Optimal Design of SIDs/STARs in Terminal Maneuvering Area
Optimisation des procédures de départ et d’arrivée dans une zone terminale
Résumé
The objective of this thesis is to propose a methodology for the optimization of departure and arrival routes in the airspace surrounding airports, named Terminal Maneuvering Area (TMA). The air traffic departing from and arriving to airports follows pre-designed routes named Standard Intrument Departure (SID) routes, that connect the runways to the TMA exit points, and Standard Terminal Arrival Routes (STAR), that connect the TMA entry points to the runways. The design of SIDs/STARs falls into the area of airspace design problems that are very critical, mainly due to the predictions of air traffic growth and the consequent traffic congestion. In fact, according to several studies, the world-wide air traffic is projected to grow 4 to 5 percent annually in the next 20 years. This sharp increase leads directly to the capacity insufficiency of the airspace surrounding airports. In order to adapt the capacity of TMAs to the increased traffic demand, new airports and runways can be constructed. However, this kind of solution usually leads to high construction costs and long construction times. Designing SIDs/STARs more efficiently is another possible way to increase the capacity of TMA airspace, and so to reduce the congestion around airports. In this thesis we propose an optimal design of SIDs/STARs, taking into account the configuration and environment around airports, and the related operational constraints, in particular the avoidance of obstacles and the separation between routes. We propose a mathematical formulation leading to a combinatorial optimization problem, as well as efficient ad hoc resolution methods for the problem. More precisely, each route is modeled in 3D, consisting of two components: a curve in the horizontal plane which is composed by a succession of arcs of circles and segments, associated with a cone in the vertical plane that contains all ascent (or descent) profiles of the aircraft flying on this route. Moreover, the obstacles as well as their protection area are modeled in cylinder shape. This route design problem is solved in two steps. In the first step, we deal with the design of one optimal route avoiding obstacles with respect to minimum route length. We propose a deterministic global optimization approach based on a Branch and Bound (B&B) method. In this B&B, the branching strategies are related to the form of a route, and are tailored to the ways the obstacles area voided (bypassing clockwise or counter-clockwise, or imposing a level flight below an obstacle in the vertical plane).In the second step, the problem of designing multiple routes is considered. The main difficulty in this case is to ensure the pairwise separation between routes. We propose two approaches to deal with the design of multiple routes. The first is a B&B-based approach, where routes are generated sequentially in a given order (for example, in a decreasing order of the traffic load). We first build routes individually using the B&B method defined previously. Then, the routes are deviated locally around the conflicting zones (zones where routes lose the minimum separation norm). In order to carry out the route deviation, fictitious obstacles in cylinder shape enveloping the conflicting zones are introduced, and then avoided by using the B&B. The quality of a solution provided by the B&B-based approach depends on the routes generation order. Thus another method building routes simultaneously is proposed, that is the Simulated Annealing (SA) method. Fictitious obstacles in cylinder shape are also introduced to envelop conflicting zones, and their avoidance strategies are randomly selected in the SA method. Our approach is validated on a set of artificially generated problems as well as on two problems corresponding to existing TMAs (Paris CDG and Zurich). Concerning the first set of test problems, several configurations of TMA (number and layout of obstacles, runways, positions of the TMA entry/exit points) are considered. We show that we obtain continuous and smooth routes which are suitable for Continuous Climb Operation (CCO) and Continuous Descent Operation (CDO).Concerning the tests performed on real data, the choice of the TMAs of Paris CDG and Zurich allows us to test our approach, on the one hand, on a TMA with numerous TMA entry/exit points, and on the other hand, on a TMA with many obstacles. The simulation results show a gain in the total route length compared with the published standard charts that can be promising in terms of reducing jet fuel consumption. Furthermore, tests on the TMA of Zurich show that our approach can be applied effectively in a TMA in the presence of several obstacles, such as the mountains surrounding the Zurich airport.
Cette thèse propose une méthodologie d'optimisation des routes de départ et d'arrivée dans une zone terminale autour d'un aéroport. La conception de ces routes prend en compte la configuration et l'environnement autour de l'aéroport, et les différentes contraintes sous-jacentes, notamment l'évitement des obstacles et la séparation des routes. Nous proposons une formulation mathématique conduisant à un problème d'optimisation combinatoire. Les obstacles sont modélisés par des cylindres, et une route est modélisée en 3D par deux éléments: une courbe dans le plan horizontal, formée par une succession d'arcs de cercles et de segments, et un cône associé dans le plan vertical, contenant tous les profils de montée (ou de descente) des vols sur cette route. Pour la résolution du problème, nous procédons en deux étapes. Nous considérons dans un premier temps la conception d'une seule route de longueur minimale évitant les obstacles, en utilisant une méthode de Branch and Bound (B&B). Les stratégies de branchement sont liées aux manières d'éviter des obstacles (contournement dans le sens horaire ou anti-horaire, ou imposition d'un palier sous un obstacle). Dans un deuxième temps, nous nous intéressons à la conception de plusieurs routes par deux approches différentes. Dans la première approche, nous construisons les routes séquentiellement suivant un ordre fixé à l'avance. Chaque route est initialement construite à l'aide de la méthode de B&B, définie précédemment. Ensuite, les zones de conflit (zones où les routes ne sont pas séparées) sont enveloppées par des obstacles fictifs cylindriques, qui sont évités à nouveau à l'aide de B&B. Dans la deuxième approche, une méthode de recuit simulé est utilisée pour construire les routes simultanément. Des obstacles fictifs cylindriques sont aussi introduits, et évités suivant des stratégies sélectionnées aléatoirement dans la méthode de recuit simulé. Les approches proposées sont validées sur un ensemble de problèmes tests générés artificiellement et sur des problèmes correspondants à des zones terminales existantes (Paris Roissy et Zurich).
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