Maximizing the number of conflict-free aircraft using mixed-integer nonlinear programming

• Published in: Computers & operations research Vol. 80; no. April 2017; pp. 147 - 158
• Main Authors: Cafieri, Sonia, Rey, David
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.04.2017; Pergamon Press Inc; Elsevier
• Subjects: Air traffic control; Aircraft; Conflict detection and resolution; Conflict resolution; Deterministic global optimization; Mathematics; Mixed-integer nonlinear programming; Modeling; Nonlinear programming; Optimization and Control; Problem solving; Studies; Conflict detection and resolution; Mixed-integer nonlinear programming; Air traffic control; Modeling; Deterministic global optimization
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2016.12.002

•Developed speed control-based air conflict avoidance models using MINLP that do not require any form of discretization.•We maximize the number of conflicts resolved subject to subliminal speed control constraints.•A pre-processing algorithm is presented to reduce the size of the MINLP formulations.•A new approach together with a greedy algorithm is proposed to find the largest set of conflict-free aircraft.•Results on benchmark instances show that the proposed models and algorithms are efficient and versatile. We address the conflict detection and resolution problem in air traffic control, where an aircraft conflict is a loss of separation between aircraft trajectories. Conflict avoidance is crucial to ensure flight safety and remains a challenging traffic control problem. We focus on speed control to separate aircraft and consider two approaches: (i) maximize the number of conflicts resolved and (ii) identify the largest set of conflict-free aircraft. Both problems are modeled using mixed-integer nonlinear programming and a tailored greedy algorithm is proposed for the latter. Computational efficiency is improved through a pre-processing algorithm which attempts to reduce the size of the conflict resolution models by detecting the existence of pairwise potential conflicts. Numerical results are provided after implementing the proposed models and algorithms on benchmark conflict resolution instances. The results highlight the benefits of using the proposed pre-processing step as well as the versatility and the efficiency of the proposed models.