Adaptive Simulated Annealing with Homogenization for Aircraft Trajectory Optimization
In air traffic management, most optimization procedures are commonly based on deterministic modeling and do not take into account the uncertainties on environmental conditions (e.g., wind) and on air traffic control operations. However, aircraft performan
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Abstract In air traffic management, most optimization procedures are commonly based on deterministic modeling and do not take into account the uncertainties on environmental conditions (e.g., wind) and on air traffic control operations. However, aircraft performances in a real-world context are highly sensitive to these uncertainties. The aim of this work is twofold. First, we provide some numerical evidence of the sensitivity of fuel consumption and flight duration with respect to random fluctuations of the wind and the air traffic control operations. Second, we develop a global stochastic optimization procedure for general aircraft performance criteria. Since we consider general (black-box) cost functions, we develop a derivative-free optimization procedure: noisy simulated annealing (NSA).
C. Bouttier (B) · O. Babando · S. Laporte Airbus Operations SAS, 316 route de Bayonne, 31060 Toulouse Cedex 9, France e-mail: [email protected] O. Babando e-mail: [email protected] S. Laporte e-mail: [email protected] S. Gadat TSE, Toulouse School of Economics, 21 allée de Brienne, 31015 Toulouse Cedex 6, France e-mail: [email protected] S. Gerchinovitz Institut de Mathématiques de Toulouse, Université Toulouse III, 118 route de Narbonne, 31062 Toulouse Cedex 9, France e-mail: [email protected] F. Nicol ENAC, 7 avenue douard Belin, 31015 Toulouse Cedex 4, France e-mail: [email protected] © Springer International Publishing Switzerland 2017 K.F. Dœrner et al. (eds.), Operations Research Proceedings 2015, Operations Research Proceedings, DOI 10.1007/978-3-319-42902-1_77
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1 Introduction The aircraft trajectory optimization problem (ATOP) aims to find a four-dimensional path connecting two cities, which minimizes the sum of costs imputable to the flight called Direct Operating Costs (DOC) such as fuel consumption, salary and maintenance costs or environmental taxes [2]. Since airlines face a continuously growing competition, inaccurate DOC calculations are not affordable anymore. To ensure the robustness of the DOC computation, it is necessary to consider the uncertainty on its influence parameters. Moreover an accurate aircraft performance model should be used. This work aims to investigate uncertainty into aircraft dynamics and to give some evidence of the sensitivity of aircraft performance with respect to a combination of random inputs such as the weather or the air traffic control (ATC) operations. It relies on previous mono-source uncertainty impact investigations on simplified models such as [9]. We then provide an optimization procedure adapted to accurate stochastic aircraft performance models.
2 Mathematical Models of Uncertainty Sources and NSA Optimization Procedure The wind information available on-board of aircrafts as well as in the airline operation centres is far from today’s meteorological centre maximal capabilities. Meteorological data transmission to the aeronautical community has not evolved since the standardi
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