A characterization of the solutions of steady Hamilton-Jacobi equations

In this note, we propose to revisit the approximate stationary Hamilton-Jacobi equations and analyse the corresponding solutions following certain properties of the hamiltonian. This enables us to give a characterization of the zero set of the limiting solution. We also remark that the analysis can be applied for evolution equations with a time periodic source term

Single-machine scheduling with periodic and flexible periodic maintenance to minimize maximum tardiness.

International audienceThis paper considers a single machine scheduling problem with several maintenances periods. Specially, two situations are investigated. In the first one, maintenance periods are periodically fixed : maintenance is required after a periodic time interval. In the second one, the maintenance is not fixed but the maximum continuous working time of the machine which is allowed is determined. The objective is to minimize the maximum tardiness. These problems are known to be strongly NP-hard. We propose some dominance properties and an efficient heuristic. Branch-and-bound algorithms, in which the heuristics, the lower bounds and the dominance properties are incorporated, are proposed and tested computationally

Optimization of Arrival and Departure Routes in Terminal Maneuvering Area

International audienceAirport is both the starting and ending point of air traffic. The sharp increase in air traffic flow causes directly traffic congestion in Terminal Maneuvering Area (TMA) which affects the normal operation of the flights. Optimizing departure and arrival procedures is therefore crucial to regulate air traffic flow. This research focuses on generating 3D Standard Instrument Departure routes and Standard Terminal Arrival Routes in TMA at a strategic level. We propose an optimization approach to generate 3D routes avoiding obstacles and assuring a minimum separation between routes. The method combines Fast Marching Method and Simulated Annealing

Spectral properties of general advection operators and weighted translation semigroups

We investigate the spectral properties of a class of weighted shift semigroups associated to abstract transport equations with a Lipschitz--continuous vector field with no--reentry boundary conditions. We illustrate our results with various examples taken from collisionless kinetic theory

Optimization-Based Design of Departure and Arrival Routes in Terminal Maneuvering Area

International audienceThe efficient design of departure and arrival routes in the airspace surrounding airports, called the Terminal Maneuvering Area (TMA), is crucial for increasing the capacity of such areas, and thus alleviating congestion around airports caused by worldwide air traffic growth. In this paper, an efficient method of designing departure and arrival routes in TMA is proposed, taking into account the configuration of the airport and nearby environment, as well as related operational constraints, such as obstacle avoidance and route separation. Each route is modeled in three dimensions (3D), and consists of two components: a curve in the horizontal plane and a cone in the vertical plane. A Branch and Bound (B&B)-based approach is developed, whose branching strategies are tailored to how the obstacles are avoided. Routes are generated sequentially, and each route is initially built in isolation. If the route is found to be in conflict with previously generated routes, it is perturbed locally around the conflict zones. Numerical tests, performed on artificially generated problems and the TMA of Paris Charles-de-Gaulle (CDG) airport, demonstrate that the proposed method is efficient and could be embedded in a decision-aid tool for procedure design

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

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

Optimisation des routes de départ et d’arrivée dans la TMA

National audienceLa forte augmentation du trafic aérien induit une congestion dans la zone proche des aéroports appelée TMA1. Les départs et les arrivées des aéroports se font suivant des routes dites SID 2 et STAR3. L’optimisation de ces routes est un moyen pour réguler le trafic et donc de réduire la congestion autour des aéroports. Dans ce travail nous étudions le problème de la conception de SID et STAR en prenant en compte la configuration et l’environnement autour des aéroports. Il existe beaucoup de travaux consacrés à la conception de trajectoires (voir [1]pour un survol), mais à notre connaissance peu de travaux sont dédiés à la conception de SID et STAR (e.g. [3]). Dans cette dernière, on doit tenir compte de contraintes opérationnelles (la séparation verticale et horizontale entre les routes, l’évitement d’obstacles, la courbure desroutes, la pente des routes tenant compte des taux de montée et de descente des aéronefs) et environnementales (des nuisances sonores, des zones urbaines)

Integrated Traffic Flow Based Optimization of Airport and Terminal Area

International audienceAs air traffic demand exceeds available capacity, severe congestion during peak periods occurring at airports and the surrounding terminal airspace leads to flight delays as well as potential safety issues. This paper addresses the optimization problem of integrated traffic management of airport and terminal airspace on macroscopic level. Instead of evaluating the flight conflicts as we did in our previous research, a congestion evaluation model is proposed to quantify the flights for traffic flows in the terminal airspace and the runways, meanwhile, the occupancy evaluations of taxiway network and terminals are conducted. An adapted heuristic optimization method simulated annealing is implemented to solve the problem. Optimization process is put forward based on the case studies of Paris Charles De-Gaulle airport with 2.5-hour data. The comparisons between initial traffic data and optimized solution are provided and the advantage of the proposed model is analyzed. In the aspect of time uncertainty, simulations based on the proposed model and the model of our previous work are conducted, the final results indicate that our model shows an advantage in uncertainty absorption over the previous work

Analyse spectrale de modèles neutroniques

This dissertation is mainly devoted to spectral analysis of various neutron transport models. It is composed of three complementary parts. Part 1 deals with spectral mapping theorems in unbounded geometries where, due to the lack of compactness, the classical arguments do not work. Using some functional analytic results on the critical spectrum of perturbed semigroups, we show under fairly general assumptions that the spectral mapping theorem holds. In Part 2 we provide a new approach, called resolvent approach, to study the stability of essential and critical spectra of perturbed $C_(0)$-semigroups on Hilbert spaces. We show how these results apply to neutron transport equations in both bounded or unbounded geometries. The third part deals with a partly elastic collision model introduced by E.W. Larsen and P.F. Zweifel. To display the large time behavior of the semigroup governing this model, we present its spectral theory. We analyze compactness properties related to the model, which enable us, in particular, to derive some stability results on the essential type. Then we examine the incidences of the positivity: irreducibility, strict monotonicity properties of the leading eigenvalue, reality of the peripheral spectrum.Cette thèse porte principalement sur l'étude spectrale de divers modèles neutroniques. Elle consiste en trois parties complémentaires. La première partie est consacrée aux problèmes d'applications spectrales dans les domaines non bornés, où faute de compacité les méthodes usuelles n'opèrent plus. A l'aide d'arguments d'analyse fonctionnelle sur le spectre critique des semigroupes perturbés nous cernons une large classe de paramètres liés à l'équation pour lesquels le théorème d'application spectrale a lieu. Dans la deuxième partie, nous apportons une nouvelle approche, dite résolvante, de la stabilité des spectres essentiel et critique des semigroupes perturbés dans les espaces de Hilbert. En neutronique, par le biais de cette approche, nous retrouvons des résultats classiques de stabilité de spectre essentiel dans les domaines bornés et nous améliorons certains résultats de la première partie dans les domaines non bornés. La troisième partie traite d'un modèle de collision partiellement élastique introduit par E.W. Larsen et P.F. Zweifel. Afin de dégager le comportement asymptotique en temps grands du semigroupe gouvernant ce modèle nous ferons sa théorie spectrale. Nous étudions les propriétés de compacité à la base de cette théorie, ce qui nous permettra notamment d'obtenir des résultats de stabilité du type essentiel. Nous examinons ensuite les incidences de la positivité : irréductibilité, propriétés de monotonie stricte de la valeur propre principale, réalité du spectre périphériqu