A space-discretized mixed-integer linear model for air-conflict resolution with speed and heading maneuvers

International audienceAir-conflict resolution is a bottleneck of air traffic management that will soon require powerful decision-aid systems to avoid the proliferation of delays. Since reactivity is critical for this application, we develop a mixed-integer linear model based on space discretization so that complex situations can be solved in near real-time. The discretization allows us to model the problem with finite and potentially small sets of variables and constraints by focusing on important points of the planned trajectories, including the points where trajectories intersect. A major goal of this work is to use space discretization while allowing velocity and heading maneuvers. Realistic trajectories are also ensured by considering speed vectors that are continuous with respect to time, and limits on the velocity, acceleration, and yaw rate. A classical indicator of economic efficiency is then optimized by minimizing a weighted sum of fuel consumption and delay. The experimental tests confirm that the model can solve complex situations within a few seconds without incurring more than a few kilograms of extra fuel consumption per aircraft

Optimization for Decision Making II

In the current context of the electronic governance of society, both administrations and citizens are demanding the greater participation of all the actors involved in the decision-making process relative to the governance of society. This book presents collective works published in the recent Special Issue (SI) entitled “Optimization for Decision Making II”. These works give an appropriate response to the new challenges raised, the decision-making process can be done by applying different methods and tools, as well as using different objectives. In real-life problems, the formulation of decision-making problems and the application of optimization techniques to support decisions are particularly complex and a wide range of optimization techniques and methodologies are used to minimize risks, improve quality in making decisions or, in general, to solve problems. In addition, a sensitivity or robustness analysis should be done to validate/analyze the influence of uncertainty regarding decision-making. This book brings together a collection of inter-/multi-disciplinary works applied to the optimization of decision making in a coherent manner

Multiobjective simulated annealing for collision avoidance in ATM accounting for three admissible maneuvers

Technological advances are required to accommodate air traffic control systems for the future growth of air traffic. Particularly, detection and resolution of conflicts between aircrafts is a problem that has attracted much attention in the last decade becoming vital to improve the safety standards in free flight unstructured environments. We propose using the archive simulated annealing- based multiobjective optimization algorithm to deal with such a problem, accounting for three admissible maneuvers (velocity, turn, and altitude changes) in a multiobjective context. The minimization of the maneuver number and magnitude, time delays, or deviations in the leaving points are considered for analysis. The optimal values for the algorithm parameter set are identified in the more complex instance in which all aircrafts have conflicts between each other accounting for 5, 10, and 20 aircrafts. Moreover, the performance of the proposed approach is analyzed by means of a comparison with the Pareto front, computed using brute force for 5 aircrafts and the algorithm is also illustrated with a random instance with 20 aircraft

Applied Metaheuristic Computing

For decades, Applied Metaheuristic Computing (AMC) has been a prevailing optimization technique for tackling perplexing engineering and business problems, such as scheduling, routing, ordering, bin packing, assignment, facility layout planning, among others. This is partly because the classic exact methods are constrained with prior assumptions, and partly due to the heuristics being problem-dependent and lacking generalization. AMC, on the contrary, guides the course of low-level heuristics to search beyond the local optimality, which impairs the capability of traditional computation methods. This topic series has collected quality papers proposing cutting-edge methodology and innovative applications which drive the advances of AMC

Dispatching and Rescheduling Tasks and Their Interactions with Travel Demand and the Energy Domain: Models and Algorithms

Abstract The paper aims to provide an overview of the key factors to consider when performing reliable modelling of rail services. Given our underlying belief that to build a robust simulation environment a rail service cannot be considered an isolated system, also the connected systems, which influence and, in turn, are influenced by such services, must be properly modelled. For this purpose, an extensive overview of the rail simulation and optimisation models proposed in the literature is first provided. Rail simulation models are classified according to the level of detail implemented (microscopic, mesoscopic and macroscopic), the variables involved (deterministic and stochastic) and the processing techniques adopted (synchronous and asynchronous). By contrast, within rail optimisation models, both planning (timetabling) and management (rescheduling) phases are discussed. The main issues concerning the interaction of rail services with travel demand flows and the energy domain are also described. Finally, in an attempt to provide a comprehensive framework an overview of the main metaheuristic resolution techniques used in the planning and management phases is shown

Modèles déterministes et stochastiques pour la résolution de conflits entre aéronefs

RÉSUMÉ : Cette thèse s’inscrit dans le domaine de la programmation mathématique appliquée au problème de détection et de résolution de conflits entre aéronefs. Un conflit est une perte de séparation entre deux ou plusieurs aéronefs qui se retrouvent trop proches selon des normes de sécurité prédéfinies. Étant donnée une configuration initiale d’un ensemble d’aéronefs (position, vitesse, accélération), le problème de détection et de résolution de conflits entre aéronefs consiste à trouver une nouvelle configuration sans conflits futurs et minimisant une fonction de coût choisie par l’utilisateur (critère économique, critère sécuritaire, etc.). Dans le système de gestion du trafic aérien actuel, cette tâche est gérée par un contrôleur aérien visualisant le trafic sur un moniteur. Quand le contrôle anticipe un conflit, il transmet des manœuvres d’évitement aux pilotes des aéronefs concernés. Les pilotes appliquent ces manoeuvres avant de rejoindre leur trajectoire prévue par leur plan de vol. Les enjeux de l’optimisation du maintien de séparation entre aéronefs sont multiples. En particulier, le développement de modèles d’aide à la décision pour le contrôle permettrait l’augmentation de la capacité des secteurs aériens. Ainsi, plus d’aéronefs pourraient circuler en même temps, et ce le long de leur trajectoire optimale, tout en diminuant les retards. De plus, au-delà de la complexité du trafic, les imprécisions relatives aux données météorologiques et à l’état des aéronefs, ainsi que les délais de communication, mettent en avant la nécessité de robustesse dans la résolution du problème. Dans cette optique, la communauté de recherche opérationnelle s’est attaquée durant les deux dernières décennies à des variantes du problème de plus en plus complexes permettant de prendre en compte des contraintes opérationnelles difficiles à traiter. Cette thèse s’insère dans cette tendance. Dans un premier temps, cette thèse présente une étude économique destinée à valider le besoin opérationnel d’outils automatisés d’aide à la décision pour le contrôleur aérien. Plus particulièrement, les interactions entre les décisions tactiques faites lors de l’affectation des créneaux de décollage et les décisions opérationnelles faites lors de la résolution de conflits sont étudiées dans un contexte de trafic augmenté. Pour cela, un simulateur de trafic permettant de travailler avec différents paradigmes d’allocations de créneaux de décollage, de capacité de secteurs, d’augmentation de trafic est utilisé. À partir de données de trafic français datant de 2012, une semaine de trafic standard est générée pour différentes années jusqu’à un horizon allant à 2035. L’étude montre alors que les coûts des retards dus à l’allocation de créneaux de décollage augmentent exponentiellement avec l’augmentation du trafic si la capacité du réseau n’est pas augmentée, tandis que l’augmentation des coûts de résolution de conflits augmente de façon beaucoup plus acceptable avec un réseau de plus grande capacité. Cependant, l’augmentation de la capacité du réseau entraîne une charge de travail ingérable pour un contrôleur avec les outils actuellement disponibles. L’étude propose ensuite un compromis entre une forte augmentation des coûts de retards et une forte charge de travail, en contrôlant la hausse des coûts des retards en augmentant les capacités des secteurs. La valeur ajoutée de cette étude est que nous sommes désormais capables de quantifier les objectifs de recherche en optimisation du trafic aérien, tout en donnant une légitimité aux travaux déjà existants. Dans un second temps, cette thèse présente un modèle mathématique de détection et de résolution de conflits dans un cadre déterministe. Le design de la méthode repose sur la volonté d’obtenir un modèle robuste. En d’autres termes, le formalisme mathématique doit demeurer valable, et ce quelles que soient les hypothèses considérées. Pour cela, les aspects relatifs à la modélisation de la dynamique des avions, des manoeuvres ainsi que la fonction de coût sont complètement séparés du modèle mathématique de résolution. Formellement, le problème est modélisé comme une recherche de clique de cardinalité maximale et de poids minimum dans un graphe. Les sommets du graphe correspondent à un ensemble de manoeuvres possibles pour les aéronefs, et les arêtes lient des manoeuvres sans conflit pour des aéronefs différents. Afin de garder un graphe compact, nous modélisons les coûts de façon originale : en effet, ces coûts dépendent des sommets appartenant à la clique et ne sont ainsi plus connus a priori. Ce choix de modélisation en fait une nouvelle variante d’un problème de recherche de clique de cardinalité maximale de poids minimum. Nous formulons ensuite le problème comme un programme linéaire à variables mixtes. Deux méthodes de décomposition sont également développées. La première vise à utiliser l’influence du nombre de manoeuvres par aéronef sur le temps d’exécution afin de trouver un compromis entre efficacité et temps de résolution, alors que la seconde vise à exploiter les caractéristiques géométriques des instances. Des instances ayant jusqu’à 250 avions répartis sur 20 niveaux sont résolues en moins de 10 secondes de calcul. La dernière partie de cette thèse traite la prise en compte d’incertitudes lors de la résolution de conflits. Plus particulièrement, nous considérons les incertitudes dues aux erreurs de prévisions météorologiques sur le vent, ainsi que les erreurs de mesure de la vitesse venant de la connaissance incomplète des paramètres physiques des avions. Nous introduisons également un nouveau type d’incertitude : le délai dû aux communications entre le contrôleur et les pilotes. Ces perturbations induisent une erreur longitudinale sur la trajectoire des avions que nous quantifions, afin d’établir une formule analytique de la probabilité de conflit entre chaque paire d’avions. Nous utilisons ensuite cette formule pour modifier la définition des arêtes du graphe présenté dans la seconde partie de la thèse. Nous abordons ensuite le problème de résolution de conflits sous un angle bi-objectif. Pour ce faire, nous considérons un critère économique correspondant à la consommation de carburant pour exécuter les manoeuvres, ainsi qu’un critère de sécurité décrit par l’espérance du nombre de conflits. Nous présentons ensuite une méthode itérative permettant de générer un ensemble de solutions approximant le front de Pareto du problème. Cette approche est innovante car elle nous permet d’avoir une approche bi-objectif du problème de résolution de conflits, ce qui correspond plus à la nature intrinsèque du problème, et elle permet de fournir au contrôleur un ensemble de solutions. Ce dernier point est le plus pertinent car la notion d’optimalité est discutable en résolution de conflits à cause de l’existence de plusieurs “bonnes solutions” proches de la solution optimale, et il peut être intéressant de laisser au contrôleur des options dans sa prise de décision. En moyenne, 6 solutions sont générées en moins de 3 minutes pour des instances ayant jusqu’à 35 avions.----------ABSTRACT : This thesis is related to the field of mathematical programming applied to the conflict detection and resolution problem between aircraft. A conflict happens when two or more aircraft are too close to each other regarding pre-defined separation distances. Given the initial configuration (position, speed, acceleration) of a set of aircraft, the conflict detection and resolution problem consists in finding a new conflict-free configuration that minimizes a cost function chosen by the user (economical criterion, safety criterion, etc.). In the current air traffic management system, this task is managed by an air traffic controller who monitors traffic on a screen. When he/she anticipates a conflict, he/she communicates avoidance maneuvers to the pilots of the corresponding aircraft. The pilots execute these maneuvers before recovering the trajectory described on their flight plan. The stakes behind the optimization of separation between aircraft are multiple. In particular, the development of automated decision tools for air traffic control would allow the increase in airspace capacity. As a consequence, more aircraft could fly simultaneously while following their optimal trajectory and reducing potential delays. Besides, in addition to traffic complexity, the imprecisions related to weather forecasts, to the aircraft physical parameters and the potential communication delays highlight the need for robustness in the problem resolution. To this end, in the last decades the research community has tackled more complex problems that consider hard-to-solve operational constraints. This thesis follows this trend. First, this thesis presents an economical study aiming at the validation of an operational need for the development of automated decision tools for the air traffic controller. More specifically, we study the interactions between strategic decisions for take-off slot allocation and the tactical decisions of conflict resolution in a context of increasing traffic. To this end, we use a complete traffic simulator allowing us to consider different paradigms of take-off slot allocation, sector capacities and traffic increase. Using historical French traffic data from 2012, a typical week of traffic is generated to represent traffic for different years until 2035. The study highlights on the one hand that the costs of delays due to the take-off slot allocation increase exponentially with the traffic increase if the network capacity is not increased. On the other hand, the costs of conflict resolution increase in an acceptable fashion in a network of larger capacity but the workload becomes unmanageable for an air traffic controller using the currently available tools. The study then proposes a compromise between a huge increase of delay costs and a heavy workload by controlling the growth of delay costs by increasing sector capacity. This is of great value, since we are now capable of quantifying research objectives for air traffic optimization while legitimizing the research already existing. Second, this thesis presents a deterministic mathematical model to solve the conflict detection and resolution problem between aircraft. The design of the presented method was driven by robustness. In other words, the proposed mathematical framework must remain valid, whatever the hypotheses considered. To this end, the aspects related to the modeling of aircraft dynamics, maneuvers and the cost function are fully separated from the mathematical resolution process. Formally, the problem is modeled as a search for a clique of maximal cardinality and minimum weight in a graph. The vertices of the graph correspond to possible aircraft maneuvers and edges connect conflict-free maneuvers of different aircraft. To keep the graph compact, we model the vertex costs in an innovative fashion: indeed, these costs depend on the vertices in the clique, and thus cannot be known a priori. This choice of modeling corresponds to a new variant of the minimum-weight maximum-cardinality clique problem. We formulate this problem as a mixed integer linear program. We also develop two decomposition methods. The first one aims at taking advantage of the effect of the number of maneuvers per aircraft on the solution time to find a trade-off between solution efficiency and time, while the second one exploits the geometrical characteristics of the set of aircraft. Instances with up to 250 aircraft divided between 20 flight levels are solved within 10 seconds. The last part of this thesis takes into account uncertainties in the conflict resolution process. More specifically, we consider uncertainties due to errors in weather forecasts, in the aircraft speed measure resulting from the incomplete knowledge of the physical paremeters of the aircraft. We introduce a new type of uncertainty: the delay in the execution of maneuvers due to communications. Those perturbations induce an along-track error on the aircraft trajectory that we can quantify in order to derive an analytical formula of the probability of conflict between every pair of aircraft. We use this formula to modify the definition of edges in the graph presented in the previous section of the thesis. We then tackle the conflict resolution problem as a bi-objective problem. To this end, we consider an economical criterion corresponding to the fuel consumption induced by the execution of maneuvers, along with a safety criterion represented by the expected number of conflicts. We also present an iterative method generating a set of solutions approximating the Pareto front of the problem. This method is innovative, since it uses a bi-objective approach of conflict resolution, which fits more with the inner nature of the problem, while providing the controller with a set of solutions. This last feature is the most relevant because the notion of optimality in conflict resolution is questionable, since there exist several ”good solutions” close to the optimal one, and it could be interesting to give the controller some options in his/her decision making. On average, 6 solutions are generated within 3 minutes for instances with up to 35 aircraft

Application of machine learning and artificial intelligence techniques to improve autonomy in maritime surveillance radar systems

Executive Summary. Current maritime radar surveillance missions are typically carried out using an airborne platform with one or more operators on board. The workload of human operators is a bottleneck in surveillance performance as they can only perform on a single platform discontinuously. Additionally, with progress being made towards the use of remotely operated UAVs for radar surveillance missions, an increase in radar operational autonomy is required to maximise the UAV’s surveillance potential. Consequently, the focus of this research is to improve the autonomy of current maritime radar surveillance missions. By reducing the workload of the current radar operator, then surveillance missions can be performed for longer. This research breaks the autonomy of the radar surveillance mission into two aspects: the platform operator autonomy and the radar operator autonomy. However, the implemented autonomous methods must “complement rather than compete with one another". In order to implement algorithms for the platform operator autonomy and radar operator autonomy, a maritime radar surveillance simulation and user interface is required. Consequently, this work outlines a real-time maritime surveillance radar simulation and graphical user interface which can be used to carry out missions in the same manner as an operator would with a real system. For the platform operator autonomy aspect, there is a trade-off between maximising information obtained from the surveillance search area and minimising fuel consumption. The research presented here provides an approach for the optimisation of a UAV’s trajectory for maritime radar wide area persistent surveillance to simultaneously minimise fuel consumption, maximise mean probability of detection, and minimise mean revisit time. Quintic polynomials are used to generate UAV trajectories due to their ability to provide complete and complex solutions while requiring few inputs. A wide area search radar model is used within this article in conjunction with a discretised grid in order to determine the search area’s mean probability of detection and mean revisit time. The trajectory generation method is then used in conjunction with a multi-objective particle swarm optimisation algorithm to obtain a global optimum in terms of path, airspeed (and thus time), and altitude. The performance of the approach is then tested over two common maritime surveillance scenarios and compared to an industry recommended baseline. In terms of the radar operator autonomy, imitation learning, as opposed to other forms of machine learning, are advantageous as they act in the same manner as the operator, thus reducing the deviation from the current operational standard and allowing for easier system qualification and human operator interaction. The developed radar simulation and interface is used to obtain operator decision data from a human operator. The operator data is then used with two imitation learning methods, namely Bayesian networks and inverse reinforcement learning, with the methods used in place of the operator with their performance compared and their suitability discussed

Proceedings of the XIII Global Optimization Workshop: GOW'16

[Excerpt] Preface: Past Global Optimization Workshop shave been held in Sopron (1985 and 1990), Szeged (WGO, 1995), Florence (GO’99, 1999), Hanmer Springs (Let’s GO, 2001), Santorini (Frontiers in GO, 2003), San José (Go’05, 2005), Mykonos (AGO’07, 2007), Skukuza (SAGO’08, 2008), Toulouse (TOGO’10, 2010), Natal (NAGO’12, 2012) and Málaga (MAGO’14, 2014) with the aim of stimulating discussion between senior and junior researchers on the topic of Global Optimization. In 2016, the XIII Global Optimization Workshop (GOW’16) takes place in Braga and is organized by three researchers from the University of Minho. Two of them belong to the Systems Engineering and Operational Research Group from the Algoritmi Research Centre and the other to the Statistics, Applied Probability and Operational Research Group from the Centre of Mathematics. The event received more than 50 submissions from 15 countries from Europe, South America and North America. We want to express our gratitude to the invited speaker Panos Pardalos for accepting the invitation and sharing his expertise, helping us to meet the workshop objectives. GOW’16 would not have been possible without the valuable contribution from the authors and the International Scientific Committee members. We thank you all. This proceedings book intends to present an overview of the topics that will be addressed in the workshop with the goal of contributing to interesting and fruitful discussions between the authors and participants. After the event, high quality papers can be submitted to a special issue of the Journal of Global Optimization dedicated to the workshop. [...

From metaheuristics to learnheuristics: Applications to logistics, finance, and computing

Un gran nombre de processos de presa de decisions en sectors estratègics com el transport i la producció representen problemes NP-difícils. Sovint, aquests processos es caracteritzen per alts nivells d'incertesa i dinamisme. Les metaheurístiques són mètodes populars per a resoldre problemes d'optimització difícils en temps de càlcul raonables. No obstant això, sovint assumeixen que els inputs, les funcions objectiu, i les restriccions són deterministes i conegudes. Aquests constitueixen supòsits forts que obliguen a treballar amb problemes simplificats. Com a conseqüència, les solucions poden conduir a resultats pobres. Les simheurístiques integren la simulació a les metaheurístiques per resoldre problemes estocàstics d'una manera natural. Anàlogament, les learnheurístiques combinen l'estadística amb les metaheurístiques per fer front a problemes en entorns dinàmics, en què els inputs poden dependre de l'estructura de la solució. En aquest context, les principals contribucions d'aquesta tesi són: el disseny de les learnheurístiques, una classificació dels treballs que combinen l'estadística / l'aprenentatge automàtic i les metaheurístiques, i diverses aplicacions en transport, producció, finances i computació.Un gran número de procesos de toma de decisiones en sectores estratégicos como el transporte y la producción representan problemas NP-difíciles. Frecuentemente, estos problemas se caracterizan por altos niveles de incertidumbre y dinamismo. Las metaheurísticas son métodos populares para resolver problemas difíciles de optimización de manera rápida. Sin embargo, suelen asumir que los inputs, las funciones objetivo y las restricciones son deterministas y se conocen de antemano. Estas fuertes suposiciones conducen a trabajar con problemas simplificados. Como consecuencia, las soluciones obtenidas pueden tener un pobre rendimiento. Las simheurísticas integran simulación en metaheurísticas para resolver problemas estocásticos de una manera natural. De manera similar, las learnheurísticas combinan aprendizaje estadístico y metaheurísticas para abordar problemas en entornos dinámicos, donde los inputs pueden depender de la estructura de la solución. En este contexto, las principales aportaciones de esta tesis son: el diseño de las learnheurísticas, una clasificación de trabajos que combinan estadística / aprendizaje automático y metaheurísticas, y varias aplicaciones en transporte, producción, finanzas y computación.A large number of decision-making processes in strategic sectors such as transport and production involve NP-hard problems, which are frequently characterized by high levels of uncertainty and dynamism. Metaheuristics have become the predominant method for solving challenging optimization problems in reasonable computing times. However, they frequently assume that inputs, objective functions and constraints are deterministic and known in advance. These strong assumptions lead to work on oversimplified problems, and the solutions may demonstrate poor performance when implemented. Simheuristics, in turn, integrate simulation into metaheuristics as a way to naturally solve stochastic problems, and, in a similar fashion, learnheuristics combine statistical learning and metaheuristics to tackle problems in dynamic environments, where inputs may depend on the structure of the solution. The main contributions of this thesis include (i) a design for learnheuristics; (ii) a classification of works that hybridize statistical and machine learning and metaheuristics; and (iii) several applications for the fields of transport, production, finance and computing