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Hearnes, Warren E. II. "Near-optimal intelligent control for continuous set-point regulator problems via approximate dynamic programming." Diss., Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/24882.
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Angulo, Olivares Gustavo I. "Integer programming approaches for semicontinuous and stochastic optimization." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/51862.
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This thesis concerns the application of mixed-integer programming techniques to solve special classes of network flow problems and stochastic integer programs. We draw tools from complexity and polyhedral theory to analyze these problems and propose improved solution methods. In the first part, we consider semi-continuous network flow problems, that is, a class of network flow problems where some of the variables are required to take values above a prespecified minimum threshold whenever they are not zero. These problems find applications in management and supply chain models where orders in small quantities are undesirable. We introduce the semi-continuous inflow set with variable upper bounds as a relaxation of general semi-continuous network flow problems. Two particular cases of this set are considered, for which we present complete descriptions of the convex hull in terms of linear inequalities and extended formulations. We also consider a class of semi-continuous transportation problems where inflow systems arise as substructures, for which we investigate complexity questions. Finally, we study the computational efficacy of the developed polyhedral results in solving randomly generated instances of semi-continuous transportation problems. In the second part, we introduce and study the forbidden-vertices problem. Given a polytope P and a subset X of its vertices, we study the complexity of optimizing a linear function on the subset of vertices of P that are not contained in X. This problem is closely related to finding the k-best basic solutions to a linear problem and finds applications in stochastic integer programming. We observe that the complexity of the problem depends on how P and X are specified. For instance, P can be explicitly given by its linear description, or implicitly by an oracle. Similarly, X can be explicitly given as a list of vectors, or implicitly as a face of P. While removing vertices turns to be hard in general, it is tractable for tractable 0-1 polytopes, and compact extended formulations can be obtained. Some extensions to integral polytopes are also presented. The third part is devoted to the integer L-shaped method for two-stage stochastic integer programs. A widely used model assumes that decisions are made in a two-step fashion, where first-stage decisions are followed by second-stage recourse actions after the uncertain parameters are observed, and we seek to minimize the expected overall cost. In the case of finitely many possible outcomes or scenarios, the integer L-shaped method proposes a decomposition scheme akin to Benders' decomposition for linear problems, but where a series of mixed-integer subproblems have to be solved at each iteration. To improve the performance of the method, we devise a simple modification that alternates between linear and mixed-integer subproblems, yielding significant time savings in instances from the literature. We also present a general framework to generate optimality cuts via a cut-generating problem. Using an extended formulation of the forbidden-vertices problem, we recast our cut-generating problem as a linear problem and embed it within the integer L-shaped method. Our numerical experiments suggest that this approach can prove beneficial when the first-stage set is relatively complicated.
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Doddapaneni, Srinivas P. "Automatic dynamic decomposition of programs on distributed memory machines." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/8158.
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Tosukhowong, Thidarat. "Dynamic Real-time Optimization and Control of an Integrated Plant." Diss., Georgia Institute of Technology, 2006. http://hdl.handle.net/1853/14087.
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Applications of the existing steady-state plant-wide optimization and the single-scale fast-rate dynamic optimization strategies to an integrated plant with material recycle have been impeded by several factors. While the steady-state optimization formulation is very simple, the very long transient dynamics of an integrated plant have limited the optimizers execution rate to be extremely low, yielding a suboptimal performance. In contrast, performing dynamic plant-wide optimization at the same rate as local controllers requires exorbitant on-line computational load and may increase the sensitivity to high-frequency dynamics that are irrelevant to the plant-level interactions, which are slow-scale in nature. This thesis proposes a novel multi-scale dynamic optimization and control strategy suitable for an integrated plant. The dynamic plant-wide optimizer in this framework executes at a slow rate to track the slow-scale plant-wide interactions and economics, while leaving the local controllers to handle fast changes related to the local units. Moreover, this slow execution rate demands less computational and modeling requirement than the fast-rate optimizer.
An important issue of this method is obtaining a suitable dynamic model when first-principles are unavailable. The difficulties in the system identification process are designing proper input signal to excite this ill-conditioned system and handling the lack of slow-scale dynamic data when the plant experiment cannot be conducted for a long time compared to the settling time. This work presents a grey-box modeling method to incorporate steady-state information to improve the model prediction accuracy.
A case study of an integrated plant example is presented to address limitations of the nonlinear model predictive control (NMPC) in terms of the on-line computation and its inability to handle stochastic uncertainties. Then, the approximate dynamic programming (ADP) framework is investigated. This method computes an optimal operating policy under uncertainties off-line. Then, the on-line multi-stage optimization can be transformed into a single-stage problem, thus reducing the real-time computational effort drastically. However, the existing ADP framework is not suitable for an integrated plant with high dimensional state and action space. In this study, we combine several techniques with ADP to apply nonlinear optimal control to the integrated plant example and show its efficacy over NMPC.
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Ng, Chi Kong. "Globally convergent and efficient methods for unconstrained discrete-time optimal control." HKBU Institutional Repository, 1998. http://repository.hkbu.edu.hk/etd_ra/149.
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Papageorgiou, Dimitri Jason. "Optimization in maritime inventory routing." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/50117.
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The primary aim of this thesis is to develop effective solution techniques for large-scale maritime inventory routing problems that possess a core substructure common in many real-world applications. We use the term “large-scale” to refer to problems whose standard mixed-integer linear programming (MIP) formulations involve tens of thousands of binary decision variables and tens of thousands of constraints and require days to solve on a personal computer. Although a large body of literature already exists for problems combining vehicle routing and inventory control for road-based applications, relatively little work has been published in the realm of maritime logistics. A major contribution of this research is in the advancement of novel methods for tackling problems orders of magnitude larger than most of those considered in the literature. Coordinating the movement of massive vessels all around the globe to deliver large quantities of high value products is a challenging and important problem within the maritime transportation industry. After introducing a core maritime inventory routing model to aid decision-makers with their coordination efforts, we make three main contributions. First, we present a two-stage algorithm that exploits aggregation and decomposition to produce provably good solutions to complex instances with a 60-period (two-month) planning horizon. Not only is our solution approach different from previous methods discussed in the maritime transportation literature, but computational experience shows that our approach is promising. Second, building on the recent successes of approximate dynamic programming (ADP) for road-based applications, we present an ADP procedure to quickly generate good solutions to maritime inventory routing problems with a long planning horizon of up to 365 periods. For instances with many ports (customers) and many vessels, leading MIP solvers often require hours to produce good solutions even when the planning horizon is limited to 90 periods. Our approach requires minutes. Our algorithm operates by solving many small subproblems and, in so doing, collecting and learning information about how to produce better solutions. Our final research contribution is a polyhedral study of an optimization problem that was motivated by maritime inventory routing, but is applicable to a more general class of problems. Numerous planning models within the chemical, petroleum, and process industries involve coordinating the movement of raw materials in a distribution network so that they can be blended into final products. The uncapacitated fixed-charge transportation problem with blending (FCTPwB) that we study captures a core structure encountered in many of these environments. We model the FCTPwB as a mixed-integer linear program and derive two classes of facets, both exponential in size, for the convex hull of solutions for the problem with a single consumer and show that they can be separated in polynomial time. Finally, a computational study demonstrates that these classes of facets are effective in reducing the integrality gap and solution time for more general instances of the FCTPwB.
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Stellato, Bartolomeo. "Mixed-integer optimal control of fast dynamical systems." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:b8a7323c-e36e-45ec-ae8d-6c9eb4350629.
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Many applications in engineering, computer science and economics involve mixed-integer optimal control problems. Solving these problems in real-time is a challenging task because of the explosion of integer combinations to evaluate. This thesis focuses on the development of new algorithms for mixed-integer programming with an emphasis on optimal control problems of fast dynamical systems with discrete controls. The first part proposes two reformulations to reduce the computational complexity. The first reformulation avoids integer variables altogether. By considering a sequence of switched dynamics, we analyze the switching time optimization problem. Even though it is a continuous smooth problem, it is non-convex and the cost function and derivatives are hard to compute. We develop a new efficient method to compute the cost function and its derivatives. Our technique brings up to two orders of magnitude speedups with respect to state-of-the-art tools. The second approach reduces the number of integer decisions. In hybrid model predictive control (MPC) the computational complexity grows exponentially with the horizon length. Using approximate dynamic programming (ADP) we reduce the horizon length while maintaining good control performance by approximating the tail cost offline. This approach allows, for the first time, the application of such control techniques to fast dynamical systems with sampling times of only a few microseconds. The second part investigates embedded branch-and-bound algorithms for mixed-integer quadratic programs (MIQPs). A core component of these methods is the solution of continuous quadratic programs (QPs). We develop OSQP, a new robust and efficient general-purpose QP solver based on the alternating direction method of multipliers (ADMM) and able, for the first time, to detect infeasible problems. We include OSQP into a custom branch-and-bound algorithm suitable for embedded systems. Our extension requires only a single matrix factorization and exploits warm-starting, thereby greatly reducing the number of ADMM iterations required. Numerical examples show that our algorithm solves small to medium scale MIQPs more quickly than commercial solvers.
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Toriello, Alejandro. "Time decomposition of multi-period supply chain models." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/42704.
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Many supply chain problems involve discrete decisions in a dynamic environment. The inventory routing problem is an example that combines the dynamic control of inventory at various facilities in a supply chain with the discrete routing decisions of a fleet of vehicles that moves product between the facilities.
We study these problems modeled as mixed-integer programs and propose a time decomposition based on approximate inventory valuation. We generate the approximate value function with an algorithm that combines data fitting, discrete optimization and dynamic programming methodology. Our framework allows the user to specify a class of piecewise linear, concave functions from which the algorithm chooses the value function. The use of piecewise linear concave functions is motivated by intuition, theory and practice. Intuitively, concavity reflects the notion that inventory is marginally more valuable the closer one is to a stock-out. Theoretically, piecewise linear concave functions have certain structural properties that also hold for finite mixed-integer program value functions. (Whether the same properties hold in the infinite case is an open question, to our knowledge.) Practically, piecewise linear concave functions are easily embedded in the objective function of a maximization mixed-integer or linear program, with only a few additional auxiliary continuous variables. We evaluate the solutions generated by our value functions in a case study using maritime inventory routing instances inspired by the petrochemical industry.
The thesis also includes two other contributions. First, we review various data fitting optimization models related to piecewise linear concave functions, and introduce new mixed-integer programming formulations for some cases. The formulations may be of independent interest, with applications in engineering, mixed-integer non-linear programming, and other areas. Second, we study a discounted, infinite-horizon version of the canonical single-item lot-sizing problem and characterize its value function, proving that it inherits all properties of interest from its finite counterpart. We then compare its optimal policies to our algorithm's solutions as a proof of concept.
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Samuelsson, Björn. "Heuristic Mathematical Programming Methods for Lot-sizing, Inventory Control, and Distribution Cost Estimation in the Supply Chain." Doctoral thesis, Luleå tekniska universitet, Industriell Ekonomi, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-66246.
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The supply function has an important role to support the business to create a customer value. Two important parts of this process is to have the warehouses and production sites in the right location and to have the right items stocked at the right level. This thesis is concerned with those two parts of the supply chain management. Three different areas of inventory control are dealt with. In the first part we consider the classical dynamic lot size problem without backlogging. The second part deals with estimation of holding and shortage costs in two-level distribution inventory systems. In the third part of the thesis we consider the localisation problem in a multi-level supply network system where items are consolidated at a warehouse and distributed to customers on routes. Within the area of inventory control we have evaluated a method earlier suggested by Axsäter (1988), the method is evaluated using a set of test problems and compared other heuristic methods, including the well-known Silver-Meal’s method (Silver and Meal, 1973). The result shows that the method suggested by Axsäter does perform better than the other methods. In the latest contribution we point to the important differences between Least Period Cost and Silver-Meal when several periods have zero demand. In the area of inventory control we have also studied a two-echelon inventory system where we present methods for estimating the shortage- and stockholding costs in such inventory systems. The second part subject of the thesis concerns supply network optimization. We present a MIP formulation of the problem and evaluate in detail the approximation of the distribution cost when customers are delivered on multi-stop routes. An improved method for estimating the distribution is presented. Besides this introductory overview five research papers are included in the thesis. The first and the last paper consider evaluation of dynamic lot sizing heuristics. The second and third paper deals with cost evaluation of a stochastic two-echelon inventory system and the forth paper with evaluation of methods for estimating distribution costs in a supply network.
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Schöllig, Angela. "Optimal Control of Hybrid Systems with Regional Dynamics." Thesis, Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/19874.
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In this work, hybrid systems with regional dynamics are considered. These are systems where transitions between different dynamical regimes occur as the continuous state of the system reaches given switching surfaces. In particular, the attention is focused on the optimal control problem associated with such systems. More precisely, given a specific cost function, the goal is to determine the optimal path of going from a given starting point to a fixed final state during an a priori specified time horizon.
The key characteristic of the approach presented in this thesis is a hierarchical decomposition of the hybrid optimal control problem, yielding to a framework which allows a solution on different levels of control. On the highest level of abstraction, the regional structure of the state space is taken into account and a discrete representation of the connections between the different regions provides global accessibility relations between regions. These are used on a lower level of control to formulate the main theorem of this work, namely, the Hybrid Bellman Equation for multimodal systems, which, in fact, provides a characterization of global optimality, given an upper bound on the number of transitions along a hybrid trajectory. Not surprisingly, the optimal solution is hybrid in nature, in that it depends on not only the continuous control signals, but also on discrete decisions as to what domains the system's continuous state should go through in the first place.
The main benefit with the proposed approach lies in the fact that a hierarchical Dynamic Programming algorithm can be used to representing both a theoretical characterization of the hybrid solution's structural composition and, from a more application-driven point of view, a numerically implementable calculation rule yielding to globally optimal solutions in a regional dynamics framework. The operation of the recursive algorithm is highlighted by the consideration of numerous examples, among them, a heterogeneous multi-agent problem.
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Feigh, Karen M. "Design of cognitive work support systems for airline operations." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/26524.
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Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2009.Committee Chair: Pritchett, Amy R.; Committee Member: Clarke, John-Paul; Committee Member: Cross, Stephen; Committee Member: Endsley, Mica; Committee Member: Goldsman, David. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Kovalskyy, Valeriy. "Application of Heuristic Optimization Techniques in Land Evaluation." Ohio University / OhioLINK, 2004. http://www.ohiolink.edu/etd/view.cgi?ohiou1102709552.
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Li, Peng. "Optimization of (R, Q) policies for multi-echelon inventory systems with guaranteed service." Thesis, Troyes, 2013. http://www.theses.fr/2013TROY0014/document.
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Face à une concurrence féroce par suite de la modélisation économique, les entreprises doivent bien gérer leurs chaînes logistiques afin de réduire leurs coûts d’exploitation tout en améliorant leurs services au client. Un enjeu majeur de cette gestion et la gestion efficace des stocks multi-échelons. Dans cette thèse, nous étudions des systèmes de stocks multi-échelons avec des coûts de passation de commande à chaque stock. En raison de l’existence des coûts de passation de commande, l’optimisation d’un tel système devient très compliquée. Récemment, l’approche de service garanti (GSA) a été utilisée pour déterminer les stocks de sécurité pour les systèmes de stocks multi-échelons, mais sans coûts fixes de passation de commande. Nous généralisons la GSA pour optimiser la politique de stockage (R, Q) d’un système de stocks multi-échelons avec la demande suivant un processus de Poisson et coûts fixes de passation de commande à chaque stock. Nous considérons trois types de systèmes de stocks multi-échelons, et pour chaque type, nous d'abord établissons un modèle mathématique pour le problème d’optimisation. Ensuite, le modèle est résolu par une procédure itérative fondée sur deux algorithmes de programmation dynamique (DP). Un algorithme DP est utilisé pour résoudre le sous-problème de détermination de quantités de commande et l'autre est utilisé pour résoudre le sous-problème de détermination de points de recommande du modèle. Les résultats numériques démontrent l'efficacité des algorithmes et de la procédureWith the increasing complexity of supply chains led by economic globalization, integrated supply chain management has become an important strategy utilized by the firms to reduce the overall cost while meeting the customer service. This change has made academic researchers and industrial practitioners pay more and more attention to multi-echelon inventory management over the last two decades. In this thesis, we study multi-echelon inventory systems with fixed order costs at each stock. Because of the existence of fixed order costs, the optimization of such system becomes very complicated. Recently, Guaranteed Service Approach (GSA) was used to set safety stock for multi-echelon inventory systems, but without fixed order costs. We extend the GSA to optimize (R, Q) inventory policies for multi-echelon inventory systems with Poisson demand and fixed order costs. Our objective is to find optimal (R, Q) policy for such a system so that its total cost is minimized while achieving a service level to customer. Three types of multi-echelon inventory systems, serial systems, assembly systems and two-level distribution systems are considered. For each type, we first establish a mathematical model for the optimization problem. Then, the model is solved by an iterative procedure based on two dynamic programming (DP) algorithms. One DP algorithm is used to solve the order size decision subproblem and the other is used to solve the reorder point decision subproblem of the model. Numerical experiments demonstrate the efficiency of the algorithms and the procedure
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Tongsari, Kamphee. "Optimization of shelf space allocation in three dimensions." Ohio : Ohio University, 1995. http://www.ohiolink.edu/etd/view.cgi?ohiou1178824354.
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MBITI, JOHN N. "Deep learning for portfolio optimization." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-104567.
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In this thesis, an optimal investment problem is studied for an investor who can only invest in a financial market modelled by an Itô-Lévy process; with one risk free (bond) and one risky (stock) investment possibility. We present the dynamic programming method and the associated Hamilton-Jacobi-Bellman (HJB) equation to explicitly solve this problem. It is shown that with purification and simplification to the standard jump diffusion process, closed form solutions for the optimal investment strategy and for the value function are attainable. It is also shown that, an explicit solution can be obtained via a finite training of a neural network using Stochastic gradient descent (SGD) for a specific case.
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Miller, Michael Chad. "Global Resource Management of Response Surface Methodology." PDXScholar, 2014. https://pdxscholar.library.pdx.edu/open_access_etds/1621.
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Statistical research can be more difficult to plan than other kinds of projects, since the research must adapt as knowledge is gained. This dissertation establishes a formal language and methodology for designing experimental research strategies with limited resources. It is a mathematically rigorous extension of a sequential and adaptive form of statistical research called response surface methodology. It uses sponsor-given information, conditions, and resource constraints to decompose an overall project into individual stages. At each stage, a "parent" decision-maker determines what design of experimentation to do for its stage of research, and adapts to the feedback from that research's potential "children", each of whom deal with a different possible state of knowledge resulting from the experimentation of the "parent". The research of this dissertation extends the real-world rigor of the statistical field of design of experiments to develop an deterministic, adaptive algorithm that produces deterministically generated, reproducible, testable, defendable, adaptive, resource-constrained multi-stage experimental schedules without having to spend physical resource.
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Sau, Ignasi. "Optimization in Graphs under Degree Constraints. Application to Telecommunication Networks." Phd thesis, Université de Nice Sophia-Antipolis, 2009. http://tel.archives-ouvertes.fr/tel-00429092.
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La première partie de cette thèse s'intéresse au groupage de trafic dans les réseaux de télécommunications. La notion de groupage de trafic correspond à l'agrégation de flux de faible débit dans des conduits de plus gros débit. Cependant, à chaque insertion ou extraction de trafic sur une longueur d'onde il faut placer dans le noeud du réseau un multiplexeur à insertion/extraction (ADM). De plus il faut un ADM pour chaque longueur d'onde utilisée dans le noeud, ce qui représente un coût d'équipements important. Les objectifs du groupage de trafic sont d'une part le partage efficace de la bande passante et d'autre part la réduction du coût des équipements de routage. Nous présentons des résultats d'inapproximabilité, des algorithmes d'approximation, un nouveau modèle qui permet au réseau de pouvoir router n'importe quel graphe de requêtes de degré borné, ainsi que des solutions optimales pour deux scénarios avec trafic all-to-all: l'anneau bidirectionnel et l'anneau unidirectionnel avec un facteur de groupage qui change de manière dynamique. La deuxième partie de la thèse s'intéresse aux problèmes consistant à trouver des sous-graphes avec contraintes sur le degré. Cette classe de problèmes est plus générale que le groupage de trafic, qui est un cas particulier. Il s'agit de trouver des sous-graphes d'un graphe donné avec contraintes sur le degré, tout en optimisant un paramètre du graphe (très souvent, le nombre de sommets ou d'arêtes). Nous présentons des algorithmes d'approximation, des résultats d'inapproximabilité, des études sur la complexité paramétrique, des algorithmes exacts pour les graphes planaires, ainsi qu'une méthodologie générale qui permet de résoudre efficacement cette classe de problèmes (et de manière plus générale, la classe de problèmes tels qu'une solution peut être codé avec une partition d'un sous-ensemble des sommets) pour les graphes plongés dans une surface. Finalement, plusieurs annexes présentent des résultats sur des problèmes connexes.
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Iourtchenko, Daniil V. "Optimal bounded control and relevant response analysis for random vibrations." Link to electronic thesis, 2001. http://www.wpi.edu/Pubs/ETD/Available/etd-0525101-111407.
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Thesis (Ph. D.)--Worcester Polytechnic Institute.Keywords: Stochastic optimal control; dynamic programming; Hamilton-Jacobi-Bellman equation; Random vibration. Keywords: Stochastic optimal control; dynamic programming; Hamilton-Jacobi-Bellman equation; Random vibration; energy balance method. Includes bibliographical references (p. 86-89).
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Ludovic, Moreau. "A Contribution in Stochastic Control Applied to Finance and Insurance." Phd thesis, Université Paris Dauphine - Paris IX, 2012. http://tel.archives-ouvertes.fr/tel-00737624.
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Le but de cette thèse est d'apporter une contribution à la problématique de valorisation de produits dérivés en marchés incomplets. Nous considérons tout d'abord les cibles stochastiques introduites par Soner et Touzi (2002) afin de traiter le problème de sur-réplication, et récemment étendues afin de traiter des approches plus générales par Bouchard, Elie et Touzi (2009). Nous généralisons le travail de Bouchard {\sl et al} à un cadre plus général où les diffusions sont sujettes à des sauts. Nous devons considérer dans ce cas des contrôles qui prennent la forme de fonctions non bornées, ce qui impacte de façon non triviale la dérivation des EDP correspondantes. Notre deuxième contribution consiste à établir une version des cibles stochastiques qui soit robuste à l'incertitude de modèle. Dans un cadre abstrait, nous établissons une version faible du principe de programmation dynamique géométrique de Soner et Touzi (2002), et nous dérivons, dans un cas d'EDS controllées, l'équation aux dérivées partielles correspondantes, au sens des viscosités. Nous nous intéressons ensuite à un exemple de couverture partielle sous incertitude de Knightian. Finalement, nous nous concentrons sur le problème de valorisation de produits dérivées {\sl hybrides} (produits dérivés combinant finance de marché et assurance). Nous cherchons plus particulièrement à établir une condition suffisante sous laquelle une règle de valorisation (populaire dans l'industrie), consistant à combiner l'approches actuarielle de mutualisation avec une approche d'arbitrage, soit valable.
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Qu, Zheng. "Théorie de Perron-Frobenius non linéaire et méthodes numériques max-plus pour la résolution d'équations d'Hamilton-Jacobi." Phd thesis, Ecole Polytechnique X, 2013. http://pastel.archives-ouvertes.fr/pastel-00927122.
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Une approche fondamentale pour la résolution de problémes de contrôle optimal est basée sur le principe de programmation dynamique. Ce principe conduit aux équations d'Hamilton-Jacobi, qui peuvent être résolues numériquement par des méthodes classiques comme la méthode des différences finies, les méthodes semi-lagrangiennes, ou les schémas antidiffusifs. À cause de la discrétisation de l'espace d'état, la dimension des problèmes de contrôle pouvant être abordés par ces méthodes classiques est souvent limitée à 3 ou 4. Ce phénomène est appellé malédiction de la dimension. Cette thèse porte sur les méthodes numériques max-plus en contôle optimal deterministe et ses analyses de convergence. Nous étudions et developpons des méthodes numériques destinées à attenuer la malédiction de la dimension, pour lesquelles nous obtenons des estimations théoriques de complexité. Les preuves reposent sur des résultats de théorie de Perron-Frobenius non linéaire. En particulier, nous étudions les propriétés de contraction des opérateurs monotones et non expansifs, pour différentes métriques de Finsler sur un cône (métrique de Thompson, métrique projective d'Hilbert). Nous donnons par ailleurs une généralisation du "coefficient d'ergodicité de Dobrushin" à des opérateurs de Markov sur un cône général. Nous appliquons ces résultats aux systèmes de consensus ainsi qu'aux équations de Riccati généralisées apparaissant en contrôle stochastique.
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COSTA, PEDRO FRANCA FERREIRA DA. "OPTIMIZATION OF THE OFFLOADING LOGISTICS USING MATHEMATICAL PROGRAMMING." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2015. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=25301@1.
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O crescimento da produção diária de petróleo e os elevados custos
envolvidos na logística de petróleo, mais precisamente na logística upstream, pela
sua complexidade, e em particular, na logística de produção e ainda, somando-se a
atual queda do preço do barril, resultam que os impactos econômicos que as falhas
no processo logístico podem causar, tornam-se cada vez mais relevantes. Neste
contexto, foi desenvolvido um modelo de programação linear que promove a
otimização da operação de alivio de plataformas conjugada à programação da
janela de atendimento das diversas embarcações a fim de não haja necessidade de
interromper a produção de nenhuma plataforma e que todas as demandas sejam
cumpridas. Em qualquer circunstância o método utilizado busca a minimização
dos custos operacionais através da redução das distancias percorridas e do número
de navios afretados. O modelo matemático foi aplicado em um estudo de caso
composto por três cenários distintos. O resultado obtido fundamenta a tomada de
decisão que definirá o numero de navios aliviadores a serem afretados durante um
determinado período.The growth of daily oil production and the high costs involved in oil logistics, specifically the upstream logistics and the production logistics itself, adding to the current downturn in oil prices, are becoming increasingly relevant considering the major economic impacts caused by eventual failure in logistics processes. In this context, a linear programming model was developed. It provides the optimization of offloading platforms operation coupled to the service window of various vessels, so there is no need to interrupt the production of any of those platforms, allowing that all demands are met. In any case, this method seeks to minimize operational costs by reducing the distances traveled and the number of chartered vessels. The mathematical model was applied in a case study consisting of three different scenarios. The result obtained allows effective decision making that will define the number of shuttle tankers to be chartered for a certain period of time.
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Detournay, Sylvie. "Méthodes multigrilles pour les jeux stochastiques à deux joueurs et somme nulle, en horizon infini." Phd thesis, Ecole Polytechnique X, 2012. http://pastel.archives-ouvertes.fr/pastel-00762010.
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Dans cette thèse, nous proposons des algorithmes et présentons des résultats numériques pour la résolution de jeux répétés stochastiques, à deux joueurs et somme nulle dont l'espace d'état est de grande taille. En particulier, nous considérons la classe de jeux en information complète et en horizon infini. Dans cette classe, nous distinguons d'une part le cas des jeux avec gain actualisé et d'autre part le cas des jeux avec gain moyen. Nos algorithmes, implémentés en C, sont principalement basés sur des algorithmes de type itérations sur les politiques et des méthodes multigrilles. Ces algorithmes sont appliqués soit à des équations de la programmation dynamique provenant de problèmes de jeux à deux joueurs à espace d'états fini, soit à des discrétisations d'équations de type Isaacs associées à des jeux stochastiques différentiels. Dans la première partie de cette thèse, nous proposons un algorithme qui combine l'algorithme des itérations sur les politiques pour les jeux avec gain actualisé à des méthodes de multigrilles algébriques utilisées pour la résolution des systèmes linéaires. Nous présentons des résultats numériques pour des équations d'Isaacs et des inéquations variationnelles. Nous présentons également un algorithme d'itérations sur les politiques avec raffinement de grilles dans le style de la méthode FMG. Des exemples sur des inéquations variationnelles montrent que cet algorithme améliore de façon non négligeable le temps de résolution de ces inéquations. Pour le cas des jeux avec gain moyen, nous proposons un algorithme d'itération sur les politiques pour les jeux à deux joueurs avec espaces d'états et d'actions finis, dans le cas général multichaine (c'est-à-dire sans hypothèse d'irréductibilité sur les chaînes de Markov associées aux stratégies des deux joueurs). Cet algorithme utilise une idée développée dans Cochet-Terrasson et Gaubert (2006). Cet algorithme est basé sur la notion de projecteur spectral non-linéaire d'opérateurs de la programmation dynamique de jeux à un joueur (lequel est monotone et convexe). Nous montrons que la suite des valeurs et valeurs relatives satisfont une propriété de monotonie lexicographique qui implique que l'algorithme termine en temps fini. Nous présentons des résultats numériques pour des jeux discrets provenant d'une variante des jeux de Richman et sur des problèmes de jeux de poursuite. Finalement, nous présentons de nouveaux algorithmes de multigrilles algébriques pour la résolution de systèmes linéaires singuliers particuliers. Ceux-ci apparaissent, par exemple, dans l'algorithme d'itérations sur les politiques pour les jeux stochastiques à deux joueurs et somme nulle avec gain moyen, décrit ci-dessus. Nous introduisons également une nouvelle méthode pour la recherche de mesures invariantes de chaînes de Markov irréductibles basée sur une approche de contrôle stochastique. Nous présentons un algorithme qui combine les itérations sur les politiques d'Howard et des itérations de multigrilles algébriques pour les systèmes linéaires singuliers.
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Zhou, Fangjun. "Nonmonotone methods in optimization and DC optimization of location problems." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/21777.
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Esteban, Jaime. "A reliability-based method for optimization programming problems." Thesis, This resource online, 1992. http://scholar.lib.vt.edu/theses/available/etd-03302010-020045/.
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Vielma, Centeno Juan Pablo. "Mixed integer programming approaches for nonlinear and stochastic programming." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29624.
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Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2010.Committee Chair: Nemhauser, George; Committee Co-Chair: Ahmed, Shabbir; Committee Member: Bill Cook; Committee Member: Gu, Zonghao; Committee Member: Johnson, Ellis. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Zhu, Yuntao. "Semidefinite programming under uncertainty." Online access for everyone, 2006. http://www.dissertations.wsu.edu/Dissertations/summer2006/y%5Fzhu%5F073106.pdf.
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Girardeau, Pierre. "Résolution de grands problèmes en optimisation stochastique dynamique et synthèse de lois de commande." Phd thesis, Université Paris-Est, 2010. http://tel.archives-ouvertes.fr/tel-00587763.
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Le travail présenté ici s'intéresse à la résolution numérique de problèmes de commande optimale stochastique de grande taille. Nous considérons un système dynamique, sur un horizon de temps discret et fini, pouvant être influencé par des bruits exogènes et par des actions prises par le décideur. L'objectif est de contrôler ce système de sorte à minimiser une certaine fonction objectif, qui dépend de l'évolution du système sur tout l'horizon. Nous supposons qu'à chaque instant des observations sont faites sur le système, et éventuellement gardées en mémoire. Il est généralement profitable, pour le décideur, de prendre en compte ces observations dans le choix des actions futures. Ainsi sommes-nous à la recherche de stratégies, ou encore de lois de commandes, plutôt que de simples décisions. Il s'agit de fonctions qui à tout instant et à toute observation possible du système associent une décision à prendre. Ce manuscrit présente trois contributions. La première concerne la convergence de méthodes numériques basées sur des scénarios. Nous comparons l'utilisation de méthodes basées sur les arbres de scénarios aux méthodes particulaires. Les premières ont été largement étudiées au sein de la communauté "Programmation Stochastique". Des développements récents, tant théoriques que numériques, montrent que cette méthodologie est mal adaptée aux problèmes à plusieurs pas de temps. Nous expliquons ici en détails d'où provient ce défaut et montrons qu'il ne peut être attribué à l'usage de scénarios en tant que tel, mais plutôt à la structure d'arbre. En effet, nous montrons sur des exemples numériques comment les méthodes particulaires, plus récemment développées et utilisant également des scénarios, ont un meilleur comportement même avec un grand nombre de pas de temps. La deuxième contribution part du constat que, même à l'aide des méthodes particulaires, nous faisons toujours face à ce qui est couramment appelé, en commande optimale, la malédiction de la dimension. Lorsque la taille de l'état servant à résumer le système est de trop grande taille, on ne sait pas trouver directement, de manière satisfaisante, des stratégies optimales. Pour une classe de systèmes, dits décomposables, nous adaptons des résultats bien connus dans le cadre déterministe, portant sur la décomposition de grands systèmes, au cas stochastique. L'application n'est pas directe et nécessite notamment l'usage d'outils statistiques sophistiqués afin de pouvoir utiliser la variable duale qui, dans le cas qui nous intéresse, est un processus stochastique. Nous proposons un algorithme original appelé Dual Approximate Dynamic Programming (DADP) et étudions sa convergence. Nous appliquons de plus cet algorithme à un problème réaliste de gestion de production électrique sur un horizon pluri-annuel. La troisième contribution de la thèse s'intéresse à une propriété structurelle des problèmes de commande optimale stochastique : la question de la consistance dynamique d'une suite de problèmes de décision au cours du temps. Notre but est d'établir un lien entre la notion de consistance dynamique, que nous définissons de manière informelle dans le dernier chapitre, et le concept de variable d'état, qui est central dans le contexte de la commande optimale. Le travail présenté est original au sens suivant. Nous montrons que, pour une large classe de modèles d'optimisation stochastique n'étant pas a priori consistants dynamiquement, on peut retrouver la consistance dynamique quitte à étendre la structure d'état du système
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Demir, Ramazan. "An approximate dynamic programming approach to discrete optimization." Thesis, Massachusetts Institute of Technology, 2000. http://hdl.handle.net/1721.1/9137.
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Thesis (Ph.D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2000.Includes bibliographical references (leaves 181-189).
We develop Approximate Dynamic Programming (ADP) methods to integer programming problems. We describe and investigate parametric, nonparametric and base-heuristic learning approaches to approximate the value function in order to break the curse of dimensionality. Through an extensive computational study we illustrate that our ADP approach to integer programming competes successfully with existing methodologies including state of art commercial packages like CPLEX. Our benchmarks for comparison are solution quality, running time and robustness (i.e., small deviations in the computational resources such as running time for varying instances of same size). In this thesis, we particularly focus on knapsack problems and the binary integer programming problem. We explore an integrated approach to solve discrete optimization problems by unifying optimization techniques with statistical learning. Overall, this research illustrates that the ADP is a promising technique by providing near-optimal solutions within reasonable amount of computation time especially for large scale problems with thousands of variables and constraints. Thus, Approximate Dynamic Programming can be considered as a new alternative to existing approximate methods for discrete optimization problems.
by Ramazan Demir.
Ph.D.
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Mekarapiruk, Wichaya. "Simultaneous optimal parameter selection and dynamic optimization using iterative dynamic programming." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/NQ58926.pdf.
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Shen, Yijiang. "Binary image restoration by positive semidefinite programming and signomial programming." Click to view the E-thesis via HKUTO, 2007. http://sunzi.lib.hku.hk/HKUTO/record/B39557431.
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Dunatunga, Manimelwadu Samson 1958. "SUCCESSIVE TWO SEGMENT SEPARABLE PROGRAMMING FOR NONLINEAR MINIMAX OPTIMIZATION." Thesis, The University of Arizona, 1986. http://hdl.handle.net/10150/275509.
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Peters, Jorrit. "Dynamic Programming Heuristics for the Optimization of Hydropower Planning." Thesis, KTH, Optimeringslära och systemteori, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-188686.
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In short-term planning of a hydropower system one optimizes the choice of release of water and which generators to use. This problem is prone to Bellman's curse of dimensionality, since the amount of states increases exponentially with the amount of hydropower stations in the system. In this thesis, two different dynamic programming heuristics to this problem are derived, described and compared with a heuristic developed by Powel AS. A difficulty that extends the problem, is the addition of a power reserve on each time period. A third dynamic programming heuristic is developed to deal with a constraint on the power reserve and the parallel with knapsack problem is described. The new dynamic programming approaches perform similar to the heuristic by Powel AS. The third dynamic programming heuristic that deals with the reserve constraints, provides a better way of dealing with and fulfilling the constraint than currently in place by Powel AS.För kortsiktig planering av vattenkraftsystem optimerar man mängden vatten som släpps på och valet av generatorer att använda. Det här problemet drabbas av Bellman's dimensionalitetens förbannelse då antalet tillstånd ökar exponentiellt med antalet vattenkraftverk i systemet. I detta examensarbete härleds två dynamiska programmeringsheuristiker som jämförs med en heuristik utvecklad av Powel AS. En aspekt som försvårar uppgiften är tillägget av en effektreserv för varje tidsperiod. En tredje dynamisk programmeringsheuristik utvecklas för att hantera restriktioner på effektreserven och parallellen till knapsack problemet beskrivs. De nya dynamisk programmeringstillvägagångsätten presterar likvärdigt med Powel AS heuristik. Den tredje dynamiska programmeringsheuristiken som hanterar reservbegräsningar erbjuder en bättre lösning för att hantera och uppfylla bivillkoren jämförelse med de som i nuläget används av Powel AS.
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Bolat, Murat. "Instrumentation tool for context-aware optimization." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 64 p, 2009. http://proquest.umi.com/pqdweb?did=1885467641&sid=5&Fmt=2&clientId=8331&RQT=309&VName=PQD.
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Theußl, Stefan, Florian Schwendinger, and Kurt Hornik. "ROI: An extensible R Optimization Infrastructure." WU Vienna University of Economics and Business, 2019. http://epub.wu.ac.at/5858/1/ROI_StatReport.pdf.
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Optimization plays an important role in many methods routinely used in statistics, machine learning and data science. Often, implementations of these methods rely on highly specialized optimization algorithms, designed to be only applicable within a specific application. However, in many instances recent advances, in particular in the field of convex optimization, make it possible to conveniently and straightforwardly use modern solvers instead with the advantage of enabling broader usage scenarios and thus promoting reusability.
This paper introduces the R Optimization Infrastructure which provides an extensible infrastructure to model linear, quadratic, conic and general nonlinear optimization problems in a consistent way.
Furthermore, the infrastructure administers many different solvers, reformulations, problem collections and functions to read and write optimization problems in various formats.Series: Research Report Series / Department of Statistics and Mathematics
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Wang, Xia. "Applications of genetic algorithms, dynamic programming, and linear programming to combinatorial optimization problems." College Park, Md.: University of Maryland, 2008. http://hdl.handle.net/1903/8778.
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Thesis (Ph. D.) -- University of Maryland, College Park, 2008.Thesis research directed by: Applied Mathematics & Statistics, and Scientific Computation Program. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Yang, Yi. "Sequential convex approximations of chance constrained programming /." View abstract or full-text, 2008. http://library.ust.hk/cgi/db/thesis.pl?IELM%202008%20YANG.
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Steffy, Daniel E. "Topics in exact precision mathematical programming." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/39639.
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The focus of this dissertation is the advancement of theory and computation related to exact precision mathematical programming. Optimization software based on floating-point arithmetic can return suboptimal or incorrect resulting because of round-off errors or the use of numerical tolerances. Exact or correct results are necessary for some applications. Implementing software entirely in rational arithmetic can be prohibitively slow. A viable alternative is the use of hybrid methods that use fast numerical computation to obtain approximate results that are then verified or corrected with safe or exact computation. We study fast methods for sparse exact rational linear algebra, which arises as a bottleneck when solving linear programming problems exactly. Output sensitive methods for exact linear algebra are studied. Finally, a new method for computing valid linear programming bounds is introduced and proven effective as a subroutine for solving mixed-integer linear programming problems exactly. Extensive computational results are presented for each topic.
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Sun, Liming. "Interior point based continuous methods for linear programming." HKBU Institutional Repository, 2012. https://repository.hkbu.edu.hk/etd_ra/1414.
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沈逸江 and Yijiang Shen. "Binary image restoration by positive semidefinite programming and signomial programming." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2007. http://hub.hku.hk/bib/B39557431.
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Lee, Chae Young. "Analysis and optimization of complex nonserial dynamic programming network systems." Diss., Georgia Institute of Technology, 1985. http://hdl.handle.net/1853/24355.
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Parvizian, Jamshid. "Shape design optimization using boundary elements." Thesis, Imperial College London, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.267165.
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Miller, Simon. "Parallel computing and the molecular dynamic simulation of ionic materials." Thesis, Keele University, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.260050.
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Atamtürk, Alper. "Conflict graphs and flow models for mixed-integer linear optimization problems." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/26002.
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Carreras, Ubach Joan. "Mathematical programming for energetic, economic and environmental optimization of building design." Doctoral thesis, Universitat Rovira i Virgili, 2016. http://hdl.handle.net/10803/396315.
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L’objectiu d’aquesta tesis és desenvolupar eines sistemàtiques de suport per la presa de decisions basades en mètodes matemàtics pel disseny òptim d’edificis amb mínim cost i mínim impacte ambiental. Avui en dia la societat és cada vegada més conscient de la importància que té respectar el medi ambient. Com a resultat, les autoritats i moltes empreses i consumidors estan interessats en productes econòmicament eficients però també respectuosos amb el medi ambient. En aquest context l’eficiència energètica hi juga un paper molt important. L’aïllament d’edificis és particularment interessant, ja que fa disminuir el consum d’energia i, conseqüentment, permet reduir també l’impacte ambiental. El problema general que pretenem solucionar en aquesta tesis és el disseny d’edificis ambientalment respectuosos amb el mínim cost econòmic, centrant-nos en l’optimització de l’aïllament tèrmic exterior. Per tal de demostrar les possibilitats de les nostres eines, considerem un cas d’estudi: Una casa tipus cubicle localitzada a la regió de Lleida. No obstant les nostres metodologies són suficientment generals per treballar amb diferents models d’edifici, variables de decisió i funcions objectiu. Els nostres mètodes s’han desenvolupat amb la intenció d’ajudar als agents involucrats en el disseny d’edificis.El objetivo de esta tesis es desarrollar herramientas sistemáticas de soporte para la toma de decisiones basadas en métodos matemáticos para el diseño óptimo de edificios con mínimo coste y mínimo impacto ambiental. Hoy en día la sociedad es cada vez más consciente de la importancia que tiene respetar el medio ambiente. Como resultado, las autoridades y muchas empresas y consumidores están interesados en productos económicamente eficientes pero también respetuosos con el medio ambiente. En este contexto la eficiencia energética juega un papel muy importante. El aislamiento de edificios es particularmente interesante, ya que hace disminuir el consumo de energía y, consecuentemente, permite reducir también el impacto ambiental. El problema general que pretendemos solucionar en esta tesis es el diseño de edificios ambientalmente respetuosos con el mínimo coste económico, centrándonos en la optimización del aislamiento térmico exterior. Para demostrar las posibilidades de nuestras herramientas, consideramos un caso de estudio: Una casa tipo cubículo localizada en la región de Lleida. No obstatnte nuestras metodologías son suficientemente generales para trabajar con diferentes modelos de edificio, variables de decisión y funciones objetivo. Nuestros métodos se han desarrollado con la intención de ayudar a los agentes involucrados en el diseño de edificios.
The goal of this thesis is to provide systematic mathematical decision-support tools for the design of optimal buildings with minimum cost and minimum environmental impact. Nowadays the society is becoming more aware of the importance of being environmentally conscious. As a result, the authorities and many companies and consumers seek for products that are cost efficient but also environmentally friendly. Here energy efficiency plays an important role. Building insulation is particularly appealing, since it decreases the energy demand, thereby leading to significant environmental savings. The general problem we aim to solve in this thesis is the design of environmentally friendly buildings with the lowest possible cost focusing on the optimization of the external thermal insulation. To illustrate the capabilities of our approaches, we consider a case study: A house-like cubicle located in the Lleida region. However our methodology is general enough to work with different building models, decision variables and objective functions. Our methods are intended to assist decision-makers in the design of buildings.
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Pujari, Nikhil Ajay. "Integrated Supply Chain Optimization Model Using Mathematical Programming and Continuous Approximation." Ohio University / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1132114913.
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Sivakumar, Ishwar Krishnan Ashok 1980. "Stochastic optimization of electricity transmission : dynamic programming algorithms under uncertainties." Thesis, Massachusetts Institute of Technology, 2002. http://hdl.handle.net/1721.1/80655.
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Thesis (M.Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2002.Includes bibliographical references (leaves 141-144).
by Ishwar Krishnan Ashok Sivakumar.
M.Eng.
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Ramachandran, Adithya. "HEV fuel optimization using interval back propagation based dynamic programming." Thesis, Georgia Institute of Technology, 2016. http://hdl.handle.net/1853/55054.
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In this thesis, the primary powertrain components of a power split hybrid electric vehicle are modeled. In particular, the dynamic model of the energy storage element (i.e., traction battery) is exactly linearized through an input transformation method to take advantage of the proposed optimal control algorithm. A lipschitz continuous and nondecreasing cost function is formulated in order to minimize the net amount of consumed fuel. The globally optimal solution is obtained using a dynamic programming routine that produces the optimal input based on the current state of charge and the future power demand. It is shown that the global optimal control solution can be expressed in closed form for a time invariant and convex incremental cost function utilizing the interval back propagation approach. The global optimality of both time varying and invariant solutions are rigorously proved. The optimal closed form solution is further shown to be applicable to the time varying case provided that the time variations of the incremental cost function are sufficiently small. The real time implementation of this algorithm in Simulink is discussed and a 32.84 % improvement in fuel economy is observed compared to existing rule based methods.
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Ross, Roderick. "Dynamic operability assessment : a mathematical programming approach based on Q-parametrization." Doctoral thesis, University of Cape Town, 1997. http://hdl.handle.net/11427/19814.
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Bibliography: pages 197-208.The ability of a process plant to guarantee high product quality, in terms of low variability, is emerging as a defining feature when distinguishing between alternative suppliers. The extent to which this can be achieved is termed a plant's dynamic operability and is a function of both the plant design and the control system design. In the limit, however, the closedloop performance is determined by the properties inherent in the plant. This realization of the interrelationship between a plant design and its achievable closed-loop performance has motivated research toward systematic techniques for screening inherently inferior designs. Pioneering research in the early 1980's identified right-half-plane transmission zeros, time delays, input constraints and model uncertainty as factors that limit the achievable closedloop performance of a process. Quantifying the performance-limiting effect of combinations of these factors has proven to be a challenging problem, as reflected in the literature. It is the aim of this thesis to develop a systematic procedure for dynamic operability assessment in the presence of combinations of performance-limiting factors. The approach adopted in this thesis is based on the Q-parametrization of stabilizing linear feedback controllers and involves posing dynamic operability assessment as a mathematical programming problet? In the proposed formulation, a convex objective function, reflecting a measure of closed-loop performance, is optimized over all stable Q, subject. to a set of constraints on the closed-loop behavior, which for many specifications of interest is convex. A discrete-time formulation is chosen so as to allow for the convenient hand.ling of time delays and time-domain constraints. An important feature of the approach is that, due to the convexity, global optimality is guaranteed. Furthermore, the fact that Q parametrizes all stabilizing linear feedback controllers implies that the performance at the optimum represents the best possible performance for any such controller. The results are thus not biased by controller type or tuning, apart from the requirement that the controller be linear.
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Cha, Kyungduck. "Cancer treatment optimization." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/22604.
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Thesis (Ph. D.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2008.Committee Chair: Lee, Eva K.; Committee Member: Barnes, Earl; Committee Member: Hertel, Nolan E.; Committee Member: Johnson, Ellis; Committee Member: Monteiro, Renato D.C.
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Drouven, Markus G. "Mixed Integer Programming Models for Shale Gas Development." Research Showcase @ CMU, 2017. http://repository.cmu.edu/dissertations/874.
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Shale gas development is transforming the energy landscape in the United States. Advances in production technologies, notably the dual application of horizontal drilling and hydraulic fracturing, allow the extraction of vast deposits of trapped natural gas that, until recently, were uneconomic to produce. The objective of this work is to develop mixed-integer programming models to support upstream operators in making faster and better decisions that ensure low-cost and responsible natural gas production from shale formations. We propose a multiperiod mixed-integer nonlinear programming (MINLP) model along with a tailored solution strategy for strategic, quality-sensitive shale gas development planning. The presented model coordinates planning and design decisions to maximize the net present value of a field-wide development project. By performing a lookback analysis based on data from a shale gas producer in the Appalachian Basin, we find that return-to-pad operations are the key to cost-effective shale gas development strategies. We address impaired water management challenges in active development areas through a multiperiod mixed-integer linear programming (MILP) model. This model is designed to schedule the sequence of fracturing jobs and coordinate impaired- and freshwater deliveries to minimize water management expenses, while simultaneously maximizing revenues from gas sales. Based on the results of a real-world case study, we conclude that rigorous optimization can support upstream operators in cost-effectively reducing freshwater consumption significantly, while also achieving effective impaired water disposal rates of less than one percent. We also propose a multiperiod MINLP model and a tailor-designed solution strategy for line pressure optimization in shale gas gathering systems. The presented model determines when prospective wells should be turned in-line, and how the pressure profile within a gathering network needs to be managed to maximize the net present value of a development project. We find that backoff effects associated with turn-in line operations can be mitigated through preventive line pressure manipulations. Finally, we develop deterministic and stochastic MILP models for refracturing planning. These models are designed to determine whether or not a shale well should be restimulated, and when exactly to refracture it. The stochastic refracturing planning model explicitly considers exogenous price forecast uncertainty and endogenous well performance uncertainty. Our results suggest that refracturing is a promising strategy for combatting the characteristically steep decline curves of shale gas wells.