Exact and Approximate Solving of the Aircraft Collision Resolution Problem via Turn Changes

Antonio Alonso-Ayuso (), Laureano F. Escudero () and F. Javier Martín-Campo ()
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Antonio Alonso-Ayuso: Área de Estadística e Investigación Operativa, Universidad Rey Juan Carlos, 28933 Madrid, Spain
Laureano F. Escudero: Área de Estadística e Investigación Operativa, Universidad Rey Juan Carlos, 28933 Madrid, Spain
F. Javier Martín-Campo: Departamento de Estadística e Investigación Operativa II (Métodos de decisión), Universidad Complutense de Madrid, 28223 Madrid, Spain

Transportation Science, 2016, vol. 50, issue 1, 263-274

Abstract: The aircraft conflict detection and resolution problem in air traffic management consists of deciding the best strategy for an arbitrary aircraft configuration such that all conflicts in the airspace are avoided. A conflict situation occurs if two or more aircraft do not maintain the minimum safety distance during their flight plans. A two-step approach is presented. The first step consists of a nonconvex mixed integer nonlinear optimization (MINLO) model based on geometric constructions. The objective is to minimize the weighted aircraft angle variations to obtain the new flight configuration. The second step consists of a set of unconstrained quadratic optimization models where aircraft are forced to return to their original flight plan as soon as possible once there is no aircraft in conflict with any other. The main results of extensive computation are reported by comparing the performance of state-of-the-art nonconvex MINLO solvers and an approximation by discretizing the possible angles of motion for solving a sequence of integer linear optimization (SILO) models in an iterative way. Minotaur, one of the nonconvex MINLO solvers experimented with, gives better solutions but requires more computation time than the SILO approach, which requires only a short time to obtain a good, feasible solution. Its value in the objective function has a reasonable goodness gap compared with the Minotaur solution. Given the need to solve the problem in almost real time, the approximate SILO approach is favored because of its short computation time and solution quality for the testbeds used in the experiment, which include both small- and real-sized instances. However, Minotaur is useful in this particular case for simulation purposes and for calibrating the SILO approach.

Keywords: aircraft conflict detection and resolution problem; air traffic management; nonconvex mixed integer nonlinear optimization; heuristic sequential integer linear optimization (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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