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This research addresses the concept of radio resource allocation for cellular communications systems operating in congested and contested environments with an emphasis on end-to-end quality of service (QoS). The radio resource allocation is cast under a proportional fairness formulation which translates to a convex optimization problem. Moreover, the resource allocation scheme considers subscription-based and traffic differentiation in order to meet the QoS requirements of the applications running on the user equipment in the system. The devised resource allocation scheme is realized through a centralized and a distributed architecture and solution algorithms for the aforementioned architectures is derived and implemented in the mobile devices and the base stations. The sensitivity of the resource allocation scheme to the temporal dynamics of the quantity of the users in the system is investigated. Furthermore, the sensitivity of the resource allocation scheme to the temporal dynamics in the application usage percentages is accounted for. In addition, a transmission overhead of the centralized and distributed architectures for the resource allocation schemes is performed. Furthermore, the resource allocation scheme is modified to account for a possible additive bandwidth done through spectrum sharing in congested and contested environments, in particular spectrally coexistent radar systems. The radar-spectrum additive portion is devised in a way to ensure fairness of the allocation, high bandwidth utilization, and interference avoidance. In order to justify the aforesaid modification, the interference from radar systems into the Long Term Evolution (LTE) as the predominant 4G technology is studies to confirm the possibility of the spectrum sharing. The preceding interference analysis contains a detailed simulation of radar systems, propagation path loss models, and a third generation partnership project compliant LTE system. The propagation models are Free Space Path Loss (FSPL) and Irregular Terrain Model (ITM). The LTE systems under consideration are macro cell, outdoor small cells, and indoor small cells. Furthermore, the resource allocation under channel consideration is formalized such that the resources are allocated under a congested environment and based on the quality of channel the users have in the network as well as the quality of service requirements of the applications running on the mobile devices. / Ph. D.

Thèse réalisée en cotutelle avec l'Université d'Avignon. / Les problèmes d’optimisation discrète sont pour beaucoup difficiles à résoudre, de par leur nature combinatoire. Citons par exemple les problèmes de programmation linéaire en nombres entiers. Une approche couramment employée pour les résoudre exactement est l’approche de Séparation et Évaluation Progressive. Une approche différente appelée « Resolution Search » a été proposée par Chvátal en 1997 pour résoudre exactement des problèmes d’optimisation à variables 0-1, mais elle reste mal connue et n’a été que peu appliquée depuis. Cette thèse tente de remédier à cela, avec un succès partiel. Une première contribution consiste en la généralisation de Resolution Search à tout problème d’optimisation discrète, tout en introduisant de nouveaux concepts et définitions. Ensuite, afin de confirmer l’intérêt de cette approche, nous avons essayé de l’appliquer en pratique pour résoudre efficacement des problèmes bien connus. Bien que notre recherche n’ait pas abouti sur ce point, elle nous a amené à de nouvelles méthodes pour résoudre exactement les problèmes d’affectation généralisée et de localisation simple. Après avoir présenté ces méthodes, la thèse conclut avec un bilan et des perspectives sur l’application pratique de Resolution Search. / The combinatorial nature of discrete optimization problems often makes them diffi- cult to solve. Consider for instance integer linear programming problems, which are commonly solved using a Branch-and-Bound approach. An alternative approach, Resolution Search, was proposed by Chvátal in 1997 for solving 0-1 optimization problems, but remains little known to this day and as such has seen few practical applications. This thesis attempts to remedy this state of affairs, with partial success. Its first contribution consists in the generalization of Resolution Search to any discrete optimization problem, while introducing new definitions and concepts. Next, we tried to validate this approach by attempting to solve well-known problems efficiently with it. Although our research did not succeed in this respect, it lead us to new methods for solving the generalized assignment and uncapacitated facility location problems. After presenting these methods, this thesis concludes with a summary of our attempts at practical application of Resolution Search, along with further perspectives on this matter.

This thesis consists of two parts: digital geometry and discrete optimization. In the first part we study the structure of digital straight line segments. We also study digital curves from a combinatorial point of view. In Paper I we study the straightness in the 8-connected plane and in the Khalimsky plane by considering vertical distances and unions of two segments. We show that we can investigate the straightness of Khalimsky arcs by using our knowledge from the 8-connected plane. In Paper II we determine the number of Khalimsky-continuous functions with 2, 3 and 4 points in their codomain. These enumerations yield examples of known sequences as well as new ones. We also study the asymptotic behavior of each of them. In Paper III we study the number of Khalimsky-continuous functions with codomain Z and N. This gives us examples of Schröder and Delannoy numbers. As a byproduct we get some relations between these numbers. In Paper IV we study the number of Khalimsky-continuous functions between two points in a rectangle. Using a generating function we get a recurrence formula yielding this numbers.   In the second part we study an analogue of discrete convexity, namely lateral convexity. In Paper V we define by means of difference operators the class of lateral convexity. The functions have plus infinity in their codomain. For the real-valued functions we need to check the difference operators for a smaller number of points. We study the relation between this class and integral convexity. In Paper VI we study the marginal function of real-valued functions in this class and its generalization. We show that for two points with a certain distance we have a Lipschitz property for the points where the infimum is attained. We show that if a function is in this class, the marginal function is also in the same class. / At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 4: Submitted. Paper 5: Manuscript. Paper 6: Manuscript.

Les problèmes d’optimisation discrète sont pour beaucoup difficiles à résoudre, de par leur nature combinatoire. Citons par exemple les problèmes de programmation linéaire en nombres entiers. Une approche couramment employée pour les résoudre exactement est l’approche de Séparation et Évaluation Progressive. Une approche différente appelée « Resolution Search » a été proposée par Chvátal en 1997 pour résoudre exactement des problèmes d’optimisation à variables 0-1, mais elle reste mal connue et n’a été que peu appliquée depuis. Cette thèse tente de remédier à cela, avec un succès partiel. Une première contribution consiste en la généralisation de Resolution Search à tout problème d’optimisation discrète, tout en introduisant de nouveaux concepts et définitions. Ensuite, afin de confirmer l’intérêt de cette approche, nous avons essayé de l’appliquer en pratique pour résoudre efficacement des problèmes bien connus. Bien que notre recherche n’ait pas abouti sur ce point, elle nous a amené à de nouvelles méthodes pour résoudre exactement les problèmes d’affectation généralisée et de localisation simple. Après avoir présenté ces méthodes, la thèse conclut avec un bilan et des perspectives sur l’application pratique de Resolution Search. / The combinatorial nature of discrete optimization problems often makes them diffi- cult to solve. Consider for instance integer linear programming problems, which are commonly solved using a Branch-and-Bound approach. An alternative approach, Resolution Search, was proposed by Chvátal in 1997 for solving 0-1 optimization problems, but remains little known to this day and as such has seen few practical applications. This thesis attempts to remedy this state of affairs, with partial success. Its first contribution consists in the generalization of Resolution Search to any discrete optimization problem, while introducing new definitions and concepts. Next, we tried to validate this approach by attempting to solve well-known problems efficiently with it. Although our research did not succeed in this respect, it lead us to new methods for solving the generalized assignment and uncapacitated facility location problems. After presenting these methods, this thesis concludes with a summary of our attempts at practical application of Resolution Search, along with further perspectives on this matter. / Thèse réalisée en cotutelle avec l'Université d'Avignon.

Les méthodes de recalage d’images, qui ont pour but l’alignement de deux ou plusieurs images dans un même système de coordonnées, sont parmi les algorithmes les plus anciens et les plus utilisés en vision par ordinateur. Les méthodes de recalage servent à établir des correspondances entre des images (prises à des moments différents, par différents senseurs ou avec différentes perspectives), lesquelles ne sont pas évidentes pour l’œil humain. Un type particulier d’algorithme de recalage, connu comme « les méthodes de recalage déformables à l’aide de modèles graphiques » est devenu de plus en plus populaire ces dernières années, grâce à sa robustesse, sa scalabilité, son efficacité et sa simplicité théorique. La gamme des problèmes auxquels ce type d’algorithme peut être adapté est particulièrement vaste. Dans ce travail de thèse, nous proposons plusieurs extensions à la théorie de recalage déformable à l’aide de modèles graphiques, en explorant de nouvelles applications et en développant des contributions méthodologiques originales.Notre première contribution est une extension du cadre du recalage à l’aide de graphes, en abordant le problème très complexe du recalage d’une tranche avec un volume. Le recalage d’une tranche avec un volume est le recalage 2D dans un volume 3D, comme par exemple le mapping d’une tranche tomographique dans un système de coordonnées 3D d’un volume en particulier. Nos avons proposé une formulation scalable, modulaire et flexible pour accommoder des termes d'ordre élevé et de rang bas, qui peut sélectionner le plan et estimer la déformation dans le plan de manière simultanée par une seule approche d'optimisation. Le cadre proposé est instancié en différentes variantes, basés sur différentes topologies du graph, définitions de l'espace des étiquettes et constructions de l'énergie. Le potentiel de notre méthode a été démontré sur des données réelles ainsi que des données simulées dans le cadre d’une résonance magnétique d’ultrason (où le cadre d’installation et les stratégies d’optimisation ont été considérés).Les deux autres contributions inclues dans ce travail de thèse, sont liées au problème de l’intégration de l’information sémantique dans la procédure de recalage (indépendamment de la dimensionnalité des images). Actuellement, la plupart des méthodes comprennent une seule fonction métrique pour expliquer la similarité entre l’image source et l’image cible. Nous soutenons que l'intégration des informations sémantiques pour guider la procédure de recalage pourra encore améliorer la précision des résultats, en particulier en présence d'étiquettes sémantiques faisant du recalage un problème spécifique adapté à chaque domaine.Nous considérons un premier scénario en proposant un classificateur pour inférer des cartes de probabilité pour les différentes structures anatomiques dans les images d'entrée. Notre méthode vise à recaler et segmenter un ensemble d'images d'entrée simultanément, en intégrant cette information dans la formulation de l'énergie. L'idée principale est d'utiliser ces cartes estimées des étiquettes sémantiques (fournie par un classificateur arbitraire) comme un substitut pour les données non-étiquettées, et les combiner avec le recalage déformable pour améliorer l'alignement ainsi que la segmentation.Notre dernière contribution vise également à intégrer l'information sémantique pour la procédure de recalage, mais dans un scénario différent. Dans ce cas, au lieu de supposer que nous avons des classificateurs arbitraires pré-entraînés à notre disposition, nous considérons un ensemble d’annotations précis (vérité terrain) pour une variété de structures anatomiques. Nous présentons une contribution méthodologique qui vise à l'apprentissage des critères correspondants au contexte spécifique comme une agrégation des mesures de similarité standard à partir des données annotées, en utilisant une adaptation de l’algorithme « Latent Structured Support Vector Machine ». / Image registration methods, which aim at aligning two or more images into one coordinate system, are among the oldest and most widely used algorithms in computer vision. Registration methods serve to establish correspondence relationships among images (captured at different times, from different sensors or from different viewpoints) which are not obvious for the human eye. A particular type of registration algorithm, known as graph-based deformable registration methods, has become popular during the last decade given its robustness, scalability, efficiency and theoretical simplicity. The range of problems to which it can be adapted is particularly broad. In this thesis, we propose several extensions to the graph-based deformable registration theory, by exploring new application scenarios and developing novel methodological contributions.Our first contribution is an extension of the graph-based deformable registration framework, dealing with the challenging slice-to-volume registration problem. Slice-to-volume registration aims at registering a 2D image within a 3D volume, i.e. we seek a mapping function which optimally maps a tomographic slice to the 3D coordinate space of a given volume. We introduce a scalable, modular and flexible formulation accommodating low-rank and high order terms, which simultaneously selects the plane and estimates the in-plane deformation through a single shot optimization approach. The proposed framework is instantiated into different variants based on different graph topology, label space definition and energy construction. Simulated and real-data in the context of ultrasound and magnetic resonance registration (where both framework instantiations as well as different optimization strategies are considered) demonstrate the potentials of our method.The other two contributions included in this thesis are related to how semantic information can be encompassed within the registration process (independently of the dimensionality of the images). Currently, most of the methods rely on a single metric function explaining the similarity between the source and target images. We argue that incorporating semantic information to guide the registration process will further improve the accuracy of the results, particularly in the presence of semantic labels making the registration a domain specific problem.We consider a first scenario where we are given a classifier inferring probability maps for different anatomical structures in the input images. Our method seeks to simultaneously register and segment a set of input images, incorporating this information within the energy formulation. The main idea is to use these estimated maps of semantic labels (provided by an arbitrary classifier) as a surrogate for unlabeled data, and combine them with population deformable registration to improve both alignment and segmentation.Our last contribution also aims at incorporating semantic information to the registration process, but in a different scenario. In this case, instead of supposing that we have pre-trained arbitrary classifiers at our disposal, we are given a set of accurate ground truth annotations for a variety of anatomical structures. We present a methodological contribution that aims at learning context specific matching criteria as an aggregation of standard similarity measures from the aforementioned annotated data, using an adapted version of the latent structured support vector machine (LSSVM) framework.

Within such disciplines as Management Science, Information and Computer Science, Engineering, Mathematics and Operations Research, problems of cutting and packing (C&P) of concrete and abstract objects appear under various specifications (cutting problems, knapsack problems, container and vehicle loading problems, pallet loading, bin packing, assembly line balancing, capital budgeting, changing coins, etc.), although they all have essentially the same logical structure. In cutting problems, a large object must be divided into smaller pieces; in packing problems, small items must be combined to large objects. Most of these problems are NP-hard. Since the pioneer work of L.V. Kantorovich in 1939, which first appeared in the West in 1960, there has been a steadily growing number of contributions in this research area. In 1961, P. Gilmore and R. Gomory presented a linear programming relaxation of the one-dimensional cutting stock problem. The best-performing algorithms today are based on their relaxation. It was, however, more than three decades before the first `optimum? algorithms appeared in the literature and they even proved to perform better than heuristics. They were of two main kinds: enumerative algorithms working by separation of the feasible set and cutting plane algorithms which cut off infeasible solutions. For many other combinatorial problems, these two approaches have been successfully combined. In this thesis we do it for one-dimensional stock cutting and two-dimensional two-stage constrained cutting. For the two-dimensional problem, the combined scheme provides mostly better solutions than other methods, especially on large-scale instances, in little time. For the one-dimensional problem, the integration of cuts into the enumerative scheme improves the results of the latter only in exceptional cases. While the main optimization goal is to minimize material input or trim loss (waste), in a real-life cutting process there are some further criteria, e.g., the number of different cutting patterns (setups) and open stacks. Some new methods and models are proposed. Then, an approach combining both objectives will be presented, to our knowledge, for the first time. We believe this approach will be highly relevant for industry.

This thesis presents new solution approaches for land leveling, using optimal earthmoving vehicle routing. It addresses the Shortest Route Cut and Fill Problem (SRCFP) developed by Henderson, Vaughan, Wakefield and Jacobson [2000]. The SRCFP is a discrete optimization search problem, proven to be NP-hard. The SRCFP describes the process of reshaping terrain through a series of cuts and fills. This process is commonly done when leveling land for building homes, parking lots, etc. The model used to represent this natural system is a variation of the Traveling Salesman Problem. The model is designed to limit the time needed to operate expensive, earthmoving vehicles. The model finds a vehicle route that minimizes the total time required to travel between cut and fill locations while leveling the site. An optimal route is a route requiring the least amount of travel time for an individual earthmoving vehicle. This research addresses the SRCFP by evaluating minimum function values across an unknown response surface. The result is a cost estimating strategy that provides construction planners a strategy for contouring terrain as cheaply as possible. Other applications of this research include rapid runway repair, and robotic vehicle routing. / Master of Science

Le Problème de Tournées de Véhicules (PTV) est une clé importante pour gérér efficacement des systèmes logistiques, ce qui peut entraîner une amélioration du niveau de satisfaction de la clientèle. Ceci est fait en servant plus de clients dans un temps plus court. En terme général, il implique la planification des tournées d'une flotte de véhicules de capacité donnée basée à un ou plusieurs dépôts. Le but est de livrer ou collecter une certain quantité de marchandises à un ensemble des clients géographiquement dispersés, tout en respectant les contraintes de capacité des véhicules. Le PTV, comme classe de problèmes d'optimisation discrète et de grande complexité, a été étudié par de nombreux au cours des dernières décennies. Étant donné son importance pratique, des chercheurs dans les domaines de l'informatique, de la recherche opérationnelle et du génie industrielle ont mis au point des algorithmes très efficaces, de nature exacte ou heuristique, pour faire face aux différents types du PTV. Toutefois, les approches proposées pour le PTV ont souvent été accusées d'être trop concentrées sur des versions simplistes des problèmes de tournées de véhicules rencontrés dans des applications réelles. Par conséquent, les chercheurs sont récemment tournés vers des variantes du PTV qui auparavant étaient considérées trop difficiles à résoudre. Ces variantes incluent les attributs et les contraintes complexes observés dans les cas réels et fournissent des solutions qui sont exécutables dans la pratique. Ces extensions du PTV s'appellent Problème de Tournées de Véhicules Multi-Attributs (PTVMA). Le but principal de cette thèse est d'étudier les différents aspects pratiques de trois types de problèmes de tournées de véhicules multi-attributs qui seront modélisés dans celle-ci. En plus, puisque pour le PTV, comme pour la plupart des problèmes NP-complets, il est difficile de résoudre des instances de grande taille de façon optimale et dans un temps d'exécution raisonnable, nous nous tournons vers des méthodes approcheés à base d’heuristiques. / The Vehicle Routing Problem (VRP) is an important key to efficient logistics system management, which can result in higher level of customer satisfaction because more customers can be served in a shorter time. In broad terms, it deals with designing optimal delivery or collection routes from one or several depot(s) to a number of geographically scattered customers subject to side constraints. The VRP is a discrete optimization and computationally hard problem and has been extensively studied by researchers and practitioners during the past decades. Being complex problems with numerous and relevant potential applications, researchers from the fields of computer science, operations research and industrial engineering have developed very efficient algorithms, both of exact and heuristic nature, to deal with different types of VRPs. However, VRP research has often been criticized for being too focused on oversimplified versions of the routing problems encountered in real-life applications. Consequently, researchers have recently turned to variants of the VRP which before were considered too difficult to solve. These variants include those attributes and constraints observed in real-life planning and lead to solutions that are executable in practice. These extended problems are called Multi-Attribute Vehicle Routing Problems (MAVRPs). The main purpose of this thesis is to study different practical aspects of three multi-attribute vehicle routing problems which will be modeled in it. Besides that, since the VRP has been proved to be NP-hard in the strong sense such that it is impossible to optimally solve the large-sized problems in a reasonable computational time by means of traditional optimization approaches, novel heuristics will be designed to efficiently tackle the created models.

Máquinas insersoras de componentes são utilizadas na indústria eletrônica moderna para a montagem automática de placas de circuito impresso. Com a competição acirrada, há necessidade de se buscar todas as oportunidades para diminuir custos e aumentar a produtividade na exploração desses equipamentos. Neste trabalho, foi proposto um procedimento de otimização do processo de inserção da máquina insersora AVK da Panasonic, implementado em um sistema baseado na técnica de times assíncronos (A-Teams). Foram realizados testes com exemplos de placas de circuito impresso empregadas por uma indústria do ramo e problemas sintéticos para avaliar o desempenho do sistema. / Component inserting machines are employed in the modern electronics industry for the automatic assembly of printed circuit boards. Due the fierce competition, there is a need to search for all opportunities to reduce costs and increase the productivity in the exploitation of these equipment. In this work we propose an optimization procedure for the insertion process of the AVK Panasonic inserting machine, implemented in a system based on asynchronous teams (A-Teams). Tests were conducted using as examples both printed circuit boards used by a particular industry of the realm and synthetic problems for the evaluation of the system.