Aircraft Deconfliction via Mathematical Programming: Review and Insights

Abstract

Computer-aided air traffic management has increasingly attracted the interest of the operations research community. This includes, among other tasks, the design of decision support tools for the detection and resolution of conflict situations during flight. Even if numerous optimization approaches have been proposed, there has been little debate toward homogenization. We synthesize the efforts made by the operations research community in the past few decades to provide mathematical models to aid conflict detection and resolution at a tactical level. Different mathematical representations of aircraft separation conditions are presented in a unifying analysis. The models, which hinge on these conditions, are then revisited, providing insight into their computational performance.

Flight Conflict Resolution and Trajectory Recovery Through Mixed Integer Nonlinear Programming Based on Speed and Heading Angle Change

“…Mathematical programming methods have been reviewed (26), giving six different aircraft separation conditions and three maneuvering strategies. Mixed integer linear programming (MILP) and mixed integer nonlinear programming (MINLP) are two algorithms typically used for solving conflict resolution problems (26). The global optimal solution can be obtained easily through mathematical programming methods (27)(28)(29)(30)(31)(32)(33)(34)(35)(36)(37)(38)(39)(40) as long as the principle of optimization is satisfied.…”

“…The flight conflict resolution problem is modeled as an optimization control problem, which can be solved by intelligent optimization algorithms ( 6 ), such as genetic algorithm ( 7 – 12 ), artificial potential field ( 13 , 14 ), particle swarm algorithm ( 15 – 18 ) and ant colony algorithm ( 19 ), neural network ( 20 – 23 ), and simulated annealing method ( 24 , 25 ). Mathematical programming methods have been reviewed ( 26 ), giving six different aircraft separation conditions and three maneuvering strategies. Mixed integer linear programming (MILP) and mixed integer nonlinear programming (MINLP) are two algorithms typically used for solving conflict resolution problems ( 26 ).…”

“…A scene of circle instances was constructed, where N ( N = 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 ) aircraft are evenly distributed on a circle with the ZHO coordinate as the center and a radius ( R ) of 100 nmi ( 26 ). The initial positions of the aircraft are at the edge of the circle and the initial heading angles are all toward the ZHO coordinate.…”

Multi-Aircraft Flight Conflict Resolution and Trajectory Recovery Scheme Based on Mixed Integer Linear Programming and Geometric Rules

“…It can be concluded from the above literature that mathematical programming algorithms must satisfy the principle of optimization, and each mathematical programming algorithm has its own scope of application. In 2021, Pelegrin and D’Ambrosio reviewed mathematical programming methods used for flight conflict resolution, and pointed out that mixed integer linear programming (MILP) and mixed integer nonlinear programming (MINLP) are the two typical algorithms for solving the problem of flight conflict ( 36 ). Since MINLP may take practical constraints into account, there is no guarantee that it will lead to a feasible solution and, when it does, it will converge to a local optimum.…”

Branch‐and‐price for energy optimization in multi‐hop wireless sensor networks

“…Multi-hop wireless sensor networks (WSNs) support many applications requiring wireless communication on various platforms. We can mention unmanned aerials vehicles (UAVs) [44,47], flying taxis (vertical take-off and landing) [48], Internet-of-Things (IoT) sensor devices for monitoring [21,56], connected healthcare [30,57], agricultural monitoring, and various emerging smart city and smart mobility deployments [41,60], whose components are connected via WSNs. In all these cases, energy efficiency and traffic optimization are key challenges.…”