Le problème de localisation-routage avec capacités (PLRC) apparaît comme un problème clé dans la conception de réseaux de distribution de marchandises. Il généralisele problème de localisation avec capacités (PLC) ainsi que le problème de tournées de véhicules à multiples dépôts (PTVMD), le premier en ajoutant des décisions liées au routage et le deuxième en ajoutant des décisions liées à la localisation des dépôts. Dans cette thèse on dévelope des outils pour résoudre le PLRC à l’aide de la programmation mathématique. Dans le chapitre 3, on introduit trois nouveaux modèles pour le PLRC basés sur des flots de véhicules et des flots de commodités, et on montre comment ceux-ci dominent, en termes de la qualité de la borne inférieure, la formulation originale à deux indices [19]. Des nouvelles inégalités valides ont été dévelopées et ajoutées aux modèles, de même que des inégalités connues. De nouveaux algorithmes de séparation ont aussi été dévelopés qui dans la plupart de cas généralisent ceux trouvés dans la litterature. Les résultats numériques montrent que ces modèles de flot sont en fait utiles pour résoudre des instances de petite à moyenne taille. Dans le chapitre 4, on présente une nouvelle méthode de génération de colonnes basée sur une formulation de partition d’ensemble. Le sous-problème consiste en un problème de plus court chemin avec capacités (PCCC). En particulier, on utilise une relaxation de ce problème dans laquelle il est possible de produire des routes avec des cycles de longueur trois ou plus. Ceci est complété par des nouvelles coupes qui permettent de réduire encore davantage le saut d’intégralité en même temps que de défavoriser l’apparition de cycles dans les routes. Ces résultats suggèrent que cette méthode fournit la meilleure méthode exacte pour le PLRC. Dans le chapitre 5, on introduit une nouvelle méthode heuristique pour le PLRC. Premièrement, on démarre une méthode randomisée de type GRASP pour trouver un premier ensemble de solutions de bonne qualité. Les solutions de cet ensemble sont alors combinées de façon à les améliorer. Finalement, on démarre une méthode de type détruir et réparer basée sur la résolution d’un nouveau modèle de localisation et réaffectation qui généralise le problème de réaffectaction [48]. / The capacitated location-routing problem (CLRP) arises as a key problem in the design of distribution networks. It generalizes both the capacitated facility location problem (CFLP) and the multiple depot vehicle routing problem (MDVRP), the first by considering additional routing decisions and the second by adding the location decision variables. In this thesis we use different mathematical programming tools to develop and specialize new models and algorithms for solving the CLRP. In Chapter 3, three new models are presented for the CLRP based on vehicle-flow and commodity-flow formulations, all of which are shown to dominate, in terms of the linear relaxation lower bound, the original two-index vehicle-flow formulation [19]. Known valid inequalities are complemented with some new ones and included using separation algorithms that in many cases generalize extisting ones found in the literature. Computational experiments suggest that flow models can be efficient for dealing with small or medium size instances of the CLRP (50 customers or less). In Chapter 4, a new branch-and-cut-and-price exact algorithm is introduced for the CLRP based on a set-partitioning formulation. The pricing problem is a shortest path problem with resource constraints (SPPRC). In particular, we consider a relaxation of such problem in which routes are allowed to contain cycles of length three or more. This is complemented with the development of new valid inequalities that are shown to be effective for closing the optimality gap as well as to restrict the appearance of cycles. Computational experience supports the fact that this method is now the best exact method for the CLRP. In Chapter 5, we introduce a new metaheuristic with the aim of finding good quality solutions in short or moderate computing times. First, a bundle of good solutions is generated with the help of a greedy randomized adaptive search procedure (GRASP). Following this, a blending procedure is applied with the aim of producing a better upper bound as a combination of all the others in the bundle. An iterative destroy-and-repair method is then applied using a location-reallocation model that generalizes the reallocation model due to de Franceschi et al. [48].

Depuis une vingtaine d’années, la résolution de problèmes d’optimisation globale non convexes avec contraintes a connu un formidable essor. Les algorithmes de branch and bound basée sur l’analyse d’intervalles ont su trouver leur place, car ils ont l’avantage de prouver l’optimalité de la solution de façon déterministe, avec un niveau de certitude pouvant aller jusqu’à la précision machine. Cependant, la complexité exponentielle en temps et en mémoire de ces algorithmes induit une limite intrinsèque, c’est pourquoi il est toujours nécessaire d’améliorer les techniques actuelles. Dans cette thèse, nous avons développé de nouvelles arithmétiques basées sur l’arithmétique d’intervalles et l’arithmétique affine, afin de calculer des minorants et des majorants de meilleure qualité de fonctions explicites sur un intervalle. Nous avons ensuite développé une nouvelle méthode automatique de construction de relaxations linéaires. Cette construction est basée sur l’arithmétique affine et procède par surcharge des opérateurs. Les programmes linéaires ainsi générés ont exactement le même nombre de variables et de contraintes d’inégalité que les problèmes originaux, les contraintes d’égalité étant remplacées par deux inégalités. Cette nouvelle procédure permet de calculer des minorants fiables et des certificats d’infaisabilité pour chaque sous-domaine à chaque itération de notre algorithme de branch and bound par intervalles. De nombreux tests numériques issus du site COCONUT viennent confirmer l’efficacité de cette approche. Un autre aspect de cette thèse a été l’étude d’une extension de ce type d’algorithmes en introduisant une limite sur mémoire disponible. L’idée principale de cette approche est de proposer un processus inverse de l’optimisation par le biais d’un principe métaheuristique : plutôt que d’améliorer des solutions locales à l’aide de métaheuristiques telles que les algorithmes Taboo ou VNS, nous partons d’une méthode exacte et nous la modifions en une heuristique. De cette façon, la qualité de la solution trouvée peut être évaluée. Une étude de la complexité de ce principe métaheuristique a également été effectuée. Enfin, pour finir l’étude, nous avons appliqué notre algorithme à la résolution de problème en géométrie plane, ainsi qu’à la résolution d’un problème de dimensionnement de moteur électrique. Les résultats obtenus ont permis de confirmer l’intérêt de ce type d’algorithme, en résolvant des problèmes ouverts sur les polygones convexes et proposant des structures innovantes en génie électrique. / Since about thirty years, interval Branch and Bound algorithms are increasingly used to solve constrained global optimization problems in a deterministic way. Such algorithms are reliable, i.e., they provide an optimal solution and its value with guaranteed bounds on the error, or a proof that the problem under study is infeasible. Other approaches to global optimization, while useful and often less time-consuming than interval methods, do not provide such a guarantee. However, the exponential complexity in time and memory of interval Branch and Bound algorithms implies a limitation, so it is always necessary to improve these methods. In this thesis, we have developed new arithmetics based on interval arithmetic and affine arithmetic, to compute better lower and upper bounds of a factorable function over an interval. An automatic method for constructing linear relaxations of constrained global optimization problems is proposed. Such a construction is based on affine and interval arithmetics and uses operator overloading. These linear programs have exactly the same numbers of variables and of inequality constraints as the given problems. Each equality constraint is replaced by two inequalities. This new procedure for computing reliable bounds and certificates of infeasibility is inserted into a classical interval Branch and Bound algorithm. Extensive computation experiments, made on a sample of test problems from the COCONUT database, prove its effectiveness. Another aspect is the study of an extension of such a global optimization code by limiting the available memory. The main idea of this new kind of metaheuristique is to propose a reverse process of optimization via heuristics : rather than improving local solutions by using metaheuristics such as Taboo or VNS, we begin with an exact method and we modify it into a heuristic one. In such a way, the quality of the solution could be evaluated. Moreover, a study of the complexity of this metaheurisque has been done. Finally, we applied our algorithm to solve open problem in geometry, and to solve a design problem of an electric motor. The results have confirmed the usefulness of this kind of algorithms, solving open problems on convex polygons and offering innovative structures in electrical engineering.

Dans cette thèse, on s'intéresse à deux problèmes de conception de réseaux, utilisant la technologie OFDM multi-bandes. Le premier problème concerne la conception d'un réseau mono-couche avec contraintes spécifiques. Nous donnons une formulation en PLNE pour ce problème et étudions le polyèdre associé à sa restriction sur un arc. Nous introduisons deux familles d'inégalités valides définissant des facettes et développons un algorithme de coupes et branchements pour le problème. Nous étudions la variante multicouche du problème précédent et proposons plusieurs PLNE pour le modéliser. Nous identifions plusieurs familles de facettes et discutons des problèmes de séparation associés. Nous développons un algorithme de coupes et branchements utilisant l'ensemble des contraintes identifiées. Enfin, une formulation compacte et deux formulations basées sur des chemins sont proposées pour le problème. Nous présentons deux algorithmes de génération de colonnes et branchements pour le problème. / In this thesis we consider two capacitated network design (CND) problems, using OFDM multi-band technology. The first problem is related to single-layer network design with specific requirements. We give an ILP formulation for this problem and study the polyhedra associated with its arc-set restriction. We describe two families of facet defining inequalities. We devise a Branch-and-Cut algorithm for the problem. Next, we investigate the multilayer version of CND using OFDM technology. We propose several ILP formulations and study the polyhedron associated with the first (cut) formulation. We identify several classes of facets and discuss the related separation problem. We devise a Branch-and-Cut algorithm embedding valid inequalities of both single-layer and multilayer problems. The second formulation is compact, and holds a polynomial number of constraints and variables. Two further path formulations are given which yield two efficient Branch-and-Price algorithms for the problem.

The thesis deals with the accounting of Czech company's branch established in Slovak Republic. The first part is rather theoretical, it shows the branch from a legal point of view and consequently in terms of accounting from the perspective of the founder of the branch itself and from the perspective of the foreign branch. Other chapters are devoted to the practical example of the Czech company's branch established in Slovakia. The branch and its founder are defined in the second chapter of the thesis. The third part deals with the accounting of Slovak branch that means with the various operations carried out during the accounting period from the opening of the accounting books through regular transactions to closing the accounting books. The third chapter also describes how to capture branch in the accounting of its founder. The last part is devoted to correct mistakes, respectively infringement of the Slovak accounting standards, which were found in the accounting of the Slovak branch.

Em um contexto industrial, a programação da produção tem como objetivo alocar recursos para operações de forma a aumentar a eficiência operacional do processo de fabricação. Esta programação pode ser modelada na forma de problemas de sequenciamento de tarefas, que são resolvidos visando minimizar um determinado critério de desempenho. A aplicação de métodos exatos nestes problemas possibilita encontrar a solução ótima, tanto para aplicação direta como para a validação de métodos heurísticos e metaheurísticas. Entretanto, a literatura mostra que os métodos exatos, tanto a resolução do problema pela modelagem em programação linear-inteira mista como o branch-and-bound, têm sua aplicação restrita à problemas de menores tamanhos. O objetivo deste trabalho é propor novas formulações de limitantes inferiores para a aplicação do branch-and-bound em problemas de flowshop permutacional visando aumentar sua eficiência e aplicabilidade. Os limitantes propostos são avaliados em problemas de flowshop permutacional com tempos de setup dependente da sequência, tendo como critérios de desempenho o tempo de fluxo total e o atraso total. A avaliação da aplicabilidade de cada limitante é feita através do número de nós explorados e o tempo computacional gasto pelo branch-and-bound para resolver problemas de diversos tamanhos. / In an industrial context, production sequencing aims at allocating resources for job processing while increasing manufacturing efficiency. This task can be modelled in the form of scheduling problems, which are solved by minimizing a pre-determined performance criterion. The use of exact methods allows the optimal solution to be found, which can be applied directly in the manufacturing shop or used to validate heuristic and metaheuristic methods. However, the literature shows that MILP and branch-and-bound, both exact methods, are restrained to small-sized scheduling problems. The aim of this project is to propose new lower bound formulations to be used in the branch-and-bound method for permutational flowshop probems, in order to extend its efficiency and applicability. The proposed bounds are tested in permutational flowshop problems with sequence dependent setup times, and using as performance criteria the total flow time and the total tardiness. The evaluation of each lower bounds applicability is done considering the number of explored nodes and the required computational time for the branch-and-bound to solve problem instances of different sizes.

Linear optimization tools are used to solve many problems that arise in our day-to-day lives. The linear optimization models and methodologies help to find, for example, the best amount of ingredients in our food, the most suitable routes and timetables for the buses and trains we take, and the right way to invest our savings. We would cite many other situations that involves linear optimization, since a large number of companies around the world base their decisions in solutions which are provided by the linear optimization methodologies. In this thesis, we propose theoretical and computational developments to improve the performance of important linear optimization methods. Namely, we address simplex type methods, interior point methods, the column generation technique and the branch-and-price method. In simplex-type methods, we investigate a variant which exploits special features of problems which are formulated in the general form. We present a novel theoretical description of the method and propose how to efficiently implement this method in practice. Furthermore, we propose how to use the primal-dual interior point method to improve the column generation technique. This results in the primal-dual column generation method, which is more stable in practice and has a better overall performance in relation to other column generation strategies. The primal-dual interior point method also oers advantageous features which can be exploited in the context of the branch-and-price method. We show that these features improves the branching operation and the generation of columns and valid inequalities. For all the strategies which are proposed in this thesis, we present the results of computational experiments which involves publicly available, well-known instances from the literature. The results indicate that these strategies help to improve the performance of the linear optimization methodologies. In particular for a class of problems, namely the vehicle routing problem with time windows, the interior point branch-and-price method proposed in this study was up to 33 times faster than a state-of-the-art implementation available in the literature / Ferramentas de otimização linear são usadas para resolver diversos problemas do nosso dia-a- dia. Os modelos e as metodologias de otimização linear ajudam a obter, por exemplo, a melhor quantidade de ingredientes na nossa alimentação, os horários e as rotas de ônibus e trens que tomamos, e a maneira certa para investir nossas economias. Muitas outras situações que envolvem otimização linear poderiam ser aqui citadas, já que um grande número de empresas em todo o mundo baseia suas decisões em soluções obtidas pelos métodos de otimização linear. Nesta tese, são propostos desenvolvimentos teóricos e computacionais para melhorar o desempenho de métodos de otimização linear. Em particular, serão abordados métodos tipo simplex, métodos de pontos interiores, a técnica de geração de colunas e o método branch-and-price. Em métodos tipo simplex, é investigada uma variante que explora as características especiais de problemas formulados na forma geral. Uma nova descrição teórica do método é apresentada e, também, são propostas técnicas computacionais para a implementação eciente do método. Além disso, propõe-se como utilizar o método primal-dual de pontos interiores para melhorar a técnica de geração de colunas. Isto resulta no método primal-dual de geração de colunas, que é mais estável na prática e tem melhor desempenho geral em relação a outras estratégias de geração de colunas. O método primal-dual de pontos interiores também oferece características vantajosas que podem ser exploradas em conjunto com o método branch-and-price. De acordo com a investigação realizada, estas características melhoram a operação de ramificação e a geração de colunas e de desigualdades válidas. Para todas as estratégias propostas neste trabalho, são apresentados os resultados de experimentos computacionais envolvendo problemas de teste bem conhecidos e disponíveis publicamente. Os resultados indicam que as estratégias propostas ajudam a melhorar o desempenho das metodologias de otimização linear. Em particular para uma classe de problemas, o problema de roteamento de veículos com janelas de tempo, o método branch-and-price de pontos interiores proposto neste estudo foi até 33 vezes mais rápido que uma implementação estado-da-arte disponível na literatura

Die Habilitationsschrift beschäftigt sich mit Theorie, Algorithmen und Software zur Lösung von nichtkonvexen, gemischt-ganzzahligen, nichtlinearen Optimierungsproblemen (MINLP). Sie besteht aus 14 Kapiteln, die in zwei Teile gegliedert sind. Im ersten Teil werden grundlegende Optimierungswerkzeuge beschrieben und im zweiten Teil werden Lösungsalgorithmen vorgestellt. Fast alle vorgeschlagenen Algorithmen wurden als Teil der objektorientierten C++ Bibliothek LaGO implementiert. Numerische Experimente mit verschiedenen MINLP-Problemen zeigen die Möglichkeiten und Grenzen dieser Verfahren. / This book is concerned with theory, algorithms and software for solving nonconvex mixed integer nonlinear programs. It consists of two parts. The first part describes basic optimization tools, such as block-separable reformulations, convex and Lagrangian relaxations, decomposition methods and global optimality criteria. The second part is devoted to algorithms. Starting with a short overview on existing methods, we present deformation, rounding, partitioning and Lagrangian heuristics, and a branch-cut-and-price algorithm. The algorithms are implemented as part of an object-oriented library, called LaGO. We report numerical results on several mixed integer nonlinear programs to show abilities and limits of the proposed solution methods.

Le problème de routage de véhicules avec fenêtres de temps et routes multiples (MTVRPTW) est une généralisation du problème de routage de véhicules avec fenêtres de temps (VRPTW). Dans le MTVRPTW, on autorise un véhicule à effectuer plusieurs routes durant une période de planification, ce qui permet d'optimiser les transports lorsque le nombre de véhicules est limité et peu élevé. Nous proposons dans cette thèse la première méthode exacte permettant de résoudre ce problème. Notre modélisation prend la forme d'un problème de couverture des clients dont les variables sont des routes. Des contraintes d'exclusion mutuelle expriment la disponibilité des véhicules. Nous utilisons la Génération de Colonnes, avec un sous-problème effectuant, par programmation dynamique, une recherche de plus court chemin élémentaire contraint en ressources. Notre méthode de programmation dynamique tient compte des dépendances de plusieurs ressources grâce à la notion de label représentatif, et est ainsi plus efficace qu'une approche classique. La méthode de Génération de Colonnes est incluse dans un schéma de Branch and Price composé de deux types de branchement, l'un basé sur les arcs, l'autre sur la résolution d'un VRPTW. Nous avons mis en place diverses méthodes accélératrices spécifiques du MTVRPTW. Nous donnons les résultats de l'algorithme sur les instances de Solomon. Des résultats issus de méthodes exactes étaient disponibles dans la littérature pour le MTVRPTW avec durée limite sur les routes. Nous avons proposé un nouvel algorithme plus performant, et basé sur nos méthodes, pour cette variante du problème. / The multi-trip vehicle routing problem with time windows (MTVRPTW) is a generalization of the vehicle routing problem with time windows (VRPTW). In the MTVRPTW, one vehicle can perform several trips during a planning period. This allows optimizing the transport when the number of vehicles is limited and small.We propose here the first exact method for solving this problem.Our model is designed as a coverage problem for customers where the variables are trips. Mutual exclusion constraints express the availability of vehicles. We use a column generation scheme in which the sub-problem is an elementary shortest path problem with resource constraints (ESPPRC). Our dynamic programming method for ESPPRC takes into account dependencies of several resources through the concept of representative label. It is thus more efficient than a conventional approach. The column generation method is included in a Branch and Price scheme with two types of branching. One is based on arc selection, and the other on solving a VRPTW. We have implemented various accelerating methods which are specific to MTVRPTW. We give the results of our algorithm on Solomon instances.Results from exact methods were available in the literature for the MTVRPTW with time limit on the trips. We proposed a new and more efficient algorithm, based on our methods, to solve this variant of the problem.

Nos Estados republicanos modernos, o sistema de freios e contrapesos é um dos modelos institucionais responsável por assegurar o equilíbrio entre os Poderes e prevenir abusos por parte dos governantes. Dois questionamentos podem ser encontrados na literatura brasileira sobre o tema e fundamentam esta Dissertação: um geral sobre o suposto poder excessivo que o nosso sistema político confere ao Poder Executivo e outro, específico, de que nesse contexto, o veto teria um papel central na supremacia do presidente da república sobre o Congresso Nacional no âmbito do processo legislativo. Partindo dessas premissas, a pesquisa avalia se essas características estão condizentes com as expectativas e o desenho institucional proposto para o Estado brasileiro pela Assembleia Nacional Constituinte ANC de 1987. Com base nos anais da ANC e em referências históricas, conclui-se que, ao menos no tocante ao instituto do veto presidencial, o modelo de preponderância do Poder Executivo observado no processo legislativo decorreu de uma opção deliberada e reafirmada pela elite política em 1988, quando da promulgação da Constituição. / In modern republican states, the system of checks and balances is one of the institutional models responsible for ensuring the balance between powers and preventing abuses by rulers. Two issues can be found in the Brazilian academic literature on the matter that underlie this Dissertation: one concerning the alleged excessive power that our political system grant to the executive branch, and another one more specific that, in this context, the veto would have a main role in the supremacy of the President of the Republic over Congress in the legislative process. Beginning with these assumptions, this research evaluates whether these characteristics are consistent with the expectations and the institutional design proposed for the Brazilian State by the National Constituent Assembly (ANC) of 1987. Based on the ANC records and historical references, it concluded that, at least in regard to the presidential veto institute, the preponderance of the executive branch model observed in the legislative process derived from a deliberate and reaffirmed choice made by the political elite in 1988, at the promulgation of the Constitution.

This study provides a genre analysis of Janet Reno's apologia in response to the Mt. Carmel disaster. Discussions of the events leading up to the crisis, Reno's rhetorical response, and relevant situational constraints and exigencies are provided.