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[pt] Em 2015 quase metade da população mundial vivia em área de risco de transmissão de malária. Neste mesmo ano, estimam-se 214 milhões de casos e 438 mil fatalidades. A principal forma de prevenção e redução da transmissão da malária é através do controle dos vetores, em particular, destaca-se o uso de mosquiteiros impregnados com inseticidas de longa duração (MILD). Neste contexto, os programas de distribuição de MILDS enfrentam desafios relacionados a obtenção de fundos e à gestão da cadeia de suprimentos como, por exemplo, incertezas associadas as atividades logísticas, as variáveis de oferta e demanda, e a volatilidade de preços. À luz destes fatos, esta dissertação propõe um modelo de otimização robusta, fundamentado em extensões dos arcabouços teóricos de Bertsimas e Sim (2004) e Fernandes et al. (2016), capaz de minimizar os custos de um programa de distribuição de mosquiteiros ou, dada uma restrição orçamentária, maximizar a distribuição para áreas prioritárias. Ademais, foi realizada uma revisão da literatura acadêmica acerca de modelos de otimização robusta aplicados no contexto da logística humanitária, onde alguns aspectos ainda pouco explorados foram ressaltados e considerados no modelo proposto. Um estudo de caso real é feito sobre um projeto feito do Fundo das Nações Unidas para crianças na Costa do Marfim. Os resultados apontam que conforme esperado, à medida que o nível de robustez considerado no modelo cresce, os custos totais também aumentam. Em contrapartida, o modelo robusto fornece soluções com maior flexibilidade na cadeia de suprimentos para a eventual necessidade de se ajustar os planos de compras e distribuição. Por fim, as soluções robustas foram avaliadas através de simulações de Monte Carlo, indicando que, conforme desejado, a probabilidade de viabilidade dos planos aumentam junto com nível de conservadorismo da solução. / [en] In 2015, almost half of the world population lived in areas at risk of malaria transmission. There were around 214 million malaria cases and 438,000 associated deaths. One of the major paths to prevent and reduce malaria transmission is through vector control, especially with the use of insecticide-treated nets (ITN). In this context, ITN distribution campaigns face several challenges, such as uncertainties related to funding, transportation, market and price volatility, which might be effectively tackled through long-term agreements and proper planning. However, that might not be an option for all humanitarian organizations and governments. Besides, considering uncertainties during budgetary planning is particular relevant. In this sense, a robust optimization model, based on Bertsimas and Sim (2004) and Fernandes et al. (2016) frameworks, is proposed to minimize the involved costs or, given a budget constraint, maximize the coverage of priority areas. A literature review on robust optimization applied to humanitarian logistics is conducted, in which aspects with less academic research attention are revealed and considered in the model, such as the simultaneous account of the aforementioned uncertainties and demand prioritization. A United Nations Children s Fund campaign in Ivory Coast is studied, and reveals that, as expected, as the robustness level increases so does the total costs. In return, the robust model generally provides a solution with improved supply chain flexibility, that might minimize efforts, in case it is necessary to adjust procurement and transportation plans when uncertainty is revealed. In addition, robust solutions were assessed through Monte Carlo simulations against several realizations of uncertain parameters values, pointing that, as desired, solution feasibility increases alongside the specified level of conservatism.

abstract: Corrective transmission topology control schemes are an essential part of grid operations and are used to improve the reliability of the grid as well as the operational efficiency. However, topology control schemes are frequently established based on the operator's past knowledge of the system as well as other ad-hoc methods. This research presents robust corrective topology control, which is a transmission switching methodology used for system reliability as well as to facilitate renewable integration. This research presents three topology control (corrective transmission switching) methodologies along with the detailed formulation of robust corrective switching. The robust model can be solved off-line to suggest switching actions that can be used in a dynamic security assessment tool in real-time. The proposed robust topology control algorithm can also generate multiple corrective switching actions for a particular contingency. The solution obtained from the robust topology control algorithm is guaranteed to be feasible for the entire uncertainty set, i.e., a range of system operating states. Furthermore, this research extends the benefits of robust corrective topology control to renewable resource integration. In recent years, the penetration of renewable resources in electrical power systems has increased. These renewable resources add more complexities to power system operations, due to their intermittent nature. This research presents robust corrective topology control as a congestion management tool to manage power flows and the associated renewable uncertainty. The proposed day-ahead method determines the maximum uncertainty in renewable resources in terms of do-not-exceed limits combined with corrective topology control. The results obtained from the topology control algorithm are tested for system stability and AC feasibility. The scalability of do-not-exceed limits problem, from a smaller test case to a realistic test case, is also addressed in this research. The do-not-exceed limit problem is simplified by proposing a zonal do-not-exceed limit formulation over a detailed nodal do-not-exceed limit formulation. The simulation results show that the zonal approach is capable of addressing scalability of the do-not-exceed limit problem for a realistic test case. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2015

Submitted by Marlene Santos (marlene.bc.ufg@gmail.com) on 2016-08-22T17:32:01Z No. of bitstreams: 2 Dissertação - Raina Ribeiro Marques - 2016.pdf: 13527010 bytes, checksum: 59c283fc484a08da24fa8c5c822eeeb3 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-08-23T11:54:05Z (GMT) No. of bitstreams: 2 Dissertação - Raina Ribeiro Marques - 2016.pdf: 13527010 bytes, checksum: 59c283fc484a08da24fa8c5c822eeeb3 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-08-23T11:54:05Z (GMT). No. of bitstreams: 2 Dissertação - Raina Ribeiro Marques - 2016.pdf: 13527010 bytes, checksum: 59c283fc484a08da24fa8c5c822eeeb3 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-07-05 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The robust optimization techniques can be used in problems subject to uncertainty in order to obtain robust solutions, that is, solutions that are less sensitive to the problem variations. Problems such as the facility location, specifically, the location of ambulances, have uncertainty in your data. Thus, an integer linear programming model for allocation of ambulances and stations is investigated considering that the service time is an uncertainty parameter, since this parameter is influenced by the nature of the call, traffic, or distance traveled, for example. It is proposed a model considering the application of a robust approach that controls the amount of uncertainty parameters related with the service time. A case study with real data provided by the fire department of the city of Catalão, Goiás, is performed on the models and the results show that the number of ambulances is greater than the current need, as pointed by the model without uncertainty. However, the results on the robust model show that the real number of ambulances in the city is able to serve a limited amount of demand, so for a maximum variation of the demand, the number of available ambulances are not able to support it. The model had worked well for the first two scenarios among the three ones tested, in which for the last scenario the model was quite sensitive to changes on the uncertainty parameters. / As técnicas de otimização robusta podem ser usadas em problemas sujeitos a incertezas com o intuito de obter soluções robustas, isto é, soluções menos sensíveis as variações do problema. Problemas como o de localização de instalações, especificamente, o de localização de ambulâncias possuem incertezas em seus dados. Assim, um modelo de programação linear inteira de localização de ambulâncias e bases é investigado considerando que o tempo de atendimento das chamadas é um parâmetro incerto, uma vez que este parâmetro é influenciado pela natureza da chamada, trânsito ou distância, por exemplo. Propõe-se um modelo a partir da aplicação de uma abordagem robusta que controla a quantidade de parâmetros incertos sobre o tempo de atendimento. A partir de um estudo de caso, com dados reais fornecidos pelo batalhão de corpo de bombeiros da cidade de Catalão, Goiás, considerado sobre os modelos, os resultados mostram que a quantidade de ambulâncias existente na corporação é maior que a necessidade atual, dado o modelo sem incertezas. Porém, os resultados sobre o modelo robusto apontaram que a quantidade de ambulâncias existentes na cidade é capaz de atender até certa variação do tempo de atendimento, sendo que para uma variação máxima, a quantidade de ambulâncias disponível não é capaz de suprir a demanda. O modelo se comportou bem para os dois primeiros cenários, dentre os três testados, sendo que para o último cenário o modelo se mostrou bastante sensível a variação dos parâmetros considerados incertos.

Submitted by Marlene Santos (marlene.bc.ufg@gmail.com) on 2016-09-28T13:05:06Z No. of bitstreams: 2 Dissertação - Tatiane Nunes da Costa - 2016.pdf: 5111300 bytes, checksum: 82d5b13d4c4d57e1f4850a62f149025c (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-09-30T13:03:40Z (GMT) No. of bitstreams: 2 Dissertação - Tatiane Nunes da Costa - 2016.pdf: 5111300 bytes, checksum: 82d5b13d4c4d57e1f4850a62f149025c (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-09-30T13:03:41Z (GMT). No. of bitstreams: 2 Dissertação - Tatiane Nunes da Costa - 2016.pdf: 5111300 bytes, checksum: 82d5b13d4c4d57e1f4850a62f149025c (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-08-25 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Most of the time, modern problems of engineering are nonlinear and, may also be subject to certain types of uncertainty that can directly influence in the answers of a particular system. In this sense, the stochastic methods have been thoroughly studied in order to get the best settings for a given project. Out of the stochastic techniques, the Method of Monte Carlo stands out and, especially the Latin Hypercube Sampling (LHS) which is a simpler version of the same. For this type of modeling, the Stochastic Finite Elements Method (SFEM) is becoming more frequently used, given that, an important tool for the discretization of stochastic fields can be given by the Karhunèn-Loève (KL) expansion. In this work, the following three case studies will be used: A discrete system of 2 g.d.l., a continuous system of a coupled beam type both in linear and nonlinear springs and a rotor consisting of axis, bearings and disks. In this sense, the influence of uncertainties in the systems studied will be checked, using for this, the LHS, SFEM and the KL expansion. The stochastic study in question will be used in the construction of the great project for the rotor problem already presented. / Problemas modernos de engenharia, na maioria das vezes são não lineares e, podem também estar sujeitos a certos tipos de incertezas que podem influenciar diretamente nas respostas de um dado sistema. Nesse sentido, os métodos estocásticos têm sido exaustivamente estudados com o intuito de se obter as melhores configurações para um dado projeto. Dentre as técnicas estocásticas, destacam-se o Método de Monte Carlo e, principalmente o Método Hipercubo Latino (HCL) que é uma versão mais simples do mesmo. Para este tipo de modelagem, é cada vez mais utilizado o Método dos Elementos Finitos Estocásticos (MEFE), sendo que uma importante ferramenta para a discretização dos campos estocásticos pode ser dada pela expansão de Karhunèn-Loève (KL). Neste trabalho serão utilizados três estudos de casos, quais sejam: Um sistema discreto de 2 g.d.l., um sistema contínuo do tipo viga acoplada tanto em molas lineares quanto não lineares e um rotor composto por eixo, mancais e discos. Nesse sentido, será verificada a influência de incertezas nos sistemas estudados, utilizando para isto, o método HCL, MEFE e a expansão de KL. O estudo estocástico em questão será empregado na construção do projeto ótimo robusto para o problema do rotor já apresentado.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-03-19T18:02:26Z No. of bitstreams: 1 saulocustodiodeaquinoferreira.pdf: 1364913 bytes, checksum: efa844157e53551961fc063ecd615818 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-03-21T13:30:23Z (GMT) No. of bitstreams: 1 saulocustodiodeaquinoferreira.pdf: 1364913 bytes, checksum: efa844157e53551961fc063ecd615818 (MD5) / Made available in DSpace on 2018-03-21T13:30:23Z (GMT). No. of bitstreams: 1 saulocustodiodeaquinoferreira.pdf: 1364913 bytes, checksum: efa844157e53551961fc063ecd615818 (MD5) Previous issue date: 2017-12-04 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O presente trabalho apresenta uma nova metodologia para a reconfiguração de sistemas de distribuição de energia elétrica através da aplicação da técnica matemática de decomposição de Benders. Esta técnica possibilita dividir o problema global em dois subproblemas, mestre e escravo, que se comunicam através de restrições denominadas cortes, geradas a partir de informações do segundo subproblema e incluídas no primeiro de forma iterativa até que um critério de convergência seja alcançado. O objetivo do problema é a minimização de perdas técnicas na rede de distribuição através de redefinição de sua topologia, observando-se restrições operativas como níveis de tensão, conectividade e radialidade. A redução de perdas é atrativa por implicar em melhores níveis de tensão, menores esforços aos equipamentos do sistema e maior confiabilidade, proporcionando, portanto, benefícios para as concessionárias de distribuição e maior qualidade da energia aos consumidores. O problema de reconfiguração é de programação não linear inteira mista, de difícil tratamento. Na metodologia proposta, o primeiro subproblema determina as decisões de chaveamento considerando-se apenas restrições lineares associadas à topologia da rede, enquanto que o segundo avalia a operação mediante a decisão do primeiro considerando as não linearidades e as restrições de balanço de carga. A vantagem da aplicação da técnica de decomposição é que ela permite a inclusão de incertezas operativas no modelo, como a representação da aleatoriedade das cargas demandadas a rede conforme presente nesse trabalho. A representação destas incertezas é realizada no contexto de reconfiguração robusta, em que a tomada de decisões sobre topologia da rede deve otimizar a operação para o conjunto de cenários pré-definidos. Sistemas conhecidos da literatura especializada são utilizados para a avaliação da metodologia proposta. / This work shows a new methodology for the reconfiguration of electric energy distribution systems by the application of the mathematical technique named Benders decomposition. This technique makes it possible to divide the global problem into two subproblems, master and slave, which communicate with each other through constraints called slices, generated from information of the second subproblem and included in the first one iteratively until a convergence criterion is reached. The objective of the problem is to minimize technical losses in the distribution network by redefining its topology, observing operational constraints such as levels of voltage, connectivity and radiality. Loss reduction is attractive because it implies better voltage levels, less system equipment effort and greater reliability, thus providing benefits to distribution dealers and higher energy quality to consumers. The reconfiguration problem is non-linear mixed integer programming, difficult to process. In the proposed methodology, the first subproblem determines the switching decisions considering only linear constraints associated with the network topology, while the second one evaluates the operation by means of the decision of the first recital considering the nonlinearities and the load balance constraints. The advantage of the application of the proposed technique is that the decomposition model is potential for the representation of operational uncertainties, as well as the load demands according to the present work. The representation of these uncertainties is carried out in the context of robust reconfiguration, in which the decision making on network topology must optimize the operation under scenarios of a predefined set. Systems known in the literature are used for the evaluation of the proposed methodology.

La présente thèse a pour objet d’explorer les potentialités d’une méthode prometteuse de l’optimisation conique, la programmation semi-définie positive (SDP), pour les problèmes de management d’énergie, à savoir relatifs à la satisfaction des équilibres offre-demande électrique et gazier.Nos travaux se déclinent selon deux axes. Tout d’abord nous nous intéressons à l’utilisation de la SDP pour produire des relaxations de problèmes combinatoires et quadratiques. Si une relaxation SDP dite « standard » peut être élaborée très simplement, il est généralement souhaitable de la renforcer par des coupes, pouvant être déterminées par l'étude de la structure du problème ou à l'aide de méthodes plus systématiques. Nous mettons en œuvre ces deux approches sur différentes modélisations du problème de planification des arrêts nucléaires, réputé pour sa difficulté combinatoire. Nous terminons sur ce sujet par une expérimentation de la hiérarchie de Lasserre, donnant lieu à une suite de SDP dont la valeur optimale tend vers la solution du problème initial.Le second axe de la thèse porte sur l'application de la SDP à la prise en compte de l'incertitude. Nous mettons en œuvre une approche originale dénommée « optimisation distributionnellement robuste », pouvant être vue comme un compromis entre optimisation stochastique et optimisation robuste et menant à des approximations sous forme de SDP. Nous nous appliquons à estimer l'apport de cette approche sur un problème d'équilibre offre-demande avec incertitude. Puis, nous présentons une relaxation SDP pour les problèmes MISOCP. Cette relaxation se révèle être de très bonne qualité, tout en ne nécessitant qu’un temps de calcul raisonnable. La SDP se confirme donc être une méthode d’optimisation prometteuse qui offre de nombreuses opportunités d'innovation en management d’énergie. / The present thesis aims at exploring the potentialities of a powerful optimization technique, namely Semidefinite Programming, for addressing some difficult problems of energy management. We pursue two main objectives. The first one consists of using SDP to provide tight relaxations of combinatorial and quadratic problems. A first relaxation, called “standard” can be derived in a generic way but it is generally desirable to reinforce them, by means of tailor-made tools or in a systematic fashion. These two approaches are implemented on different models of the Nuclear Outages Scheduling Problem, a famous combinatorial problem. We conclude this topic by experimenting the Lasserre's hierarchy on this problem, leading to a sequence of semidefinite relaxations whose optimal values tends to the optimal value of the initial problem.The second objective deals with the use of SDP for the treatment of uncertainty. We investigate an original approach called “distributionnally robust optimization”, that can be seen as a compromise between stochastic and robust optimization and admits approximations under the form of a SDP. We compare the benefits of this method w.r.t classical approaches on a demand/supply equilibrium problem. Finally, we propose a scheme for deriving SDP relaxations of MISOCP and we report promising computational results indicating that the semidefinite relaxation improves significantly the continuous relaxation, while requiring a reasonable computational effort.SDP therefore proves to be a promising optimization method that offers great opportunities for innovation in energy management.

La construction de modèles qui protègent contre les incertitudes dans les données, telles que la variabilité de l'information et l'imprécision est une des principales préoccupations en optimisation sous incertitude. L'incertitude peut affecter différentes domaines, comme le transport, les télécommunications, la finance, etc. ainsi que les différentes parts d'un problème d'optimisation, comme les coefficients de la fonction objectif et /ou les contraintes. De plus, l'ensemble des données incertaines peut être modélisé de différentes façons, comme sous ensembles compactes et convexes de l´espace réel de dimension n, polytopes, produits Cartésiens des intervalles, ellipsoïdes, etc.<p><p>Une des approches possibles pour résoudre des tels problèmes est de considérer les versions minimax regret, pour lesquelles résoudre un problème sous incertitude revient à trouver une solution qui s'écarte le moins possible de la valeur solution optimale dans tout les cas. <p><p>Dans le cas des incertitudes définies par intervalles, les versions minimax regret de nombreux problèmes combinatoires polynomiaux sont NP-difficiles, d'ou l'importance d'essayer de réduire l'espace des solutions. Dans ce contexte, savoir quand un élément du problème, représenté par une variable, fait toujours ou jamais partie d'une solution optimal pour toute réalisation des données (variables 1-persistentes et 0-persistentes respectivement), constitue une manière de réduire la taille du problème. Un des principaux objectifs de cette thèse est d'étudier ces questions pour quelques problèmes d'optimisation combinatoire sous incertitude.<p><p>Nous étudions les versions minimax regret du problème du choix de p éléments parmi m, de l'arbre couvrant minimum et des deux problèmes de plus court chemin. Pour de tels problèmes, dans le cas des incertitudes définis par intervalles, nous étudions le problème de trouver les variables 1- et 0-persistentes. Nous présentons une procédure de pre-traitement du problème, lequel réduit grandement la taille des formulations des versions de minimax regret.<p><p>Nous nous intéressons aussi à la version minimax regret du problème de programmation linéaire dans le cas où les coefficients de la fonction objectif sont incertains et l'ensemble des données incertaines est polyédral. Dans le cas où l'ensemble des incertitudes est défini par des intervalles, le problème de trouver le regret maximum est NP-difficile. Nous présentons des cas spéciaux ou les problèmes de maximum regret et de minimax regret sont polynomiaux. Dans le cas où l´ensemble des incertitudes est défini par un polytope, nous présentons un algorithme pour trouver une solution exacte au problème de minimax regret et nous discutons les résultats numériques obtenus dans un grand nombre d´instances générées aléatoirement.<p><p>Nous étudions les relations entre le problème de 1-centre continu et la version minimax regret du problème de programmation linéaire dans le cas où les coefficients de la fonction objectif sont évalués à l´aide des intervalles. En particulier, nous décrivons la géométrie de ce dernier problème, nous généralisons quelques résultats en théorie de localisation et nous donnons des conditions sous lesquelles certaines variables peuvet être éliminées du problème. Finalement, nous testons ces conditions dans un nombre d´instances générées aléatoirement et nous donnons les conclusions. / Doctorat en sciences, Orientation recherche opérationnelle / info:eu-repo/semantics/nonPublished

The thesis focuses on a mixed integer linear programming (MILP) formulation for a bi-level mathematical program with equilibrium constraints (MPEC) considering chance constraints. The particular MPEC problem relates to a power producer’s bidding strategy: maximize its total benefit through determining bidding price and bidding power output while considering an electricity pool’s operation and guessing the rival producer’s bidding price. The entire decision-making process can be described by a bi-level optimization problem. The contribution of our thesis is the MILP formulation of this problem considering the use of chance constrained mathematical program for handling the uncertainties. First, the lower-level poor operation problem is replaced by Karush-Kuhn-Tucker (KKT) optimality condition, which is further converted to an MILP formulation except a bilinear item in the objective function. Secondly, duality theory is implemented to replace the bilinear item by linear items. Finally, two types of chance constraints are examined and modeled in MILP formulation. With the MILP formulation, the entire MPEC problem considering randomness in price guessing can be solved using off-shelf MIP solvers, e.g., Gurobi. A few examples and a case study are given to illustrate the formulation and show the case study results.

This doctoral thesis investigates the application of simulation-based optimization (SBO) as an alternative to conventional optimization techniques when the inherent uncertainty and complex features of real manufacturing systems need to be considered. Inspired by a real-world production planning setting, we provide a general formulation of the situation as an extended knapsack problem. We proceed by proposing a solution approach based on single and multi-objective SBO models, which use simulation to capture the uncertainty and complexity of the manufacturing system and employ meta-heuristic optimizers to search for near-optimal solutions. Moreover, we consider the design of matheuristic approaches that combine the advantages of population-based meta-heuristics with mathematical programming techniques. More specifically, we consider the integration of mathematical programming techniques during the initialization stage of the single and multi-objective approaches as well as during the actual search process. Using data collected from a manufacturing company, we provide evidence for the advantages of our approaches over conventional methods (integer linear programming and chance-constrained programming) and highlight the synergies resulting from the combination of simulation, meta-heuristics and mathematical programming methods. In the context of the same real-world problem, we also analyse different single and multi-objective SBO models for robust optimization. We demonstrate that the choice of robustness measure and the sample size used during fitness evaluation are crucial considerations in designing an effective multi-objective model.