O objetivo deste trabalho é propor uma metodologia para a priorização de obras do sistema de distribuição de média tensão - até 36 kV - voltada ao cumprimento do índice de continuidade DEC e FEC imposto pela ANEEL, visando reduzir a quantidade de conjuntos que estão fora dos limites e que geram multas para a empresa frente ao órgão regulador e aos consumidores. Inicialmente, os diversos tipos de obras têm seu benefício calculado com o uso do Método do Payoff Simplificado, baseado no Método do Payoff COPEL, que consiste na extração somente da parcela relativa a interrupção, no DEC ou FEC, que determinada obra trará ao sistema. De posse deste benefício estimado, as obras foram analisadas de duas maneiras: geral e por conjunto. A análise Geral consiste em observar as obras propostas de maneira independente, preocupando-se com o benefício que elas trarão para a empresa como um todo. Na análise por conjunto, as obras são agrupadas por conjunto ANEEL, e o objetivo é a colocação da maior quantidade de conjuntos dentro dos limites de continuidade impostos pelo órgão regulador. A definição do objetivo apropriado é que irá orientar todo o processo de seleção das obras. Para isso são propostos modelos matemáticos, e para trabalhar com eles, foi utilizada como ferramenta a programação matemática. Foram realizadas simulações divididas em dois grupos: no primeiro, análise geral, a otimização é executada diretamente. Já no segundo, na análise por conjunto, é aplicada a programação multi-nível, mais especificamente, a programação em dois níveis (\"Bilevel Programming Problem\"), utilizando a programação inteira ou por metas (\"goal programming\"). Os resultados das simulações mostraram que o objetivo principal, que é tirar a maior quantidade de conjuntos da transgressão, foi atingido com menor orçamento com o uso da metodologia e dos modelos matemáticos empregados neste trabalho. A metodologia proposta pretende ser uma ferramenta adicional para as concessionárias de distribuição de energia elétrica que normalmente elaboram programas de obras específicos para redução de índices de continuidade ou quando pressionados pelo órgão regulador elaboram programas alternativos que competem pelo mesmo orçamento frente aos programas de obras tradicionais. / The purpose of this paper is to propose a methodology to prioritize planned works in the medium-voltage distribution system - up to 36 kV - aiming to adequate the DEC and FEC continuity index to the limits defined by the Brazilian regulatory agency (ANEEL) through the reduction of the number of sets out of target and consequently the reduction of monetary penalties to the utility imposed by the regulatory agency and consumers. At first every planned work has its benefit calculated by the Simplified Payoff Method which is based on COPEL Payoff Method and which consists in extracting just the interruption event from the DEC or FEC which a given work will bring to the system. Once you have got the estimated benefit, the planned works are analyzed in two different ways - general analysis and set analysis. General analysis consists in checking up proposed works independently, focusing on the benefit they will bring to the company as a whole. In the set analysis, works are grouped by \"ANEEL sets\" and the main aim is to gather the greatest number of sets into the continuity limits defined by the regulatory agency. The aims definition will lead the whole work selection process. To achieve that mathematical models are proposed and mathematical programming tools are used. Two groups of simulations were done - in the first one which is also called general analysis, optimization is executed directly. The second one called set analysis, is applied the bilevel programming using the integer programming or goal programming. The simulation results showed that the main aim which was to eliminate the greatest number of sets from the transgression was reached with a lower budget using the methodology and mathematical models. The proposed methodology intends to be an additional tool to the electricity distribution companies (utilities). These companies usually plan specific works to reduce the continuity index or when they are pressed by regulatory agencies, they plan alternative programs which compete by the same budget facing traditional work programs.

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

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Em um problema de natureza hierárquica, o nível mais influente toma certas decisões que afetam o comportamento dos níveis inferiores. Cada decisão do nível mais influente é considerada como fixa pelos níveis inferiores, que, com tais informações, tomam decisões que maximizam seus objetivos. Essas decisões podem influenciar os resultados obtidos pelo nível superior, que, por sua vez, também anseia pela decisão ótima. Em programação matemática, este problema é modelado como um problema de programação em níveis. Neste trabalho, consideramos uma classe particular de problemas de programação em níveis: os problemas de programação matemática em dois níveis. Estudamos uma técnica de resolução que consiste em substituir o problema do nível inferior por suas condições necessárias de primeira ordem, que podem ser formuladas de diversas maneiras, conforme as restrições de complementaridade são modificadas. O novo problema torna-se um problema de programação não linear e pode ser resolvido com algoritmos clássicos de otimização. Com o auxílio de condições de otimalidade de primeira e segunda ordem mostramos as relações entre o problema original e o problema reformulado. Aplicamos a técnica a problemas encontrados na literatura, analisamos o seu comportamento e apresentamos estratégias para eliminar certos inconvenientes encontrados. / In problems of hierarchical nature, the choices made by the most influential level - the so-called leader - affect the behavior of the lower levels. For each one of the leader\'s decisions there is a response from the lower levels, which maximizes the value of their respective objectives. These optimal choices, in return, may have influence in the results achieved by the leader, which also wants to make the optimal choices. In mathematical programming, this kind of problem is described as a multilevel programming problem. The present work considers a specific kind of multilevel problem: the bilevel mathematical problem. We study a resolution technique which consists in replacing the lower level problem by its necessary first order conditions, which can be formulated in various ways, as complementarity constraints occur and are modified. The new reformulated problem is a nonlinear programming problem which can be solved by classical optimization methods. Using first and second order optimality conditions, we show the relations between the original bilevel problem and the reformulated problem. We apply the described technique to solve a set of bilevel problems taken from the literature, analyse their behavior and discuss strategies to prevent undesirable difficulties that may arise.

The presented thesis discusses bilevel programming problems with the focus on solution algorithms. Bilevel programming problem is a hierarchical programming problem, where constraints contain another programming problem. We formulate basic bilevel optimization theory and describe three types of so- lution algorithms for bilevel programming problems: Algorithms based on KKT reformulation where the lower level is replaced by its KKT conditions, algorithms based on optimal value function where the bilevel programming problem is re- duced to a single level problem using the optimal value function of the lower level problem, and algorithms solving linear bilevel programming problems. Using real data for portfolio optimization bilevel programming problems, we compare ability to solve the problems and computing time of some of the pre- sented algorithms. 1

In the dissertation the solution approaches for different fuzzy optimization problems are presented. The single-level optimization problem with fuzzy objective is solved by its reformulation into a biobjective optimization problem. A special attention is given to the computation of the membership function of the fuzzy solution of the fuzzy optimization problem in the linear case. Necessary and sufficient optimality conditions of the the convex nonlinear fuzzy optimization problem are derived in differentiable and nondifferentiable cases. A fuzzy optimization problem with both fuzzy objectives and constraints is also investigated in the thesis in the linear case. These solution approaches are applied to fuzzy bilevel optimization problems. In the case of bilevel optimization problem with fuzzy objective functions, two algorithms are presented and compared using an illustrative example. For the case of fuzzy linear bilevel optimization problem with both fuzzy objectives and constraints k-th best algorithm is adopted.

Le génome est très organisé au sein du noyau cellulaire. Cette organisation et plus spécifiquement la localisation et la dynamique des gènes et chromosomes contribuent à l'expression génétique et la différenciation des cellules que ce soit dans le cas de pathologies ou non. L'exploration de cette organisation pourrait dans le futur aider à diagnostiquer et identifier de nouvelles cibles thérapeutiques. La conformation des chromosomes peut être analysée grâce au marquage ADN sur plusieurs sites et aux mesures de distances entre ces différents marquages fluorescents. Dans ce contexte, l'organisation spatiale du chromosome III de levure a montré que les deux types de cellules, MATa et MATalpha, sont différents. Par contre, les données issues de l'imagerie electronique sont bruitées à cause de la résolution des systèmes de microscope et du fait du caractère vivant des cellules observées. Dans cette thèse, nous nous intéressons au développement de méthodes de classification pour différencier les types de cellules sur la base de mesures de distances entre 3 loci du chromosome III et d'une estimation du bruit. Dans un premier temps, nous nous intéressons de façon générale aux problèmes de classification binaire à l'aide de SVM de grandes tailles et passons en revue les algorithmes d'optimisation stochastiques du premier ordre. Afin de prendre en compte les incertudes, nous proposons un modèle d'apprentissage qui ajuste sa robustesse en fonction du bruit. La méthode évite les situations où le modèle est trop conservatif et que l'on rencontre parfois avec les formulations SVM robustes. L'amplitude des pertubations liées au bruit qui sont incorporées dans le modèle est controllée par l'optimisation d'une erreur de généralisation. Aucune hypothèse n'est faite sur la distribution de probabilité du bruit. Seule une borne estimée des pertubations est nécessaire. Le problème peut s'écrire sous la forme d'un programme biniveaux de grande taille. Afin de le résoudre, nous proposons un algorithme biniveau qui réalise des déplacements stochastiques très peu coûteux et donc adapté aux problèmes de grandes tailles. La convergence de l'algorithme est prouvée pour une classe générale de problèmes. Nous présentons des résultats numériques très encourageants qui confirment que la technique est meilleure que l'approche SOCP (Second Order Cone Programming) pour plusieurs bases de données publiques. Les expériences numériques montrent également que la nonlinéarité additionnelle générée par l'incertitude sur les données pénalise la classification des chromosomes et motivent des recherches futures sur une version nonlinéaire de la technique proposée. Enfin, nous présentons également des résultats numériques de l'algorithme biniveau stochastique pour la sélection automatique de l'hyperparamètre de pénalité dans les SVM. L'approche évite les coûteux calculs que l'on doit inévitablement réaliser lorsque l'on effectue une validation croisée sur des problèmes de grandes tailles. / The genome is highly organized within the cell nucleus. This organization, in particular the localization and dynamics of genes and chromosomes, is known to contribute to gene expression and cell differentiation in normal and pathological contexts. The exploration of this organization may help to diagnose disease and to identify new therapeutic targets. Conformation of chromosomes can be analyzed by distance measurements of distinct fluorescently labeled DNA sites. In this context, the spatial organization of yeast chromosome III was shown to differ between two cell types, MATa and MATa. However, imaging data are subject to noise, due to microscope resolution and the living state of yeast cells. In this thesis, the aim is to develop new classification methods to discriminate two mating types of yeast cells based on distance measurements between three loci on chromosome III aided by estimation the bound of the perturbations. We first address the issue of solving large scale SVM binary classification problems and review state of the art first order optimization stochastic algorithms. To deal with uncertainty, we propose a learning model that adjusts its robustness to noise. The method avoids over conservative situations that can be encountered with worst case robust support vector machine formulations. The magnitude of the noise perturbations that is incorporated in the model is controlled by optimizing a generalization error. No assumption on the distribution of noise is taken. Only rough estimates of perturbations bounds are required. The resulting problem is a large scale bi-level program. To solve it, we propose a bi-level algorithm that performs very cheap stochastic gradient moves and is therefore well suited to large datasets. The convergence is proven for a class of general problems. We present encouraging experimental results confirming that the technique outperforms robust second order cone programming formulations on public datasets. The experiments also show that the extra nonlinearity generated by the uncertainty in the data penalizes the classification of chromosome data and advocates for further research on nonlinear robust models. Additionally, we provide the experimenting results of the bilevel stochastic algorithm used to perform automatic selection of the penalty parameter in linear and non-linear support vector machines. This approach avoids expensive computations that usually arise in k-fold cross validation.

In der Dissertation werden Zwei-Ebenen-Optimierungsaufgaben mit spezieller Struktur untersucht. Von Interesse sind hierbei für den sogenannten pessimistischen Lösungszugang Existenzresultate für Lösungen, die Eckpunkteigenschaft einer Lösung, eine Regularisierungstechnik, Optimalitätsbedingungen sowie für den linearen Fall ein Verfahren zur Bestimmung einer global pessimistischen Lösung. Beim optimistischen Lösungszugang wird zunächst eine Verallgemeinerung des Lösungsbegriffes angegeben. Anschließend finden sich Betrachtungen zur Komplexität des Problems, zu Optimalitätsbedingungen sowie ein Abstiegs- und Branch&Bound-Verfahren für den linearen Fall wieder. Den Abschluss der Arbeit bilden ein Anwendungsbeispiel und numerische Testrechnungen.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-09-04T12:20:42Z No. of bitstreams: 1 erickmariodonascimentooliveira.pdf: 3492871 bytes, checksum: 845fa85f6d95efe2e7ad13563f342bc3 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-09-04T13:21:49Z (GMT) No. of bitstreams: 1 erickmariodonascimentooliveira.pdf: 3492871 bytes, checksum: 845fa85f6d95efe2e7ad13563f342bc3 (MD5) / Made available in DSpace on 2018-09-04T13:21:49Z (GMT). No. of bitstreams: 1 erickmariodonascimentooliveira.pdf: 3492871 bytes, checksum: 845fa85f6d95efe2e7ad13563f342bc3 (MD5) Previous issue date: 2018-06-26 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho é apresentado o comportamento do algoritmo IED quando aplicado a problemas de programação em dois níveis. Para isso, o problema do seguidor é substituído pelas condições necessárias de primeira ordem de Karush-Kuhn-Tucker e, dessa maneira, o problema de programação em dois níveis é transformado em um problema de otimização com restrições não lineares. Dessa forma, as condições necessárias para utilização do algoritmo IED (Interior Epigraph Directions) são satisfeitas. Esse método tem como característica resolver problemas de otimização não convexa e não diferenciáveis via utilização da técnica de dualidade Lagrangiana, onde as funções de restrições são introduzidas na função objetivo para formar a função Lagrangiana. Além disso, o método considera o problema dual induzido por um esquema generalizado da dualidade Lagrangiana aumentada e obtém a solução primal produzindo uma sequência de pontos no interior do epígrafo da função dual. Dessa forma, o valor da função dual, em algum ponto do espaço dual, é dado pela minimização da Lagrangiana. Por fim, experimentos numéricos são apresentados em relação à utilização do algoritmo IED em problemas de programação em dois níveis encontrados na literatura. / This work presents the behavior of the IED algorithm when applied to bilevel programming problems. For this, the follower problem is replaced by the first-order necessary Karush-Kuhn-Tucker’s conditions and thus, the problem of bilevel programming turns into an optimization problem with non-linear constraints. Thus, the conditions required for use of the IED (Interior Epigraph Directions) algorithm are satisfied. This method has the characteristic of solving non-convex and non-differentiable optimization problems using the Lagrangian duality technique, where the constraint functions are introduced into the objective function for formulation of the Lagrangian. Furthermore, the method considers the dual problem induced by a generalized scheme of augmented Lagrangian duality and obtains the primal solution by producing a sequence of points inside the dual function epigraph. Then the value of the dual function, at some point in the dual space, is given by Lagrangian minimization. Finally, numerical experiments are presented showing the use of the IED algorithm in bilevel programming problems found in the literature.

In this thesis we study the problem of road taxation. This problem consists in finding the toll on the roads belonging to the government or a private company in order to maximize the revenue. An optimal taxation policy consists in determining level of tolls low enough to favor the use of toll arcs, and high enough to get important revenues. Since there are twolevels of decision, the problem is formulated as a bilevel bilinear program. / Doctorat en sciences, Orientation recherche opérationnelle / info:eu-repo/semantics/nonPublished