Nesta tese é abordado o problema da mochila compartimentada e o problema de corte de estoque unidimensional acoplado ao problema dimensionamento de lotes. Para o problema da mochila compartimentada é apresentada a versão unidimensional e proposta a versão bidimensional, denominados como problema da mochila compartimentada unidimensional e problema da mochila compartimentada bidimensional, respectivamente. Para o problema de corte de estoque acoplado ao dimensionamento de lotes são apresentadas três variações: uma máquina para produzir um tipo de objeto; uma máquina para produzir vários tipos de objetos; múltiplas máquinas para produzir vários tipos de objetos. Algumas formulações matemáticas de programação inteira e inteira-mista, decomposições dos problemas em problema mestre e subproblemas e heurísticas baseadas no método geração de colunas são propostas para os problemas da mochila compartimenta e o problema acoplado. Em específico, para o problema acoplado são aplicadas decomposições Dantzig-Wolfe, que podem ser por período, por máquina ou por período e máquina. Além disso, uma heurística baseada em grafo E/OU é proposta para o problema da mochila compartimentada bidimensional / In this thesis we present the constrained compartmentalized knapsack problem and the one dimensional cutting stock problem integrated with the capacitated lot sizing problem. For the constrained compartmentalized knapsack problem, the one dimensional version is presented and the two dimensional version is proposed, called one-dimensional compartmentalized knapsack problem and two-dimensional compartmentalized knapsack problem, respectively. For the cutting stock problem integrated with the capacitated lot sizing problem three variations are considered: one machine to produce one type of object; one machine to produce multiple types of objects; multiple machines to produce multiple types of objects. Some integer and mixed programming formulations, decompositions of the problems in master problem and subproblems and heuristics based on column generation method are proposed for the compartmentalized knapsack problem and the cutting stock problem integrated with the capacitated lot sizing problem. In particular, the period, the machine, and the period and machine Dantzig- Wolfe decompositions are applied for the integrated problem. Moreover, a heuristic based on the graph AND/OR is proposed for the two-dimensional compartmentalized knapsack problem. Computational results show that these mathematical formulations and methods provide good solutions

A opção por sistemas biológicos prevalece para o tratamento do esgoto sanitário. Nas décadas recentes, sistemas que possuem regiões e/ou zonas anaeróbia, anóxica e aeróbia têm-se mostrado como alternativas atraentes para remoção simultânea de matéria orgânica, nitrogênio e fósforo. No entanto, os aspectos operacionais ainda merecem ser objeto de estudo para alcançar desempenho otimizado. Nesse cenário, com intuito de comparar alternativas para a operação das unidades de tratamento de esgoto, o presente trabalho propôs-se a estudar estratégias operacionais associadas ao monitoramento, em tempo real, sem adição de fonte externa de carbono, para um reator aerado não compartimentado com crescimento suspenso e fluxo contínuo precedido de reator anaeróbio. O sistema experimental, em escala de bancada, era constituído de um reator anaeróbio, com volume útil de 43,54 L, e reator aerado, com volume útil de 68,07 L; sendo que este era formado por sete setores, em série, sem separação física. O estudo foi dividido em duas etapas: I - estudo da variação dos volumes da região aerada e da não aerada; II - estudo da aeração intermitente com ciclo de aeração/agitação pré-fixado e controlado em tempo real por sistema informatizado. Em todas as Etapas do estudo ocorreu elevada remoção de DBO e conversão de NTK para nitrato, contudo não se conseguiu obter desnitrificação em nível desejado. O uso de reatores com setores sequenciais sem divisão física (Etapa I) dificultou a obtenção de regiões distintas predominantemente anóxica e aeróbia, comprometendo a remoção de nitrogênio (principalmente a desnitrificação). A maior eficiência média de remoção de nitrogênio alcançada no reator aerado foi de 35,6% (Etapa II), quando o reator era operado com aeração intermitente sendo o ciclo de aeração/agitação controlado em tempo real. A estratégia de operação com aeração intermitente, estudada na Etapa II, favoreceu a remoção de nitrogênio. A aeração intermitente demonstrou ser uma opção promissora comparada à aeração contínua em setores específicos do reator. O controle automatizado e informatizado em tempo real dos ciclos de aeração/agitação pode ser aplicado no aperfeiçoamento da operação dos sistemas de tratamento de esgoto sanitário. / The option of biological systems prevails for the treatment of sewage waste and in recent decades, systems that have anaerobic, anoxic, aerobic regions and / or zones have proven attractive for simultaneous removal of organic matter, nitrogen and phosphorus. However, the operational aspects still deserve to be studied in order to achieve the optimized performance of these systems. In this scenario, in order to compare alternatives for the operation of sewage treatment plants, the present work aimed to study operational strategies associated with monitoring, in real time, without the addition of external carbon source, for a non-compartmentalized aerated reactor with growth suspended and continuous flow preceded by anaerobic reactor. The experimental system in bench scale consisted of an anaerobic reactor, with a volume of 43.54 L and an aerated reactor, with a volume of 68.07 L; consisting of seven sectors, in series, without physical separation. The study was divided into two stages: I - study of the variation of the volume of the aerated and non-aerated regions; II - study of intermittent aeration with cycle of aeration/agitation controlled by a pre-fixed time interval; and controlled in real time by a computerized system. In all Stages of the study high BOD removal and conversion of TKN to nitrate occurred, but were unable to obtain denitrification at desired level. The use of reactors with sequential sectors without physical division (Stage I) made it difficult to obtain predominantly distinct anoxic and aerobic regions, compromising the removal of nitrogen (mainly the denitrification). The highest average removal efficiency of nitrogen attained in aerated reactor was 35.6% when the reactor was operated with intermittent aeration with aeration cycle controlled in real time. The operation strategy with intermittent aeration, studied in Stage II, favored the removal of nitrogen. The intermittent aeration proved to be a promising option compared to continuous aeration in specific sectors of the reactor. The automated and computerized control in real-time of the aeration / agitation cycles can be applied in improving the operation of sewage waste treatment systems.

A opção por sistemas biológicos prevalece para o tratamento do esgoto sanitário. Nas décadas recentes, sistemas que possuem regiões e/ou zonas anaeróbia, anóxica e aeróbia têm-se mostrado como alternativas atraentes para remoção simultânea de matéria orgânica, nitrogênio e fósforo. No entanto, os aspectos operacionais ainda merecem ser objeto de estudo para alcançar desempenho otimizado. Nesse cenário, com intuito de comparar alternativas para a operação das unidades de tratamento de esgoto, o presente trabalho propôs-se a estudar estratégias operacionais associadas ao monitoramento, em tempo real, sem adição de fonte externa de carbono, para um reator aerado não compartimentado com crescimento suspenso e fluxo contínuo precedido de reator anaeróbio. O sistema experimental, em escala de bancada, era constituído de um reator anaeróbio, com volume útil de 43,54 L, e reator aerado, com volume útil de 68,07 L; sendo que este era formado por sete setores, em série, sem separação física. O estudo foi dividido em duas etapas: I - estudo da variação dos volumes da região aerada e da não aerada; II - estudo da aeração intermitente com ciclo de aeração/agitação pré-fixado e controlado em tempo real por sistema informatizado. Em todas as Etapas do estudo ocorreu elevada remoção de DBO e conversão de NTK para nitrato, contudo não se conseguiu obter desnitrificação em nível desejado. O uso de reatores com setores sequenciais sem divisão física (Etapa I) dificultou a obtenção de regiões distintas predominantemente anóxica e aeróbia, comprometendo a remoção de nitrogênio (principalmente a desnitrificação). A maior eficiência média de remoção de nitrogênio alcançada no reator aerado foi de 35,6% (Etapa II), quando o reator era operado com aeração intermitente sendo o ciclo de aeração/agitação controlado em tempo real. A estratégia de operação com aeração intermitente, estudada na Etapa II, favoreceu a remoção de nitrogênio. A aeração intermitente demonstrou ser uma opção promissora comparada à aeração contínua em setores específicos do reator. O controle automatizado e informatizado em tempo real dos ciclos de aeração/agitação pode ser aplicado no aperfeiçoamento da operação dos sistemas de tratamento de esgoto sanitário. / The option of biological systems prevails for the treatment of sewage waste and in recent decades, systems that have anaerobic, anoxic, aerobic regions and / or zones have proven attractive for simultaneous removal of organic matter, nitrogen and phosphorus. However, the operational aspects still deserve to be studied in order to achieve the optimized performance of these systems. In this scenario, in order to compare alternatives for the operation of sewage treatment plants, the present work aimed to study operational strategies associated with monitoring, in real time, without the addition of external carbon source, for a non-compartmentalized aerated reactor with growth suspended and continuous flow preceded by anaerobic reactor. The experimental system in bench scale consisted of an anaerobic reactor, with a volume of 43.54 L and an aerated reactor, with a volume of 68.07 L; consisting of seven sectors, in series, without physical separation. The study was divided into two stages: I - study of the variation of the volume of the aerated and non-aerated regions; II - study of intermittent aeration with cycle of aeration/agitation controlled by a pre-fixed time interval; and controlled in real time by a computerized system. In all Stages of the study high BOD removal and conversion of TKN to nitrate occurred, but were unable to obtain denitrification at desired level. The use of reactors with sequential sectors without physical division (Stage I) made it difficult to obtain predominantly distinct anoxic and aerobic regions, compromising the removal of nitrogen (mainly the denitrification). The highest average removal efficiency of nitrogen attained in aerated reactor was 35.6% when the reactor was operated with intermittent aeration with aeration cycle controlled in real time. The operation strategy with intermittent aeration, studied in Stage II, favored the removal of nitrogen. The intermittent aeration proved to be a promising option compared to continuous aeration in specific sectors of the reactor. The automated and computerized control in real-time of the aeration / agitation cycles can be applied in improving the operation of sewage waste treatment systems.

La stimulation électrique neurale, appliquée au système nerveux périphérique pour la restauration des fonctions motrices ou la neuromodulation, est une technologie en plein essor, en particulier la stimulation implantée avec des électrodes Cuff positionnées autour d’un nerf périphérique. Le principal frein au développement des systèmes de stimulation est la difficulté à obtenir la stimulation ou l’inhibition des fonctions cibles de manière précise et indépendante, c’est-à-dire, obtenir une sélectivité des fonctions. Les paramètres impliqués dans la sélectivité au sens large ne sont pas toujours intuitifs, et le nombre de degrés de libertés (choix de l’électrode, nombre de contacts, forme du pulse etc.) est important. Tester toutes ces hypothèses en expérimentation n’est pas faisable et inenvisageable dans le réglage des neuroprothèses en contexte clinique. La modélisation a priori nous permet d’établir des critères de choix, de déterminer les stratégies les plus efficaces et de les optimiser. Par ailleurs, un grand nombre d’études ont pu prévoir des stratégies de sélectivité inédites grâce à la modélisation, et validées a posteriori par l’expérimentation. Le schéma de calcul scientifique est composé de deux parties. On modélise, d’une part, la propagation du champ de potentiels électriques générés par les électrodes à l’intérieur d’un volume conducteur représentant le nerf (étude biophysique), et d’autre part l’interaction entre ce champ de potentiels et les neurones (réponse électrophysiologique). Notre première contribution propose une méthode originale de modélisation et d’optimisation de la sélectivité spatiale avec une électrode Cuff, sans connaissance a priori de la topographie de nerf. Partant de ce constat, nous déterminons de nouveaux critères, l’efficacité et la robustesse, complémentaires à la sélectivité, nous permettant de faire un choix entre des configurations multipolaires concurrentes. Ainsi, en fonction de la pondération de ces critères, nous avons développé un algorithme d’optimisation pour déterminer la configuration optimale en fonction de la zone choisie, du diamètre des fibres visées ainsi que de la durée de stimulation, pour un pulse type rectangulaire de référence. Des expérimentations sur modèle animal nous ont permis d’évaluer l’efficacité de la méthode et sa généricité. Ce travail est partie intégrante d’un projet plus vaste de stimulation du nerf vague (projet INTENSE), où l’une des applications concerne le traitement des troubles cardiaques. L’objectif est d’activer sélectivement une population spécifique de fibres nerveuses pour obtenir des effets plus ciblés conduisant à une thérapie améliorée, tout en diminuant les effets secondaires. La deuxième contribution consiste à combiner la sélectivité spatiale et la sélectivité au diamètre de fibre avec un modèle générique de nerf et une électrode Cuff à 12 contacts. L’utilisation d’une forme d’onde particulière (prépulse) combinée avec des configurations multipolaires permet d’activer des fibres d’un diamètre défini dans un espace ciblé. Les perspectives cliniques sont nombreuses, notamment sur la réduction de la fatigue liée à l’utilisation prolongée de la stimulation ou la diminution des effets secondaires. Dans le cadre du projet INTENSE, la seconde application liée à la stimulation du nerf vague vise le problème de l’obésité morbide. L’activation des axones cibles liés aux fonctions gastriques nécessite une quantité de charges conséquente. Plusieurs études suggèrent que les formes de pulse non rectangulaires peuvent activer les axones du système nerveux périphérique avec une quantité de charges réduite comparée à la forme de pulse rectangulaire de référence. Notre dernière contribution concerne l’étude expérimentale et de modélisation de ces formes d’ondes complexes. L’approche par modélisation, si elle est bien maîtrisée, apporte une analyse pertinente voire même indispensable au réglage clinique des neuroprothèses. / Neural electrical stimulation, applied to the peripheral nervous system for motor functions restoration or neuromodulation, is a thriving technology, especially implanted stimulation using Cuff electrodes positioned around a peripheral nerve. The main obstacle to the development of stimulation systems is the difficulty in obtaining the independent stimulation or inhibition of specific target functions (i.e. functional selectivity). The parameters involved in selectivity are not always intuitive and the number of degrees of freedom (choice of electrode, number of contacts, pulse shape etc.) is substantial. Thus, testing all these hypotheses in a clinical context is not conceivable. This choice of parameters can be guided using prior numerical simulations predicting the effect of electrical stimulation on the neural tissue. Numerous studies developed new strategies to achieve selectivity based on modeling results that have been validated a posteriori by experimental works. The computation scheme is composed of two parts : the modeling of the potential field generated by the electrodes inside a conductive medium representing the nerve on the one hand; and the determination of the interaction between this field of potentials and neurons on the other. Our first contribution is an original method of modeling and optimization of the spatial selectivity with a Cuff electrode, without prior knowledge of the nerve topography. Based on this observation, we determined new criteria, efficiency and robustness, complementary to selectivity, allowing us to choose between multipolar configurations. Thus, according to the weighting applied to these criteria, we developed an optimization algorithm to determine the optimal configuration as a function of the target zone, fiber diameter and the stimulation duration for a typical rectangular pulse. Experiments on animal model allowed us to evaluate the effectiveness and genericness of the method. This work was performed as part of a larger project on vagus nerve stimulation (INTENSE project) in which one of the applications focused on the treatment of cardiac disorders. The main objective was to selectively activate a specific population of nerve fibers to improve therapy and decrease side effects. In a second contribution, numerical simulations were used to investigate the combination of multipolar configurations and the prepulses technique, in order to obtain fiber recruitment in a spatially reverse order. The main objective was to achieve both spatial and fiber diameter selectivity. Expected clinical perspectives of this work are the reduction of fatigue related to a prolonged use of stimulation and the reduction of side effects. Within the framework of the INTENSE project, the second application investigated vagus nerve stimulation as a therapy for morbid obesity. Activation of target axons related to gastric functions requires a significant amount of charge injection. Several studies suggest that non-rectangular waveforms can activate axons of the peripheral nervous system with a reduced amount of charge compared to the reference rectangular pulse shape. Our last contribution focuses on the experimental study and the modeling of these complex waveforms. The modeling approach, if performed properly and while bearing in mind its limits, provides a relevant and even indispensable analysis tool for the clinical adjustment of neuroprostheses.