Hybrid metaheuristic optimization algorithm for strategic planning of {4D} aircraft trajectories at the continent scale

International audienceGlobal air-traffic demand is continuously increasing. To handle such a tremendous traffic volume while maintaining at least the same level of safety, a more efficient strategic trajectory planning is necessary. In this work, we present a strategic trajectory planning methodology which aims to minimize interaction between aircraft at the European-continent scale. In addition, we propose a preliminary study that takes into account uncertainties of aircraft positions in the horizontal plane. The proposed methodology separates aircraft by modifying their trajectories and departure times. This route/departure-time assignment problem is modeled as a mixed-integer optimization problem. Due to the very high combinatorics involved in the continent-scale context (involving more than 30,000 flights), we develop and implement a hybrid-metaheuristic optimization algorithm. In addition, we present a computationally-efficient interaction detection method for large trajectory sets. The proposed methodology is successfully implemented and tested on a full-day simulated air traffic over the European airspace, yielding to an interaction-free trajectory plan

L'usage du crayon à mine et le droit à l'erreur dans l'apprentissage des mathématiques

Je suis Quebecois, j'ai fait toutes mes etudes au Canada et je suis enseignant-chercheur en France depuis 15 ans. Une des dierences principales en enseignement que je remarque entre les deux pays est l'usage systematique du stylo a encre par les eleves et etudiants francais pour tout rediger, y compris les solutions aux problemes de mathematiques...

Optimisation globale pour la résolution de problèmes parcimonieux en norme l0l_0

International audienceL’approximation parcimonieuse vise à obtenir une solution approchée d’un système linéaire ayant le moins de composantes nonnulles possible. Elle peut s’exprimer sous la forme d’un problème d’optimisation bi-objectif dans lequel sont minimisées une mesure de fidélitéaux données et la « norme » $l_0$ mesurant la parcimonie. Ce problème, essentiellement combinatoire, est souvent contourné par la relaxationconvexe de la norme $l_0$ , ou par des techniques heuristiques d’exploration combinatoire partielle. Cependant, pour de nombreux problèmesinverses, de telles approches échouent à déterminer le minimum global. Nous proposons l’optimisation globale de ces problèmes en norme $l_0$par l’intermédiaire de programmes mixtes en nombres entiers, mêlant variables réelles et entières. Des formulations contraintes et pénaliséessont proposées, pour différentes mesures $l_p$ de fidélité aux données. L’efficacité algorithmique de ces formulations est évaluée sur des donnéessimulées de déconvolution impulsionnelle. Nous montrons que la résolution exacte de tels problèmes est faisable pour des problèmes inverses detaille raisonnable, pour lesquels les solutions classiques échouent à localiser la solution et l’exploration combinatoire serait prohibitive

Computing In-Service Aircraft Reliability

International audienceThis paper deals with the modeling and computation of in-service aircraft reliability at the preliminary design stage. This problem is crucial for aircraft designers because it enables them to evaluate in-service interruption rates, in view of designing the system and of optimizing aircraft support. In the context of a sequence of flight cycles, standard reliability methods are not computationally conceivable with respect to industrial timing constraints. In this paper, first we construct the mathematical framework of in-service aircraft reliability. Second, we use this model in order to demonstrate recursive formulae linking the probabilities of the main failure events. Third, from these analytic developments, we derive relevent reliability bounds. We use these bounds to design an efficient algorithm to estimate operational interruption rate indicators. Finally, we show the usefulness of our approach on real-world cases provided by Airbus

Merging Flows in Terminal Moneuvering Area using Time Decomposition Approach

International audienceWith a continuous growth of air traffic demand, more effort must be made to alleviate the current overloaded airspace charges. This research focuses on the aircraft merging and sequencing problem at Terminal Maneuvering Area. Tactical conflict detection and resolution methods are applied to a predefined route network structure. Speed and time changes are proposed via an optimization methodology to resolve conflicts and maintain separation between aircraft with regard to the wake turbulence constraints and runway occupancy time. A new time decomposition approach is introduced. It consists in partitioning the whole time interval under consideration into several overlapping time windows, and in solving the merging and sequencing problem individually in each such sub-window. Four aircraft status are defined to classify flights according to their temporal position relative to the current sliding window. Moreover, an adapted simulated annealing heuristic is proposed to solve the corresponding sub-problems. Finally, computational experiments of the proposed algorithm, performed on real-world case studies of Paris Charles De-Gaulle airport, show the benefits of this sliding-window time-decomposition approac

Plunge milling time optimization via mixed-integer nonlinear programming

International audiencePlunge milling is a recent and efficient production mean for machining deep workpieces, notably in aeronautics. This paper focuses on the minimization of the machining time by optimizing the values of the cutting parameters. Currently, neither Computer-Aided Manufacturing (CAM) software nor standard approaches take into account the tool path geometry and the control laws driving the tool displacements to propose optimal cutting parameter values, despite their significant impact. This paper contributes to plunge milling optimization through a Mixed-Integer NonLinear Programming (MINLP) approach, which enables us to determine optimal cutting parameter values that evolve along the tool path. It involves both continuous (cutting speed, feed per tooth) and, in contrast with standard approaches, integer (number of plunges) optimization variables, as well as nonlinear constraints. These constraints are related to the Computer Numerical Control (CNC) machine tool and to the cutting tool, taking into account the control laws. Computational results, validated on CNC machines and on representative test cases of engine housing, show that our methodology outperforms standard industrial engineering know-how approaches by up to 55% in terms of machining time

Aircraft Conflict Resolution by Genetic Algorithm and B-Spline Approximation

International audienceConflict resolution has always been a sensitive matter in air-traffic management. Current European projects aim partial or total automation of air-traffic control to deal with the constant growth of air-traffic. Technological advances on flight management system allows us to consider an automatic conflict resolution using continuous trajectories. In this paper, we present a new methodology that, first, relies on B-splines to model trajectories, secondly models air-traffic conflict resolution as an optimization problem whose decision variables are the spline control points. Finally, we use genetic algorithms to tackle this optimization problem in order to generate optimal conflict-free situations

North Atlantic Aircraft Trajectory Optimization

International audienceNorth Atlantic oceanic airspace accommodates air traffic between North America and Europe. Radar-based surveillance is not applicable in this vast and highly congested airspace. For conflict-free flight progress, the organized track system is established in the North Atlantic and flights are prescribed to follow predefined oceanic tracks. Rerouting of aircraft from one track to another is very rarely applied because of large separation standards. As a result, aircraft often follow routes that are not optimal in view of their departure and destination points. This leads to an increase in aircraft cruising time and congestion level in continental airspace at input and output. Implementing new technologies and airborne-based control procedures will enable a significant decrease in the present separation standards and improvement of the traffic situation in the North Atlantic. The aim of the present study is to show the benefits that can be expected from such a reduction of separation standards. Optimal conflict-free trajectories are constructed for several flight sets based on the new proposed separation standards, with respect to the flight input data and oceanic winds. This paper introduces a mathematical model, proposes an optimization formulation of the problem, constructs two test problems based on real air-traffic data, and presents very encouraging results of simulations for these data

Optimal location of dynamic military areas within civil aviation traffic

International audienceIn this study, we focus on the problem of locating optimally dynamic military areas with the aim of minimizing the number of civil flight trajectories potentially impacted by the military activity, and the distance between the military area and the military base. We model the military areas by 2D geometry shapes with a vertical extension associated to given flight levels during the temporary area-activation time window. We propose a mathematical formulation of this problem as a constrained-optimization problem. We then introduce a global-optimization methodology based on a simulated annealing algorithm featuring tailored neighborhood-search strategies and an astute computational evaluation of the otherwise costly objective function. This is applied to one day of French traffic involving 8,836 civil flights. The results show that the proposed method is efficient to locate the military area that is nearest from the military base, while minimizing the potential impact on civil flight trajectories

Discontinuous piecewise differentiable optimization I : theory

A theoretical framework and a practical algorithm are presented to solve discontinuous piecewise linear optimization problems. A penalty approach allows one to consider such problems subject to a wide range of constraints involving piecewise linear functions. Although the theory is expounded in detail in the special case of discontinuous piecewise linear functions, it is straightforwardly extendable, using standard non linear programming techniques, to the nonlinear (discontinuous piecewise differentiable) situation to yield a first order algorithm. This work is presented in two parts. We introduce the theory in this first paper. The descent algorithm which is elaborated uses active set and projected gradient approaches. It is generalization of the ideas used by Conn to deal with nonsmoothness in the l1 exact penalty function, and it is based on the notion of decomposition of a function into a smooth and a nonsmooth part. In an accompanying paper, we shall tackle constraints via a penalty approach, we shall discuss the degenerate situation, the implementation of the algorithm, and numerical results will be presented