation hereon.  ... 
doi:10.1109/mis.2005.25 fatcat:4u4satg25bbwna4egn6srw6pg4

Interpretable Categorization of Heterogeneous Time Series Data [chapter]

Ritchie Lee, Mykel J. Kochenderfer, Ole J. Mengshoel, Joshua Silbermann
2018 Proceedings of the 2018 SIAM International Conference on Data Mining  
Furthermore, we show how GBDTs can also be used for categorization, which is a combination of clustering and generating interpretable explanations for each cluster.  ...  We propose grammar-based decision trees (GBDTs) and an algorithm for learning them. GBDTs extend decision trees with a grammar framework.  ...  Acknowledgements We thank Neal Suchy at the FAA, Michael Owen and Cindy McLain at MIT Lincoln Laboratory, and the ACAS X team. This work was supported by the SASO Project under NASA ARMD's AOSP.  ... 
doi:10.1137/1.9781611975321.25 dblp:conf/sdm/LeeKMS18 fatcat:hmjjp236brhl7k75gqclaj2g7q
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