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Prefetching control for on-demand contents distribution : a Markov decision process study / Contrôle du préchargement pour la distribution de contenus à la demande : une approche par les processus de décision markoviensMorad, Olivia 17 September 2014 (has links)
Le contexte de la thèse porte sur le contrôle des réseaux de distribution de contenu à la demande. La performance des systèmes distribués interactifs dépend essentiellement sur la prévision du comportement de l'utilisateur et la bande passante en tant que ressource de réseau critique. Le préchargement est une approche prédictive bien connu dans le World Wide Web ce qui évite les délais de réponse en exploitant un temps d'arrêt que permet d'anticiper les futures demandes de l'utilisateur et prend avantage des ressources réseau disponibles. Le contrôle de préchargement est une opération vitale pour les systèmes à la demande interactifs où la réponse instantanée est le facteur crucial pour la réussite du système. Le contrôleur en ce type de système interactif fonctionne dans un environnement incertain et rend séquences de décisions à court et long terme effets stochastique. La difficulté est alors de déterminer à chaque état du système les contenus préchargés dans le cache. Le plan de préchargement pendant une session en flux continu interactif peut être modélisé comme un problème de décision séquentielle par les processus de décision de Markov (MDP). Nous nous concentrons sur le problème de contrôle de préchargement, dans lequel le contrôleur cherche à atteindre l'état du système à coût zéro aussi vite que possible. Nous modélisons ce problème de contrôle comme un problème de programmation dynamique stochastique négatif dans lequel nous minimisons le coût total prévu. Dans ce contexte, nous avons abordé les questions de recherche suivantes: 1) Comment fournir un politique de préchargement optimale/ approximative optimale qui maximise l'utilisation de la bande passante tout en minimisant les coûts de blocage et de la latence de l'utilisateur engagés sur le chemin? 2) Comment exploiter la structure du modèle de contrôle de préchargement pour aider efficacement calculer la politique de contrôle de préchargement avec la réduction des efforts de calcul et la mémoire de stockage? 3) Comment mener une étude d'évaluation pour évaluer le préchargement de différents algorithmes heuristiques basée sur le contexte de l'optimisation au lieu du cadre de l'empirique / simulation. Pour l'étude de notre problème de recherche, nous avons développé notre modèle MDP de préchargement, PREF-CT, nous avons établi ses propriétés théoriques et nous avons résolu par l'algorithme Value Iteration comme algorithme MDP pour calculer la politique de préchargement optimale. Pour calcul de la politique de préchargement optimale efficace, nous avons détecté une structure spéciale qui réalise un modèle de contrôle plus compact. Cette structure spéciale permet de développer deux algorithmes différents stratégiquement qui améliorent la complexité du calcul de la politique de préchargement optimale: - la première est « ONE-PASS » le second est « TREE-DEC ». Pour surmonter le problème de la dimensionnalité résultant du calcul de la politique de préchargement optimale, nous avons proposé l'algorithme de préchargement heuristique: « Relevant Blocks Prefetching » (RBP). Pour évaluer et comparer le préchargement politiques calculés par des algorithmes de préchargement heuristiques différents, nous avons présenté un cadre fondé sur des différentes mesures de performance. Nous avons appliqué le cadre proposé sous différentes configurations de coûts et différents comportements des utilisateurs pour évaluer les politiques de préchargement calculées par notre algorithme de préchargement proposé; RBP. Par rapport aux politiques de préchargement optimales, l'analyse expérimentale a prouvé des performances significatives des politiques de préchargement de l'heuristique du RBP algorithme. En outre, l'algorithme heuristique de préchargement; RBP se distingue par une propriété de clustériser qui est important pour réduire considérablement la mémoire nécessaire pour stocker la politique de préchargement. / The thesis context is concerned with the control of theOn-demand contents distribution networks. The performance of suchinteractive distributed systems basically depends on the prediction ofthe user behavior and the bandwidth as a critical network resource.Prefetching is a well-known predictive approach in the World Wide Webwhich avoids the response delays by exploiting some downtime thatpermits to anticipate the user future requests and takes advantage ofthe available network resources. Prefetching control is a vitaloperation for the On-demand interactive systems where the instantaneousresponse is the crucial factor for the system success. The controller insuch type of interactive system operates in an uncertain environment andmakes sequences of decisions with long and short term stochasticeffects. The difficulty, then, is to determine at every system statewhich contents to prefetch into the cache. The prefetching plan duringan interactive streaming session can be modeled as a sequential decisionmaking problem by a Markov Decision Process (MDP). We focus on theprefetching control problem in which the controller seeks to reach aZero-Cost system state as quickly as possible. We model this controlproblem as a Negative Stochastic Dynamic Programming problem in which weminimize the undiscounted total expected cost. Within this context, weaddressed the following research questions: 1) How to provide anoptimal/approximate-optimal prefetching policy that, maximizes thebandwidth utilization while minimizes the user's blocking and latencycosts incurred along the way? 2) How to exploit structure in theprefetching control model to help efficiently compute such prefetchingcontrol policy with both computational efforts and storage memoryreduction? 3) How to conduct a performance evaluation study to evaluatedifferent prefetching heuristic algorithms based on the context of thecontrol optimization rather than the context of theempirical/simulation. For studying our research problem, we developedour MDP prefetching control model, PREF-CT, we established itstheoretical properties and we solved it by the Value Iteration algorithmas MDP algorithm for computing the optimal prefetching policy. Forcomputing the optimal prefetching policy efficiently, we detected aspecial structure that achieves more compact control model. This specialstructure permits to develop two strategically different algorithmswhich improve the complexities of computing the optimal prefetchingpolicy: - the first one is the ONE-PASS which is based mainly on solvinga system of linear equations simultaneously in only one iteration,whereas the second is the TREE-DEC which is based on Markov decisiontree decomposition in which sequential sets of systems of equations aresolved. For overcoming the problem of the curse of dimensionalityresulting from the computation of the optimal prefetching policy, weproposed the prefetching heuristic algorithm: the Relevant BlocksPrefetching algorithm (RBP). For evaluating and comparing prefetchingpolicies computed by different prefetching heuristic algorithms, wepresented a framework based on different performance measures. Weapplied the suggested framework under different costs configurations anddifferent user behaviors to evaluate the prefetching policies computedby our proposed prefetching heuristic algorithm; the RBP. Compared tothe optimal prefetching policies, the experimental analysis provedsignificant performance of the prefetching policies of the RBP heuristicalgorithm. In addition, the RBP prefetching heuristic algorithm isdistinguished by a clustering property which is of importance to reducesignificantly the memory necessary to store the prefetching policy tothe controller.
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Estratégias para otimização do algoritmo de Iteração de Valor Sensível a Risco / Strategies for optimization of Risk Sensitive Value Iteration algorithmIgor Oliveira Borges 11 October 2018 (has links)
Processos de decisão markovianos sensíveis a risco (Risk Sensitive Markov Decision Process - RS-MDP) permitem modelar atitudes de aversão e propensão ao risco no processo de tomada de decisão usando um fator de risco para representar a atitude ao risco. Para esse modelo, existem operadores que são baseados em funções de transformação linear por partes que incluem fator de risco e fator de desconto. Nesta dissertação são formulados dois algoritmos de Iteração de Valor Sensível a Risco baseados em um desses operadores, esses algoritmos são chamados de Iteração de Valor Sensível a Risco Síncrono (Risk Sensitive Value Iteration - RSVI) e Iteração de Valor Sensível a Risco Assíncrono (Asynchronous Risk Sensitive Value Iteration- A-RSVI). Também são propostas duas heurísticas que podem ser utilizadas para inicializar os valores dos algoritmos de forma a torná-los mais eficentes. Os resultados dos experimentos no domínio de Travessia do Rio em dois cenários de recompensas distintos mostram que: (i) o custo de processamento de políticas extremas a risco, tanto de aversão quanto de propensão, é elevado; (ii) um desconto elevado aumenta o tempo de convergência do algoritmo e reforça a sensibilidade ao risco adotada; (iii) políticas com valores para o fator de risco intermediários possuem custo computacional baixo e já possuem certa sensibilidade ao risco dependendo do fator de desconto utilizado; e (iv) o algoritmo A-RSVI com a heurística baseada no fator de risco pode reduzir o tempo para o algoritmo convergir, especialmente para valores extremos do fator de risco / Risk Sensitive Markov Decision Process (RS-MDP) allows modeling risk-averse and risk-prone attitudes in decision-making process using a risk factor to represent the risk-attitude. For this model, there are operators that are based on a piecewise linear transformation function that includes a risk factor and a discount factor. In this dissertation we formulate two Risk Sensitive Value Iteration algorithms based on one of these operators, these algorithms are called Synchronous Risk Sensitive Value Iteration (RSVI) and Asynchronous Risk Sensitive Value Iteration (A-RSVI). We also propose two heuristics that can be used to initialize the value of the RSVI or A-RSVI algorithms in order to make them more efficient. The results of experiments with the River domain in two distinct rewards scenarios show that: (i) the processing cost in extreme risk policies, for both risk-averse and risk-prone, is high; (ii) a high discount value increases the convergence time and reinforces the chosen risk attitude; (iii) policies with intermediate risk factor values have a low computational cost and show a certain sensitivity to risk based on the discount factor; and (iv) the A-RSVI algorithm with the heuristic based on the risk factor can decrease the convergence time of the algorithm, especially when we need a solution for extreme values of the risk factor
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Localização multirrobo cooperativa com planejamento / Planning for multi-robot localizationPinheiro, Paulo Gurgel, 1983- 11 September 2018 (has links)
Orientador: Jacques Wainer / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação / Made available in DSpace on 2018-09-11T21:14:07Z (GMT). No. of bitstreams: 1
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Previous issue date: 2009 / Resumo: Em um problema de localização multirrobô cooperativa, um grupo de robôs encontra-se em um determinado ambiente, cuja localização exata de cada um dos robôs é desconhecida. Neste cenário, uma distribuição de probabilidades aponta as chances de um robô estar em um determinado estado. É necessário então, que os robôs se movimentem pelo ambiente e gerem novas observações que serão compartilhadas, para calcular novas estimativas. Nos últimos anos, muitos trabalhos têm focado no estudo de técnicas probabilísticas, modelos de comunicação e modelos de detecções, para resolver o problema de localização. No entanto, a movimentação dos robôs é, em geral, definida por ações aleatórias. Ações aleatórias geram observações que podem ser inúteis para a melhoria da estimativa. Este trabalho apresenta uma proposta de localização com suporte a planejamento de ações. O objetivo é apresentar um modelo cujas ações realizadas pelos robôs são definidas por políticas. Escolhendo a melhor ação a ser realizada, é possível receber informações mais úteis dos sensores internos e externos e estimar as posturas mais rapidamente. O modelo proposto, denominado Modelo de Localização Planejada - MLP, utiliza POMDPs para modelar os problemas de localização e algoritmos específicos de geração de políticas. Foi utilizada a localização de Markov como técnica probabilística de localização e implementadas versões de modelos de detecção e propagação de informação. Neste trabalho, um simulador de problemas de localização multirrobô foi desenvolvido, no qual foram realizados experimentos em que o modelo proposto foi comparado a um modelo que não faz uso de planejamento de ações. Os resultados obtidos apontam que o modelo proposto é capaz de estimar as posturas dos robôs com uma menor quantidade de passos, sendo significativamente mais e ciente do que o modelo comparado sem planejamento. / Abstract: In a cooperative multi-robot localization problem, a group of robots is in a certain environment, where the exact location of each robot is unknown. In this scenario, there is only a distribution of probabilities indicating the chance of a robot to be in a particular state. It is necessary for the robots to move in the environment generating new observations, which will be shared to calculate new estimates. Currently, many studies have
focused on the study of probabilistic techniques, models of communication and models of detection to solve the localization problem. However, the movement of robots is generally defined by random actions. Random actions generate observations that can be useless for improving the estimate. This work describes a proposal for multi-robot localization with support planning of actions. The objective is to describe a model whose actions performed by robots are defined by policies. Choosing the best action to be performed, the robot gets more useful information from internal and external sensors and estimates the posture more quickly. The proposed model, called Model of Planned Localization - MPL, uses POMDPs to model the problems of location and specific algorithms to generate policies. The Markov localization was used as probabilistic technique of localization and implemented versions of detection models and information propagation model. In this work, a simulator to multi-robot localization problems was developed, in which experiments were performed. The proposed model was compared to a model that does not make use of planning actions. The results showed that the proposed model is able to estimate the positions of robots with lower number of steps, being more e-cient than model compared. / Mestrado / Inteligencia Artificial / Mestre em Ciência da Computação
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Estratégias para otimização do algoritmo de Iteração de Valor Sensível a Risco / Strategies for optimization of Risk Sensitive Value Iteration algorithmBorges, Igor Oliveira 11 October 2018 (has links)
Processos de decisão markovianos sensíveis a risco (Risk Sensitive Markov Decision Process - RS-MDP) permitem modelar atitudes de aversão e propensão ao risco no processo de tomada de decisão usando um fator de risco para representar a atitude ao risco. Para esse modelo, existem operadores que são baseados em funções de transformação linear por partes que incluem fator de risco e fator de desconto. Nesta dissertação são formulados dois algoritmos de Iteração de Valor Sensível a Risco baseados em um desses operadores, esses algoritmos são chamados de Iteração de Valor Sensível a Risco Síncrono (Risk Sensitive Value Iteration - RSVI) e Iteração de Valor Sensível a Risco Assíncrono (Asynchronous Risk Sensitive Value Iteration- A-RSVI). Também são propostas duas heurísticas que podem ser utilizadas para inicializar os valores dos algoritmos de forma a torná-los mais eficentes. Os resultados dos experimentos no domínio de Travessia do Rio em dois cenários de recompensas distintos mostram que: (i) o custo de processamento de políticas extremas a risco, tanto de aversão quanto de propensão, é elevado; (ii) um desconto elevado aumenta o tempo de convergência do algoritmo e reforça a sensibilidade ao risco adotada; (iii) políticas com valores para o fator de risco intermediários possuem custo computacional baixo e já possuem certa sensibilidade ao risco dependendo do fator de desconto utilizado; e (iv) o algoritmo A-RSVI com a heurística baseada no fator de risco pode reduzir o tempo para o algoritmo convergir, especialmente para valores extremos do fator de risco / Risk Sensitive Markov Decision Process (RS-MDP) allows modeling risk-averse and risk-prone attitudes in decision-making process using a risk factor to represent the risk-attitude. For this model, there are operators that are based on a piecewise linear transformation function that includes a risk factor and a discount factor. In this dissertation we formulate two Risk Sensitive Value Iteration algorithms based on one of these operators, these algorithms are called Synchronous Risk Sensitive Value Iteration (RSVI) and Asynchronous Risk Sensitive Value Iteration (A-RSVI). We also propose two heuristics that can be used to initialize the value of the RSVI or A-RSVI algorithms in order to make them more efficient. The results of experiments with the River domain in two distinct rewards scenarios show that: (i) the processing cost in extreme risk policies, for both risk-averse and risk-prone, is high; (ii) a high discount value increases the convergence time and reinforces the chosen risk attitude; (iii) policies with intermediate risk factor values have a low computational cost and show a certain sensitivity to risk based on the discount factor; and (iv) the A-RSVI algorithm with the heuristic based on the risk factor can decrease the convergence time of the algorithm, especially when we need a solution for extreme values of the risk factor
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A Partially Observable Markov Decision Process for Breast Cancer ScreeningHudson, Joshua January 2019 (has links)
In the US, breast cancer is one of the most common forms of cancer and the most lethal. There are many decisions that must be made by the doctor and/or the patient when dealing with a potential breast cancer. Many of these decisions are made under uncertainty, whether it is the uncertainty related to the progression of the patient's health, or that related to the accuracy of the doctor's tests. Each possible action under consideration can have positive effects, such as a surgery successfully removing a tumour, and negative effects: a post-surgery infection for example. The human mind simply cannot take into account all the variables involved and possible outcomes when making these decisions. In this report, a detailed Partially Observable Markov Decision Process (POMDP) for breast cancer screening decisions is presented. It includes 151 states, covering 144 different cancer states, and 2 competing screening methods. The necessary parameters were first set up using relevant medical literature and a patient history simulator. Then the POMDP was solved optimally for an infinite horizon, using the Perseus algorithm. The resulting policy provided several recommendations for breast cancer screening. The results indicated that clinical breast examinations are important for screening younger women. Regarding the decision to operate on a woman with breast cancer, the policy showed that invasive cancers with either a tumour size above 1.5 cm or which are in metastasis, should be surgically removed as soon as possible. However, the policy also recommended that patients who are certain to be healthy should have a breast biopsy. The cause of this error was explored further and the conclusion was reached that a finite horizon may be more appropriate for this application.
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A Reinforcement Learning Approach To Obtain Treatment Strategies In Sequential Medical Decision ProblemsPoolla, Radhika 14 August 2003 (has links)
Medical decision problems are extremely complex owing to their dynamic nature, large number of variable factors, and the associated uncertainty. Decision support technology entered the medical field long after other areas such as the airline industry and the manufacturing industry. Yet, it is rapidly becoming an indispensable tool in medical decision making problems including the class of sequential decision problems. In these problems, physicians decide on a treatment plan that optimizes a benefit measure such as the treatment cost, and the quality of life of the patient. The last decade saw the emergence of many decision support applications in medicine. However, the existing models have limited applications to decision problems with very few states and actions. An urgent need is being felt by the medical research community to expand the applications to more complex dynamic problems with large state and action spaces. This thesis proposes a methodology which models the class of sequential medical decision problems as a Markov decision process, and solves the model using a simulation based reinforcement learning (RL) algorithm. Such a methodology is capable of obtaining near optimal treatment strategies for problems with large state and action spaces. This methodology overcomes, to a large extent, the computational complexity of the value-iteration and policy-iteration algorithms of dynamic programming. An average reward reinforcement-learning algorithm is developed. The algorithm is applied on a sample problem of treating hereditary spherocytosis. The application demonstrates the ability of the proposed methodology to obtain effective treatment strategies for sequential medical decision problems.
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Scaling Up Reinforcement Learning without Sacrificing Optimality by Constraining ExplorationMann, Timothy 1984- 14 March 2013 (has links)
The purpose of this dissertation is to understand how algorithms can efficiently learn to solve new tasks based on previous experience, instead of being explicitly programmed with a solution for each task that we want it to solve. Here a task is a series of decisions, such as a robot vacuum deciding which room to clean next or an intelligent car deciding to stop at a traffic light. In such a case, state-of-the-art learning algorithms are difficult to employ in practice because they often make thou- sands of mistakes before reliably solving a task. However, humans learn solutions to novel tasks, often making fewer mistakes, which suggests that efficient learning algorithms may exist. One advantage that humans have over state- of-the-art learning algorithms is that, while learning a new task, humans can apply knowledge gained from previously solved tasks. The central hypothesis investigated by this dissertation is that learning algorithms can solve new tasks more efficiently when they take into consideration knowledge learned from solving previous tasks. Al- though this hypothesis may appear to be obviously true, what knowledge to use and how to apply that knowledge to new tasks is a challenging, open research problem.
I investigate this hypothesis in three ways. First, I developed a new learning algorithm that is able to use prior knowledge to constrain the exploration space. Second, I extended a powerful theoretical framework in machine learning, called Probably Approximately Correct, so that I can formally compare the efficiency of algorithms that solve only a single task to algorithms that consider knowledge from previously solved tasks. With this framework, I found sufficient conditions for using knowledge from previous tasks to improve efficiency of learning to solve new tasks and also identified conditions where transferring knowledge may impede learning. I present situations where transfer learning can be used to intelligently constrain the exploration space so that optimality loss can be minimized. Finally, I tested the efficiency of my algorithms in various experimental domains.
These theoretical and empirical results provide support for my central hypothesis. The theory and experiments of this dissertation provide a deeper understanding of what makes a learning algorithm efficient so that it can be widely used in practice. Finally, these results also contribute the general goal of creating autonomous machines that can be reliably employed to solve complex tasks.
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Delay-aware Scheduling in Wireless Coding Networks: To Wait or Not to WaitRamasamy, Solairaja 2010 December 1900 (has links)
Wireless technology has become an increasingly popular way to gain network access. Wireless networks are expected to provide efficient and reliable service and support a broad range of emerging applications, such as multimedia streaming and video conferencing. However, limited wireless spectrum together with interference and fading pose signi cant challenges for network designers. The novel technique of network coding has a significant potential for improving the throughput and reliability of wireless networks by taking advantage of the broadcast nature of wireless medium. Reverse carpooling is one of the main techniques used to realize the benefits of network coding in wireless networks. With reverse carpooling, two flows are traveling in opposite directions, sharing a common path. The network coding is performed in the intermediate (relay) nodes, which saves up to 50% of transmissions. In this thesis, we focus on the scheduling at the relay nodes in wireless networks with reverse carpooling. When two packets traveling in opposite directions are available at the relay node, the relay node combines them and broadcasts the resulting packet. This event is referred to as a coding opportunity. When only one packet is available, the relay node needs to decide whether to wait for future coding opportunities, or to transmit them without coding. Though the choice of holding packets exploits the positive aspects of network coding, without a proper policy in place that controls how long the packets should wait, it will have an adverse impact on delays and thus the overall network performance. Accordingly, our goal is to find an optimal control strategy that delicately balances the tradeoff between the number of transmissions and delays incurred by the packets. We also address the fundamental question of what local information we should keep track of and use in making the decision of of whether to transmit uncoded packet or wait for the next coding opportunity. The available information consists of queue length and time stamps indicating the arrival time of packets in the queue. We could also store history of all previous states and actions. However, using all this information makes the control very complex and so we try to find if the overhead in collecting waiting times and historical information is worth it. A major contribution of this thesis is a stochastic control framework that uses state information based on what can be observed and prescribes an optimal action. For that, we formulate and solve a stochastic dynamic program with the objective of minimizing the long run average cost per unit time incurred due to transmissions and delays. Subsequently, we show that a stationary policy based on queue lengths is optimal, and the optimal policy is of threshold-type. Then, we describe a non-linear optimization procedure to obtain the optimal thresholds. Further, we substantiate our analytical ndings by performing numerical experiments under varied settings. We compare systems that use only queue length with those where more information is available, and we show that optimal control that uses only the queue length is as good as any optimal control that relies on knowing the entire history.
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Lifetime Condition Prediction For BridgesBayrak, Hakan 01 October 2011 (has links) (PDF)
Infrastructure systems are crucial facilities. They supply the necessary transportation, water and energy utilities for the public. However, while aging, these systems gradually deteriorate in time and approach the end of their lifespans. As a result, they require periodic maintenance and repair in order to function and be reliable throughout their lifetimes. Bridge infrastructure is an essential part of the transportation infrastructure. Bridge management systems (BMSs), used to monitor the condition and safety of the bridges in a bridge infrastructure, have evolved considerably in the past decades. The aim of BMSs is to use the resources in an optimal manner keeping the bridges out of risk of failure. The BMSs use the lifetime performance curves to predict the future condition of the bridge elements or bridges. The most widely implemented condition-based performance prediction and maintenance optimization model is the Markov Decision Process-based models (MDP). The importance of the Markov Decision Process-based model is that it defines the time-variant deterioration using the Markov Transition Probability Matrix and performs the lifetime cost optimization by finding the optimum maintenance policy. In this study, the Markov decision process-based model is examined and a computer program to find the optimal policy with discounted life-cycle cost is developed. The other performance prediction model investigated in this study is a probabilistic Bi-linear model which takes into account the uncertainties for the deterioration process and the application of maintenance actions by the use of random variables. As part of the study, in order to further analyze and develop the Bi-linear model, a Latin Hypercube Sampling-based (LHS) simulation program is also developed and integrated into the main computational algorithm which can produce condition, safety, and life-cycle cost profiles for bridge members with and without maintenance actions. Furthermore, a polynomial-based condition prediction is also examined as an alternative performance prediction model. This model is obtained from condition rating data by applying regression analysis. Regression-based performance curves are regenerated using the Latin Hypercube sampling method. Finally, the results from the Markov chain-based performance prediction are compared with Simulation-based Bi-linear prediction and the derivation of the transition probability matrix from simulated regression based condition profile is introduced as a newly developed approach. It has been observed that the results obtained from the Markov chain-based average condition rating profiles match well with those obtained from Simulation-based mean condition rating profiles. The result suggests that the Simulation-based condition prediction model may be considered as a potential model in future BMSs.
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Extensions of Multistage Stochastic Optimization with Applications in Energy and HealthcareKuznia, Ludwig Charlemagne 01 January 2012 (has links)
This dissertation focuses on extending solution methods in the area of stochastic optimization. Attention is focused to three specific problems in the field. First, a solution method for mixed integer programs subject to chance constraints is discussed. This class of problems serves as an effective modeling framework for a wide variety of applied problems. Unfortunately, chance constrained mixed integer programs tend to be very challenging to solve. Thus, the aim of this work is to address some of these challenges by exploiting the structure of the deterministic reformulation for the problem. Second, a stochastic program for integrating renewable energy sources into traditional energy systems is developed. As the global push for higher utilization of such green resources increases, such models will prove invaluable to energy system designers. Finally, a process for transforming clinical medical data into a model to assist decision making during the treatment planning phase for palliative chemotherapy is outlined. This work will likely provide decision support tools for oncologists. Moreover, given the new requirements for the usage electronic medical records, such techniques will have applicability to other treatment planning applications in the future.
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