Este trabalho tem como objetivo avaliar a viabilidade da aplicação de técnicas de otimização robusta (OR) no planejamento da operação de reservatórios para geração de energia hidrelétrica. A OR é uma técnica de otimização que visa encontrar resultados que sejam menos sensíveis às incertezas nas variáveis do modelo através da minimização da variância da função objetivo para diferentes cenários. Desta forma foi desenvolvido um modelo de otimização robusta aplicado à operação de reservatórios para a geração de energia hidrelétrica, chamado HIDRO-OR, utilizando o software General Algebraic Modeling System (GAMS). Para estudo de caso foram utilizados os dados da UHE Sinop, a ser instalada no rio Teles Pires MT. Inicialmente foi realizada uma análise de sensibilidade utilizando diferentes combinações dos coeficientes de ponderação da função objetivo e três conjuntos de cenários. Nesta abordagem, o modelo resultou em vertimentos indesejados para realizar a diminuição do desvio padrão dos resultados entre os diferentes cenários. Uma solução encontrada para o problema foi realizar a otimização em duas etapas. Na primeira etapa ocorre a otimização robusta propriamente dita e são fixados os resultados para o primeiro mês de operação. Na segunda etapa, apenas a função objetivo principal é otimizada e, assim, são corrigidos os vertimentos indesejados. No entanto, com a otimização em duas etapas, não ocorreram mudanças na operação do reservatório para os diferentes coeficientes de ponderação. Ao final do trabalho conclui-se que, apesar dos resultados da análise de sensibilidade terem sido praticamente iguais com a otimização em duas etapas, estes podem ser considerados robustos pois são factíveis para todos os cenários. Por fim, são realizadas sugestões para a continuidade das pesquisas utilizando as técnicas de OR para a operação de usinas hidrelétricas. / This work aims to evaluate the feasibility of robust optimization techniques (OR) for reservoir management for hydropower production. The OR is an optimization technique which aims to find results that are less sensitive to the randomness of variables in the model by minimizing the variance of the objective function for different scenarios. One OR model was developed to the operation of reservoirs for hydropower production, called HYDRO-OR, using the software General Algebraic Modeling System (GAMS). As study case, data from the Sinop hydropower plant were used, which will be constructed in the Teles Pires river - MT. First, a sensitivity analysis was performed using different combinations of weigh coefficients of the objective function with three sets of scenarios. Preliminary results in this approach showed that the model resulted in unwanted spills to force the reduction of the standard deviation of the results from different scenarios. To correct this, the model was reconfigured to perform the optimization in two stages, the first one being the OR itself in which the results were obtained for the first month of planning. In the second step, the model was optimized again for subsequent months. In this case the model corrected the unnecessary spills but the results were quite similar for the three combinations of the weight coefficients. However the results can be considered robust because it is feasible for all scenarios. Finally, suggestions are made for further studies using the techniques of OR for the operation of hydropower plants.

O setor sucroalcooleiro vem ganhando cada vez mais destaque no agronegócio brasileiro. O Produto Interno Bruto (PIB) do setor na safra de 2015 gerou mais de US$113 bilhões ao longo de toda cadeia produtiva (UNICA, 2016). Esse período de ascensão é acompanhado de novos desafios e oportunidades, o que torna o setor um tema fértil para a pesquisa acadêmica, teórica e aplicada. Dada à pluralidade do setor que hoje extravasa seu nicho tradicional, álcool e açúcar, e atua cada vez mais intensamente nos setores energéticos, eletricidade e combustíveis renováveis, faz-se necessário a incorporação da nova dinâmica de produção que esses produtos trazem à realidade administrativa do setor. Assim, além de discutir teoria e metodologia correlatas à modelagem matemática empregada no auxilio à gestão do setor, esse trabalho visa contribuir com a literatura, incorporando e discutindo as novas possibilidades produtivas que a produção de biogás trás ao mix de produção tradicional. As principais ferramentas utilizadas nessa análise são a teoria de portfólios e o arcabouço teórico da otimização robusta. A partir dessas técnicas construiu-se um modelo de otimização onde se busca a minimização do risco para um dado retorno, princípio da teoria de portfólios, avaliando o risco com o CVaR, uma medida de risco mais adequada do que a tradicional variância. Construído esse modelo, analisa-se o papel do biogás, um produto ainda pouco usual nas usinas brasileiras, no portfólio produtivo de uma usina hipotética. Com base nesse modelo implementou-se as técnicas de otimização robusta com o intuito de aferir se os resultados verificados no modelo determinístico se mantém no caso robusto. / The sugarcane sector is gaining a huge prominence in the Brazilian agribusiness. The GDP of the sector in 2015 crop was over then US$ 113 billion along the entire production chain (UNICA, 2016). This auspicious period is accompanied by new challenges and opportunities, which makes the sector a hot field for academic research, theoretical and applied. Given the industry plurality which today goes beyond its traditional niche, alcohol and sugar, the sector is increasingly strongly its share in the energy sector, electricity and renewable fuels. Thus it is necessary to incorporate the new dynamic of production that these products bring to the administrative reality of the sector. Therefore, in addition to discussing theory and methodology related to the mathematical modeling used as a support to sector management, this work aims to contribute to the literature by incorporating and discussing the new production possibilities that biogas production brings to the traditional production mix. The main tools used in this analysis are the portfolio theory and the theoretical and applied framework of robust optimization. From these techniques it is built up an optimization model where one seeks to minimize risk for a given return, the principle of portfolio theory, assessing the risk with CVaR, a better measure of risk than traditional variance. Through this model, the role of biogas, an unusual product in the Brazilian plants, is analyzed considering a hypothetical plant. Based on this model it is implemented robust optimization techniques in order to assess whether the results observed in the deterministic model remains in the case robust.

We propose a general methodology based on robust optimization to address the problem of optimally controlling a supply chain subject to stochastic demand in discrete time. The attractive features of the proposed approach are: (a) It incorporates a wide variety of phenomena, including demands that are not identically distributed over time and capacity on the echelons and links; (b) it uses very little information on the demand distributions; (c) it leads to qualititatively similar optimal policies (basestock policies) as in dynamic programming; (d) it is numerically tractable for large scale supply chain problems even in networks, where dynamic programming methods face serious dimensionality problems; (e) in preliminary computation experiments, it often outperforms dynamic programming based solutions for a wide range of parameters. / Singapore-MIT Alliance (SMA)

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 67-72).

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. 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. 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. 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. 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. 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.

A previous approach to robust intensity-modulated radiation therapy (IMRT) treatment planning for moving tumours in the lung involves solving a single planning problem before treatment and using the resulting solution in all of the subsequent treatment sessions. In this thesis, we develop two adaptive robust IMRT optimization approaches for lung cancer, which involve using information gathered in prior treatment sessions to guide the reoptimization of the treatment for the next session. The first method is based on updating an estimate of the uncertain effect, while the second is based on additionally updating the dose requirements to account for prior errors in dose. We present computational results using real patient data for both methods and an asymptotic analysis for the first method. Through these results, we show that both methods lead to improvements in the final dose distribution over the traditional robust approach, but differ greatly in their daily dose performance.

A previous approach to robust intensity-modulated radiation therapy (IMRT) treatment planning for moving tumours in the lung involves solving a single planning problem before treatment and using the resulting solution in all of the subsequent treatment sessions. In this thesis, we develop two adaptive robust IMRT optimization approaches for lung cancer, which involve using information gathered in prior treatment sessions to guide the reoptimization of the treatment for the next session. The first method is based on updating an estimate of the uncertain effect, while the second is based on additionally updating the dose requirements to account for prior errors in dose. We present computational results using real patient data for both methods and an asymptotic analysis for the first method. Through these results, we show that both methods lead to improvements in the final dose distribution over the traditional robust approach, but differ greatly in their daily dose performance.

We introduce methods for dealing with linear programming (LP) problems with uncertain data, using the notion of weighted analytic centers. Our methods are based on high interaction with the decision maker (DM) and try to find solutions which satisfy most of his/her important criteria/goals. Starting with the drawbacks of different methods for dealing with uncertainty in LP, we explain how our methods improve most of them. We prove that, besides many practical advantages, our approach is theoretically as strong as robust optimization. Interactive cutting-plane algorithms are developed for concave and quasi-concave utility functions. We present some probabilistic bounds for feasibility and evaluate our approach by means of computational experiments.

The goal of robust speech recognition is to maintain satisfactory recognition accuracy under mismatched operating conditions. This dissertation addresses the robustness issue from two directions. In the first part of the dissertation, we propose the Gauss-Newton method as a unified approach to estimating noise parameters for use in prevalent nonlinear compensation models, such as vector Taylor series (VTS), data-driven parallel model combination (DPMC), and unscented transform (UT), for noise-robust speech recognition. While iterative estimation of noise means in a generalized EM framework has been widely known, we demonstrate that such approaches are variants of the Gauss-Newton method. Furthermore, we propose a novel noise variance estimation algorithm that is consistent with the Gauss-Newton principle. The formulation of the Gauss-Newton method reduces the noise estimation problem to determining the Jacobians of the corrupted speech parameters. For sampling-based compensations, we present two methods, sample Jacobian average (SJA) and cross-covariance (XCOV), to evaluate these Jacobians. The Gauss-Newton method is closely related to another noise estimation approach, which views the model compensation from a generative perspective, giving rise to an EM-based algorithm analogous to the ML estimation for factor analysis (EM-FA). We demonstrate a close connection between these two approaches: they belong to the family of gradient-based methods except with different convergence rates. Note that the convergence property can be crucial to the noise estimation in many applications where model compensation may have to be frequently carried out in changing noisy environments to retain desired performance. Furthermore, several techniques are explored to further improve the nonlinear compensation approaches. To overcome the demand of the clean speech data for training acoustic models, we integrate nonlinear compensation with adaptive training. We also investigate the fast VTS compensation to improve the noise estimation efficiency, and combine the VTS compensation with acoustic echo cancellation (AEC) to mitigate issues due to interfering background speech. The proposed noise estimation algorithm is evaluated for various compensation models on two tasks. The first is to fit a GMM model to artificially corrupted samples, the second is to perform speech recognition on the Aurora 2 database, and the third is on a speech corpus simulating the meeting of multiple competing speakers. The significant performance improvements confirm the efficacy of the Gauss-Newton method to estimating the noise parameters of the nonlinear compensation models. The second research work is devoted to developing more effective models to take full advantage of heterogeneous speech data, which are typically collected from thousands of speakers in various environments via different transducers. The proposed synchronous HMM, in contrast to the conventional HMMs, introduces an additional layer of substates between the HMM state and the Gaussian component variables. The substates have the capability to register long-span non-phonetic attributes, such as gender, speaker identity, and environmental condition, which are integrally called speech scenes in this study. The hierarchical modeling scheme allows an accurate description of probability distribution of speech units in different speech scenes. To address the data sparsity problem in estimating parameters of multiple speech scene sub-models, a decision-based clustering algorithm is presented to determine the set of speech scenes and to tie the substate parameters, allowing us to achieve an excellent balance between modeling accuracy and robustness. In addition, by exploiting the synchronous relationship among the speech scene sub-models, we propose the multiplex Viterbi algorithm to efficiently decode the synchronous HMM within a search space of the same size as for the standard HMM. The multiplex Viterbi can also be generalized to decode an ensemble of isomorphic HMM sets, a problem often arising in the multi-model systems. The experiments on the Aurora 2 task show that the synchronous HMMs produce a significant improvement in recognition performance over the HMM baseline at the expense of a moderate increase in the memory requirement and computational complexity.

Dans cette thèse, nous nous intéressons à l’optimisation robuste. Plus précisément,nous nous intéresserons aux problèmes linéaires mixtes bi-niveaux, c’est à dire aux problèmes dans lesquels le processus de décision est divisé en deux parties : dans un premier temps, les valeurs optimales des variables dites "de décisions" seront calculées ; puis, une fois que l’incertitude sur les données est levée, nous calculerons les valeurs des variables dites "de recours". Dans cette thèse, nousnous limiterons au cas où les variables de deuxième étape, dites "de recours", sontcontinues.Dans la première partie de cette thèse, nous nous concentrerons sur l’étudethéorique de tels problèmes. Nous commencerons par résoudre un problème linéairesimplifié dans lequel l’incertitude porte seulement sur le membre droit descontraintes, et est modélisée par un polytope bien particulier. Nous supposerons enoutre que le problème vérifie une propriété dite "de recours complet", qui assureque, quelles que soient les valeurs prises par les variables de dcisions, si ces dernières sont admissibles, alors le problème admet toujours une solution réalisable, et ce, quelles que soient les valeurs prises par les paramètres incertains. Nous verrons alors une méthode permettant, à partir d’un programme robuste quelconque, de se ramener à un programme robuste équivalent dont le problème déterministe associévérifie la propriété de recours complet. Avant de traiter le cas général, nous nouslimiterons d’abord au cas o les variables de décisions sont entières. Nous testeronsalors notre approche sur un problème de production. Ensuite, après avoir remarquéque l’approche développée dans les chapitres précédents ne se généralisait pasnaturellement aux polytopes qui n’ont pas des points extrmes 0-1, nous montreronscomment, en utilisant des propriétés de convexité du problème, résoudre le problème robuste dans le cas général. Nous en déduirons alors des résultats de complexité sur le problème de deuxième étape, et sur le problème robuste. Dans la suite de cette partie nous tenterons d’utiliser au mieux les informations probabilistes que l’on a sur les données aléatoires pour estimer la pertinence de notre ensemble d’incertitude.Dans la deuxième partie de cette thèse, nous étudierons un problème de conceptionde parc hybride de production d’électricité. Plus précisément, nous chercheronsà optimiser un parc de production électrique constitué d’éoliennes, de panneauxsolaires, de batteries et d’un générateur à diesel, destiné à répondre à unedemande locale d’énergie électrique. Il s’agit de déterminer le nombre d’éoliennes,de panneaux solaires et de batteries à installer afin de répondre à la demande pourun cot minimum. Cependant, les données du problème sont très aléatoires. En effet,l’énergie produite par une éolienne dépend de la force et de la direction du vent ; celle produite par un panneau solaire, de l’ensoleillement et la demande en électricité peut tre liée à la température ou à d’autres paramètres extérieurs. Pour résoudre ce problème, nous commencerons par modéliser le problème déterministeen un programme linéaire mixte. Puis nous appliquerons directement l’approche de la première partie pour résoudre le problème robuste associé. Nous montrerons ensuite que le problème de deuxième étape associé, peut se résoudre en temps polynomial en utilisant un algorithme de programmation dynamique. Enfin, nous donnerons quelques généralisations et améliorations pour notre problème. / Robust optimization is a recent approach to study problems with uncertain datathat does not rely on a prerequisite precise probability model but on mild assumptionson the uncertainties involved in the problem.We studied a linear two-stage robustproblem with mixed-integer first-stage variables and continuous second stagevariables. We considered column wise uncertainty and focused on the case whenthe problem doesn’t satisfy a "full recourse property" which cannot be always satisfied for real problems. We also studied the complexity of the robust problemwhich is NP-hard and proved that it is actually polynomial solvable when a parameterof the problem is fixed.We then applied this approach to study a stand-alonehybrid system composed of wind turbines, solar photovoltaic panels and batteries.The aim was to determine the optimal number of photovoltaic panels, wind turbinesand batteries in order to serve a given demand while minimizing the total cost of investment and use. We also studied some properties of the second stage problem, in particular that the second stage problem can be solvable in polynomial time using dynamic programming.