Une méthode de Branch and Bound par Intervalles appliquée à la résolution en vitesse de conflits aériens

National audienceDeux avions en croisière à la même altitude séparés de moins de 5 miles nautiques sont dits en conflit. Le rôle du contrôleur aérien est d'éviter les situations de conflits en anticipant des manoeuvres de séparation (changement de cap ou de niveau de vol de l'un des deux avions). En modifiant légèrement les vitesses des avions, on peut résoudre les conflits aériens en amont, et ce à l'insu du contrôleur qui n'est pas perturbé par ce prétraitement. Le projet ERASMUS [BDG09] qui a introduit ce concept se base actuellement sur un algorithme évolutionnaire développé dans les années 90 sur le simulateur CATS [GDA01]. Le problème de résolution de conflits est un problème très combinatoire. La littérature ne propose que deux approches efficaces pour résoudre de façon centralisée des problèmes de grande taille (plus d'une vingtaine d'avions). L'approche de [PFB02] utilise la programmation linéaire mixte, mais requiert des hypothèses fortes sur les trajectoires (vitesses constantes, manoeuvres exécutées en même temps). L'approche par algorithme évolutionnaire [DA98] est plus ancienne et permet de prendre en compte des trajectoires issues d?un simulateur de trafic. Ce résumé a pour but de présenter un algorithme de Branch and Bound par Intervalle, tel que décrit par exemple par [Han92], adapté à un problème de résolution de conflits en vitesse. Un problème "jouet" est utilisé pour tester l'algorithme. n avions sont disposés sur un cercle et se dirigent vers le centre du cercle

Un algorithme de colonie de fourmis pour résoudre des conflits aériens

National audienceLe problème de résolution de conflits aériens en croisière est un problème très combinatoire impossible à résoudre avec des algorithmes d'optimisation classiques dans un contexte réaliste : d'une part l'évaluation d'une solution ne peut se faire que par une simulation prenant en compte des modèles de prévision de trajectoires complexes ; d'autre part, les variables en jeu sont en général discrètes et leur nombre peut être très élevé

Genetic algorithms for Air Traffic Control systems

International audienceThe Air Traffic Control system of a country manages all the aircrafts that fly in its airspace, designs control sectors, manages the flows between the different airports and beacons, ensures separation between aircraft during their flight, take off and landing. Thus, it operates at different levels, each one of them designed to provide control, ensure safety, and limit the traffic passed to the following level. In this paper, we show how Genetic Algorithms can improve some of the tasks manually done by the ATC system. After a brief description of GAs, some of the improvements used (simulated annealing, sharing), we study three applications of GAs to ATC. We first show an application of GAs to en-route conflict resolution. Then we give an example on GAs used to optimize air space sectoring. The last part gives an application of GAs to traffic assignment

Genetic algorithms for optimal plane conflict resolution in air traffic

International audienceAt the dawn of civil aviation, pilots resolved conflicts themselves because they always flew in good weather conditions with low speed aircrafts. Nowadays, pilots must be helped by an air traffic controller on the ground who has a global view of the current traffic distribution in the airspace and can give indications to the pilots to avoid collisions. Solutions to conflicts are empirical, controllers are trained to react to certain types of conflicts and are limited by a workload. It is clear that if the ATC is overloaded, the sky is not. Conflict resolution is a trajectory optimization problem under constraints the complexity of which is so important that it has not been solved yet. Many attempts have been made to solve this problem with classical methods, such as gradient methods, reactive technics, expert systems, but most of them failed. In this paper, we show how genetic algorithms can be used to solve en-route aircrafts conflict automatically to increase Air Traffic Control capacity in high density areas. Our main purpose is to find out the global optimum and not only a suitable solution, in a real time situation, with conflict free trajectories that respect both plane and pilot performances

Neural Nets trained by genetic algorithms for collision avoidance

As air traffic keeps increasing, many research programs focus on collision avoidance techniques. For short or medium term avoidance, new headings have to be computed almost on the spot, and feed forward neural nets are susceptible to find solutions in a much shorter amount of time than classical avoidance algorithms (A_, stochastic optimization, etc.) In this article, we show that a neural network can be built with unsupervised learning to compute nearly optimal trajectories to solve two aircraft conflicts with the highest reliability, while computing headings in a few milliseconds

Preventing premature convergence and proving the optimality in evolutionary algorithms

http://ea2013.inria.fr//proceedings.pdfInternational audienceEvolutionary Algorithms (EA) usually carry out an efficient exploration of the search-space, but get often trapped in local minima and do not prove the optimality of the solution. Interval-based techniques, on the other hand, yield a numerical proof of optimality of the solution. However, they may fail to converge within a reasonable time due to their inability to quickly compute a good approximation of the global minimum and their exponential complexity. The contribution of this paper is a hybrid algorithm called Charibde in which a particular EA, Differential Evolution, cooperates with a Branch and Bound algorithm endowed with interval propagation techniques. It prevents premature convergence toward local optima and outperforms both deterministic and stochastic existing approaches. We demonstrate its efficiency on a benchmark of highly multimodal problems, for which we provide previously unknown global minima and certification of optimality

Finding and proving the optimum : cooperative stochastic and deterministic search

In this article, we introduce a global cooperative approach between an Interval Branch and Bound Algorithm and an Evolutionary Algorithm, that takes advantage of both methods to optimize a function for which an inclusion function can be expressed. The Branch and Bound algorithm deletes whole blocks of the search space whereas the Evolutionary Algorithm looks for the optimum in the remaining space and sends to the IBBA the best evaluation found in order to improve its Bound. The two algorithms run independently and update common information through shared memory. The cooperative algorithm prevents premature and local convergence of the evolutionary algorithm, while speeding up the convergence of the branch and bound algorithm. Moreover, the result found is the proved global optimum. In part 1, a short background is introduced. Part 2.1 describes the basic Interval Branch and Bound Algorithm and part 2.2 the Evolutionary Algorithm. Part 3 introduces the cooperative algorithm and part 4 gives the results of the algorithms on benchmark functions. The last part concludes and gives suggestions of avenues of further research

Certified Global Minima for a Benchmark of Difficult Optimization Problems

PreprintWe provide the global optimization community with new optimality proofs for 6 deceptive benchmark functions (5 bound-constrained functions and one nonlinearly constrained problem). These highly multimodal nonlinear test problems are among the most challenging benchmark functions for global optimization solvers; some have not been solved even with approximate methods. The global optima that we report have been numerically certified using Charibde (Vanaret et al., 2013), a hybrid algorithm that combines an Evolutionary Algorithm and interval-based methods. While metaheuristics generally solve large problems and provide sufficiently good solutions with limited computation capacity, exact methods are deemed unsuitable for difficult multimodal optimization problems. The achievement of new optimality results by Charibde demonstrates that reconciling stochastic algorithms and numerical analysis methods is a step forward into handling problems that were up to now considered unsolvable. We also provide a comparison with state-of-the-art solvers based on mathematical programming methods and population based metaheuristics, and show that Charibde, in addition to being reliable, is highly competitive with the best solvers on the given test functions

Une preuve numérique d'optimalité pour le cluster de Lennard-Jones à cinq atomes

National audienceLe potentiel de Lennard-Jones est un modèle relativement réaliste décrivant les interactions (répulsion à courte distance et attraction à grande distance) entre deux atomes sphériques au sein d’un gaz rare