Optimisation du trafic au sol sur les grands aéroports

Une partie de plus en plus significative des retards aériens est imputable à la circulation des avions au sol sur les grands aéroports. Afin d'étudier les possibilités d'amélioration du trafic au roulage, un outil de simulation est développé et appliqué à Roissy Charles De Gaulle et Orly. La gestion du trafic est modélisée sous forme d'un problème de minimisation sous contraintes, sur lequel plusieurs méthodes d'optimisation sont comparées : une méthode déterministe, une méthode stochastique par algorithmes génétiques et une méthode hybride. L'outil de simulation résultant permet de mesurer l'influence de différents facteurs, comme l'horizon de prédiction, les incertitudes sur les vitesses de roulage ou encore l'application de sens uniques. La méthode hybride se révèle la plus efficace dans tous les scénarii envisagés et possède l'avantage d'être facilement adaptable à de nouveaux objectifs, comme le respect des créneaux de décollage imposés par la régulation européenne du trafic. ABSTRACT : Air traffic growth causes more and more significant congestion and ground delays on major airports. In order to study how this phenomenon can be improved, a ground traffic simulation tool is proposed and applied to Roissy Charles De Gaulle and Orly airports. Various optimisation methods are developed to solve the problem linked with each ground traffic situation : a deterministic method, a stochastic method using a genetic algorithm and a hybrid method. The resulting tool allows to quantify the effect of several factors, as the size of the time window for traffic prediction, the speed uncertainties or the definition of some specific oneway taxiways. The hybrid method appears to be the most efficient in each situation and has the great advantage to be easily refined to handle correctly some new goals, like the application of the takeoff slots fixed by the European traffic flow management unit

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

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

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

La première preuve 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 entre deux atomes au sein d'un gaz rare. Déterminer la configuration la plus stable d'un cluster à N atomes revient à trouver les positions relatives des atomes qui minimisent l'énergie potentielle globale ; ce potentiel joue un rôle important dans le cadre des agrégats atomiques et les nanotechnologies. Le problème de cluster est NP-difficile et ouvert pour N > 4, et n'a jamais été résolu par des méthodes globales fiables. Nous proposons de résoudre le problème de cluster à cinq atomes de manière optimale avec des méthodes d'intervalles qui garantissent un encadrement du minimum global, même en présence d'arrondis. Notre modèle spatial permet d'éliminer certaines symétries du problème et de calculer des minorants plus précis dans le branch and bound par intervalles. Nous montrons que la meilleure solution connue du problème à cinq atomes est optimale, fournissons la configuration spatiale correspondante et comparons notre solveur fiable aux solveurs BARON et Couenne. Alors que notre solution est numériquement certifiée avec une précision de 10 −9 , les solutions de BARON et Couenne sont entachées d'erreurs numériques

A fast and reliable hybrid algorithm for numerical nonlinear global optimization

PreprintHighly nonlinear and ill-conditioned numerical optimization problems take their toll on the convergence of existing resolution methods. Stochastic methods such as Evolutionary Algorithms carry out an efficient exploration of the searchspace at low cost, but get often trapped in local minima and do not prove the optimality of the solution. Deterministic methods such as Interval Branch and Bound algorithms guarantee bounds on the solution, yet struggle to converge within a reasonable time on high-dimensional problems. The contribution of this paper is a hybrid algorithm in which a Differential Evolution algorithm and an Interval Branch and Contract algorithm cooperate. Bounds and solutions are exchanged through shared memory to accelerate the proof of optimality. It prevents premature convergence toward local optima and outperforms both deterministic and stochastic existing approaches. We demonstrate the efficiency of this algorithm on two currently unsolved problems: first by presenting new certified optimal results for the Michalewicz function for up to 75 dimensions and then by proving that the putative minimum of Lennard-Jones clusters of 5 atoms is optimal

A reliable hybrid solver for nonconvex optimization

International audienceNonconvex and highly multimodal optimization problems represent a challenge both for stochastic and deterministic global optimization methods. The former (metaheuristics) usually achieve satisfactory solutions but cannot guarantee global optimality, while the latter (generally based on a spatial branch and bound scheme [1], an exhaustive and non-uniform partitioning method) may struggle to converge toward a global minimum within reasonable time. The partitioning process is exponential in the number of variables, which prevents the resolution of large instances. The performances of the solvers even dramatically deteriorate when using reliable techniques, namely techniques that cope with rounding errors.In this paper, we present a fully reliable hybrid algorithm named Charibde (Cooperative Hybrid Algorithm using Reliable Interval-Based methods and Dierential Evolution) [2] that reconciles stochastic and deterministic techniques. An Evolutionary Algorithm (EA) cooperates with intervalbased techniques to accelerate convergence toward the global minimum and prove the optimality of the solution with user-defined precision. Charibde may be used to solve continuous, nonconvex, constrained or bound-constrained problems involving factorable functions

Impact of ATCO Training and Expertise on Dynamic Spatial Abilities

Dynamic spatial ability is supposed to be involved in a critical process of air traffic controllers, namely conflict detection. The present paper aims at testing whether dynamic spatial ability improves with air traffic control training and/or experience. We designed a laboratory task to assess the performance in predicting if two moving disks would collide or not. We conducted a crosssectional study with four groups of participants : ATCO trainees at the beginning (N=129), middle (N=80) or end of training (N=66) and experienced ATCOs (N=14). Results suggested on one hand that air traffic control training leads to a decrease in the number of extremely high proportions of undetected collisions from the middle of the training. On the other hand, air traffic control operational experience leads to a decrease in the number of extremely high proportions of falsely detected collisions