La chaine d’approvisionnement énergétique a fortement évolué aux cours des 20 dernières années. La libéralisation des marchés de l’électricité et les nouvelles technologies ont fortement influencé la manière d’envisager la production et la transmission d’électricité. Les modèles mathématiques classiques utilisés dans les problèmes lié à l’énergie ont besoin d’être revus pour intégrer les contraintes pratiques modernes.Un problème classique pour un Compagnie Génératrice (CG) est le problème de Unit Commitment (UC) qui consiste à établir un plan de production pour une demande en électricité connue. Lorsque ce problème fut considéré, le prix de l’électricité et la demande étaient relativement simple à estimer comme une seule CG nationale avait le monopole du marché. Ce problème a été étudié de manière extensive en utilisant de la Programmation Mathématique (PM). Aujourd’hui, le prix de l’électricité est relativement volatile à cause de l’introduction de marchés dérégulés et la demande du marché est répartie entre plusieurs CGs en compétition sur divers marchés. Une CG ne peut se limiter à considérer un problème de UC seul pour envisager sa production. Il y a un besoin d’intégrer les incertitudes liées au marché de l’électricité et aux quantités à produire aux modèles utilisés pour qu’une CG puisse établir un plan de production rentable.La technologie a aussi permis d’envisager de nouveaux concept tel que les Micro-Grilles (MGs). Une MG est composée d’un ensemble de consommateurs reliés à travers un réseau de transmission, possédant des générateurs d’électricité et optimisant leur consommation interne. Ce concept est possible grâce à l’utilisation croissante d’énergies renouvelables locales ainsi que l’utilisant croissante d’appareils interconnectés. Cependant, étant donné que les énergies renouvelables ont un faible rendement, sont intermittentes et que les appareils de stockage d’énergie sont encore peu efficaces, les MGs ne peuvent pas envisager d’être pleinement autonome en électricité. Il y a donc une nécessité d’avoir un fournisseur d’électricité externe pour avoir suffisamment d’électricité disponible à tout moment. Une CG jouant le rôle de fournisseur auprès d’une MG fait face énormément d’incertitude concernant la demande à cause de la gestion interne de la MG sur laquelle elle n’a pas de contrôle.Dans cette thèse, des problèmes d’optimisation intégrant de nouvelles contraintes modernes liés à l’approvisionnement énergétique sont étudiés via la PM. Plusieurs problèmes considèrant des interactions entre plusieurs acteurs sont modélisés via des formulations bi-niveau. Nous illustrons comment les difficultés liées aux contraintes modernes peuvent être exploitées pour obtenir des propriétés permettant de reformuler les problèmes étudiés en formulation linéaire en nombre entiers. Des heuristiques performantes sont obtenus à partir des formulations exactes dont certaines sont applicables à des problèmes plus généraux. Une analyse extensive de la performance des méthodes de résolution ainsi que de l’influence des contraintes modernes sont présentées dans diverses expériences numériques. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

A multi-commodity flow problem consists of moving several commodities from their respective sources to their sinks through a network where each edge has different costs and capacity constraints. This paper explores different linear programming algorithms and their performance regarding finding an optimal solution for multi-commodity flow problems. By testing several of different network constraints, we examine which algorithms are most suitable for specific network and problem structures. Furthermore, we implement our own multi-commodity solver and compare its performance against state-of-the-art linear programming solvers. The results show that for the methods we tested it is difficult to discern which class of linear programming methods are optimal solvers for multi-commodity flow problems and that their performance depends on how the network and commodities are structured.

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Student Number : 0214677F - PhD thesis - School of Camputational and Applied Mathematics - Faculty of Science / Many real-life problems are formulated as global optimization problems with continuous variables. These problems are in most cases nonsmooth, nonconvex and often simulation based, making gradient based methods impossible to be used to solve them. Therefore, ef#2;cient, reliable and derivative-free global optimization methods for solving such problems are needed. In this thesis, we focus on improving the ef#2;ciency and reliability of some global optimization methods. In particular, we concentrate on improving some population set-based methods for unconstrained global optimization, mainly through hybridization. Hybridization has widely been recognized to be one of the most attractive areas of unconstrained global optimization. Experiments have shown that through hybridization, new methods that inherit the strength of the original elements but not their weakness can be formed. We suggest a number of new hybridized population set-based methods based on differential evolution (de), controlled random search (crs2) and real coded genetic algorithm (ga). We propose #2;ve new versions of de. In the #2;rst version, we introduce a localization, called random localization, in the mutation phase of de. In the second version, we propose a localization in the acceptance phase of de. In the third version, we form a de hybrid algorithm by probabilistically combining the point generation scheme of crs2 with that of de in the de algorithm. The fourth and #2;fth versions are also de hybrids. These versions hybridize the mutation of de with the point generation rule of the electromagnetism-like (em) algorithm. We also propose #2;ve new versions of crs2. The #2;rst version modi#2;es the point generation scheme of crs2 by introducing a local mutation technique. In the second and third modi#2;cations, we probabilistically combine the point generation scheme of crs2 with the linear interpolation scheme of a trust-region based method. The fourth version is a crs hybrid that probabilistically combines the quadratic interpolation scheme with the linear interpolation scheme in crs2. In the #2;fth version, we form a crs2 hybrid algorithm by probabilistically combining the point generation scheme of crs2 with that of de in the crs2 algorithm. Finally, we propose #2;ve new versions of the real coded genetic algorithm (ga) with arithmetic crossover. In the #2;rst version of ga, we introduce a local technique. We propose, in the second version, an integrated crossover rule that generates two children at a time using two different crossover rules. We introduce a local technique in the second version to obtain the third version. The fourth and #2;fth versions are based on the probabilistic adaptation of crossover rules. The ef#2;ciency and reliability of the new methods are evaluated through numerical experiments using a large test suite of both simple and dif#2;cult problems from the literature. Results indicate that the new hybrids are much better than their original counterparts both in reliability and ef#2;ciency. Therefore, the new hybrids proposed in this study offer an alternative to many currently available stochastic algorithms for solving global optimization problems in which the gradient information is not readily available.

Este trabalho tem como objetivo principal o desenvolvimento de uma estratégia de integração da otimização com o controle preditivo multivariável em uma camada. Os problemas de controle e otimização econômica são resolvidos simultaneamente em um mesmo algoritmo. A função objetivo econômica foi inserida no controlador na sua forma diferencial, ou seja, o gradiente da função objetivo econômica. O método foi testado por simulação para o caso do sistema reator regenerador da UFCC (Unit of Fluid Catalytic Cracker). Esta dissertação descreve a estratégia de otimização integrada ao controlador preditivo cuja função objetivo incorpora componentes dinâmicos e estáticos. Para a determinação das condições ótimas do processo no estado estacionário do conversor (unidade de craqueamento catalítico) foi utilizado um modelo empírico do processo. A melhor trajetória para conduzir o processo para o seu ponto ótimo de operação, maximizando lucro ou produto de maior valor agregado, desde que não sejam violadas as restrições de processo, é predita utilizando um modelo dinâmico, obtido através de dados de testes em degrau em um modelo rigoroso. Este modelo linear possibilitou a obtenção das funções de transferência do processo e o modelo em variáveis de estado. O ponto ótimo que é obtido na execução deste algoritmo, leva em consideração a não violação das restrições das variáveis manipuladas e controladas do processo, tanto para o estado estacionário como para o transiente do problema. O problema de otimização não linear resultante é resolvido através de uma rotina de programação quadrática da biblioteca do Matlab. Uma segunda alternativa apresentada para a estratégia de otimização deste trabalho, é a inclusão do gradiente reduzido na função objetivo do controlador quando são observadas violações das restrições das variáveis controladas. Os resultados simulados através de um modelo não linear rigoroso (Moro&Odloak,1995) mostram um bom desempenho dos algoritmos aqui desenvolvidos tanto com relação aos benefícios econômicos como na estabilização da unidade. / This dissertation aims to develop a strategy to integrate the optimization problem of the plant into the model predictive controller in a one layer strategy, for the real time optimization or online optimization. The control and the optimization of the process are computed simultaneously in the same algorithm. The gradient of the economic objective function is included in the cost function of the controller instead of in its regular form. Thereby, this work describes a predictive control strategy, which can be classified as a one layer strategy and whose objective function has to be optimized obeying constraints, which incorporates dynamic and static components. The optimal conditions of the process in the steady state are defined through the use of an empirical process model. Furthermore, the best trajectory to be followed in order to reach the optimal conditions, without violating the constraints, maximizing profit or the production of its more valuable product, is predicted through the use of the dynamic model, that can be obtained through a plant step test. As a result transfer function and state space models are obtained. The optimal operation point is achieved through the execution of the proposed algorithm. Therefore, the solution to the optimization/control problem will always be in a feasible region, in other words, without violating the process manipulated or controlled variable constraints for both stationary and transient states of the problem. The non-linear optimization problem resulted from the implementation of the proposed algorithm is solved through the quadratic programming routine from the Matlab library. The second online optimization strategy proposed in this work is one that considers the reduced gradient method algorithm modified to evaluate the predicted trajectory. As a result, any violation of the manipulated or controlled variable constraints is prevented and this variable is not considered in the next step of the calculation of the predicted trajectory or even in the search direction of the optimization. Finally the simulations results obtained through the use of a nonlinear rigorous model (Moro&Odloak,1995) presents good performance for the algorithms here proposed, not only related to economic benefits, but also in order to stabilize the unit.

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

Em diversas indústrias de manufatura (por exemplo, papeleira, moveleira, metalúrgica, têxtil) as decisões do dimensionamento de lotes interagem com outras decisões do planejamento e programação da produção, tais como, a distribuição, o processo de corte, entre outros. Porém, usualmente, essas decisões são tratadas de forma isolada, reduzindo o espaço de soluções e a interdependência entre as decisões, elevando assim os custos totais. Nesta tese, estudamos o processo produtivo de indústrias de móveis de pequeno porte, que consiste em cortar placas grandes disponíveis em estoque para obter diversos tipos de peças que são processadas posteriormente em outros estágios e equipamentos com capacidades limitadas para, finalmente, comporem os produtos demandados. Os problemas de dimensionamento de lotes e corte de estoque são acoplados em um modelo de otimização linear inteiro cujo objetivo é minimizar os custos de produção, estoque de produtos, preparação de máquinas e perda de matéria-prima. Esse modelo mostra o compromisso existente entre antecipar ou não a fabricação de certos produtos aumentando os custos de estoque, mas reduzindo a perda de matéria-prima ao obter melhores combinações entre as peças. O impacto da incerteza da demanda (composta pela carteira de pedidos e mais uma quantidade extra estimada) foi amortizado pela estratégia de horizonte de planejamento rolante e por variáveis de decisão que representam uma produção extra para a demanda esperada no melhor momento, visando a minimização dos custos totais. Dois métodos heurísticos são desenvolvidos para resolver uma simplificação do modelo matemático proposto, o qual possui um alto grau de complexidade. Os experimentos computacionais realizados com exemplares gerados a partir de dados reais coletados em uma indústria de móveis de pequeno porte, uma análise dos resultados, as conclusões e perspectivas para este trabalho são apresentados / In the many manufacturing industries (e.g., paper industry, furniture, steel, textile), lot-sizing decisions generally arise together with other decisions of planning production, such as distribution, cutting, scheduling and others. However, usually, these decisions are dealt with separately, which reduce the solution space and break dependence on decisions, increasing the total costs. In this thesis, we study the production process that arises in small scale furniture industries, which consists basically of cutting large plates available in stock into several thicknesses to obtain different types of pieces required to manufacture lots of ordered products. The cutting and drilling machines are possibly bottlenecks and their capacities have to be taken into account. The lot-sizing and cutting stock problems are coupled with each other in a large scale linear integer optimization model, whose objective function consists in minimizing different costs simultaneously, production, inventory, raw material waste and setup costs. The proposed model captures the tradeoff between making inventory and reducing losses. The impact of the uncertainty of the demand, which is composed with ordered and forecasting products) was smoothed down by a rolling horizon strategy and by new decision variables that represent extra production to meet forecasting demands at the best moment, aiming at total cost minimization. Two heuristic methods are proposed to solve relaxation of the mathematical model. Randomly generated instances based on real world life data were used for the computational experiments for empirical analyses of the model and the proposed solution methods

Dans ce mémoire, nous avons proposé une nouvelle approche pour la stabilisation des polytopes de systèmes SISO LTI avec un contrôleur d’ordre fixe. En utilisant le théorème des segments étendus, nous avons montré que, pour stabiliser un polytope de systèmes LTI, il suffit de stabiliser simultanément tous ses sommets en considérant une condition supplémentaire associée à ces derniers. Nous avons présenté également dans ce mémoire des méthodes originales pour la synthèse des contrôleurs simultanés en combinant les techniques polynomiales et l’optimisation linéaire. Avec les méthodes de synthèse proposées, nous avons montré non seulement que le contrôleur stabilise simultanément les sommets du polytope de systèmes (commande simultanée), mais également tous les systèmes appartenant au polytope (commande robuste). Il s’agit donc de contrôleur simultané et robuste pour les polytopes de systèmes. Avant de pouvoir énoncer des résultats concernant la commande simultanée de l’ensemble des segments d’un polytope de systèmes, nous avons étudié la commande d’un segment de systèmes avec un contrôleur LTI. Ce segment de systèmes est défini par les deux systèmes situés à chacune de ses extrémités et par un paramètre appartenant à un intervalle donné. La question de la stabilisation de cette classe de systèmes incertains a été formulée comme celle d’un problème de commande simultanée de deux systèmes situés aux extrémités avec une contrainte d’égalité des parties paires de chacun des deux polynômes caractéristiques en boucle fermée. Des conditions d’existence d’un régulateur stabilisant un segment de systèmes ont été données en utilisant deux critères de stabilité polynomiaux : le critère d’Hermite-Fujiwara et le critère d’Hermite-Biehler. Les résultats obtenus pour la commande simultanée d’un segment de systèmes ont été étendus à la stabilisation d’un polytope de systèmes. Ce problème a été réduit à la stabilisation des sommets du polytope avec un contrôleur simultané générant des polynômes caractéristiques en boucle fermée ayant la même partie paire (ou impaire). Des conditions d’existence de ces contrôleurs simultanés robustes d’ordre fixe sont données en utilisant les deux critères de stabilité mentionnés ci-dessus. Des algorithmes de synthèse sont également développés pour calculer ces régulateurs / In this manuscript, a new approach is proposed for the stabilization of polytopes of SISO LTI systems with a fixed order controller. Using the extended segment theorem, we have shown that to stabilize a polytope of LTI systems, it is sufficient to simultaneously stabilize all its vertices by considering an additional condition associated with them. In this paper, we have also presented original methods for the synthesis of simultaneous controllers by combining polynomial techniques and linear optimization. With the proposed synthesis methods, we have shown not only that the controller simultaneously stabilizes the vertices of the system polytope (simultaneous control), but also all systems belonging to the polytope (robust control). It is therefore a simultaneous and robust controller for system polytopes. Before stating results concerning the simultaneous control of all the segments of a polytope of systems, we have studied the control of a segment of systems with an LTI controller. This segment of systems is defined by the two systems located at each of its ends and by a parameter belonging to a given interval. The question of the stabilization of this class of uncertain systems has been formulated as that of a problem of simultaneous control of two systems located at the ends with an equal constraint of the even parts of each of the two characteristic polynomials in closed loop. Conditions of existence of a stabilizing controller for a segment of systems have been given using two polynomial stability criteria : the Hermite-Fujiwara criterion and the Hermite-Biehler criterion. The results obtained for the simultaneous control of a segment of systems have been extended to the stabilization of a polytope of systems. This problem has been reduced to the stabilization of the vertices of the polytope with a simultaneous controller generating closed loop characteristic polynomials having the same even (or odd) part. The existence conditions of these robust, fixed-order and simultaneous controllers are given using the two stability criteria mentioned above. Synthesis algorithms are also developed to design these controllers

Essa pesquisa propõe abordar o problema da alocação de medidores em sistemas de distribuição, de forma a reduzir os custos, garantindo o monitoramento dos distúrbios que afetam a qualidade da energia elétrica, mas também de obter alocações de medidores que facilitem a localização do curto-circuito. O problema de otimização é formulado por meio da programação linear inteira e resolvido por meio de algoritmos adequados para implementar cada modelagem matemática. São considerados sistemas testes com diferentes características, com destaque para a presença de linhas monofásicas e/ou bifásicas, linhas heterogêneas e geradores distribuídos acoplados na rede de distribuição principal. O problema de otimização clássico (reduzir custos garantindo o monitoramento) é retomado e é proposta uma modelagem mais geral, aplicável também a sistemas de distribuição com a presença de ramais monofásicos e/ou bifásicos. A parte da modelagem voltada para o problema da localização de faltas visa à redução das situações de múltipla estimação do local da falta, caracterizadas pela existência de múltiplos pontos no sistema com a mesma distância elétrica até a subestação. Esses dois modelos foram resolvidos separadamente, como dois problemas de otimização mono-objetivo, e em conjunto, sendo portanto, um problema multi-objetivo. As instâncias testadas incluem conjuntos de faltas de todos os tipos, simuladas ao longo das linhas do sistema, considerando a variação da impedância de falta. Os resultados apresentaram soluções de monitoramento para os dois sistemas testes considerados contendo entre 2 e 7 medidores. As soluções alcançadas são atrativas para a concessionária, pois requerem baixo custo de investimento e manutenção dos equipamentos e da infraestrutura de comunicação. A metodologia proposta apresentou alocações dispostas estrategicamente que garantem o monitoramento da qualidade da energia elétrica e minimizam o problema da múltipla estimação da falta, possibilitando o seu uso como suporte a um sistema localizador de faltas. / This research proposes to address the monitors allocation problem in distribution systems, aiming to reduce costs, ensuring the monitoring of disturbances affecting the power quality, but also to obtain monitoring systems that facilitate the process of fault location. The optimization problem is formulated through integer linear programming and solved by suitable algorithms for each mathematical modeling. Test systems with different characteristics, emphasis on the presence of single-phase and/or biphasic lines, heterogeneous lines and distributed generators were considered. The classic optimization problem (reduce costs by ensuring disturbance monitoring) is covered and a more general modeling is proposed, also applicable to distribution systems with the presence of single-phase and/or biphasic branches. The process of fault location is supported through the reduction of the multiple estimation of fault location, characterized by the existence of multiple points in the system with the same electrical distance to the substation. These two models were solved separately, as two mono-objective optimization problems, and together, in a multi-objective perspective. The tested instances include sets of faults of all types, simulated along the lines of the system, considering the fault impedance variation. The results presented monitoring solutions for the two test systems considered containing between 2 and 7 meters. The solutions achieved are attractive to the utility, as they require low investment and maintenance costs for equipment and communication infrastructure. The proposed methodology presented allocations strategically placed that guarantee the power quality monitoring and minimize the multiple estimation problem, allowing its use as support to a faults locator system.