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Dissertations / Theses on the topic 'Mathematical optimization'
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Keanius, Erik. "Mathematical Optimization in SVMs." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-297492.
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In this thesis, support vector machines (SVMs) are studied from a mathematical optimization viewpoint. Both the linear case using hard-margin as well as soft-margin classification and the non-linear case using kernel functions are discussed. The theory of kernel Hilbert spaces is introduced and related to the non-linear SVM case. Moreover, fundamental theorems from optimization, including Lagrangian duality and KKT conditions, are introduced and proved. These theorems are then applied to the optimization problem of SVMs. Finally, the SVM optimization problem is implemented, solved, and visualized in Python.
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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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Holm, Åsa. "Mathematical Optimization of HDR Brachytherapy." Doctoral thesis, Linköpings universitet, Optimeringslära, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-99795.
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One out of eight deaths throughout the world is due to cancer. Developing new treatments and improving existing treatments is hence of major importance. In this thesis we have studied how mathematical optimization can be used to improve an existing treatment method: high-dose-rate (HDR) brachytherapy. HDR brachytherapy is a radiation modality used to treat tumours of for example the cervix, prostate, breasts, and skin. In HDR brachytherapy catheters are implanted into or close to the tumour volume. A radioactive source is moved through the catheters, and by adjusting where the catheters are placed, called catheter positioning, and how the source is moved through the catheters, called the dwelling time pattern, the dose distribution can be controlled. By constructing an individualized catheter positioning and dwelling time pattern, called dose plan, based on each patient's anatomy, it is possible to improve the treatment result. Mathematical optimization has during the last decade been used to aid in creating individualized dose plans. The dominating optimization model for this purpose is a linear penalty model. This model only considers the dwelling time pattern within already implanted catheters, and minimizes a weighted deviation from dose intervals prescribed by a physician. In this thesis we show that the distribution of the basic variables in the linear penalty model implies that only dwelling time patterns that have certain characteristics can be optimal. These characteristics cause troublesome inhomogeneities in the plans, and although various measures for mitigating these are already available, it is of fundamental interest to understand their cause. We have also shown that the relationship between the objective function of the linear penalty model and the measures commonly used for evaluating the quality of the dose distribution is weak. This implies that even if the model is solved to optimality there is no guarantee that the generated plan is optimal with respect to clinically relevant objectives, or even near-optimal. We have therefore constructed a new model for optimizing the dwelling time pattern. This model approximates the quality measures by the concept conditional value-at-risk, and we show that the relationship between our new model and the quality measures is strong. Furthermore, the new model generates dwelling time patterns that yield high-quality dose distributions. Combining optimization of the dwelling time pattern with optimization of the catheter positioning yields a problem for which it is rarely possible to find a proven optimal solution within a reasonable time frame. We have therefore developed a variable neighbourhood search heuristic that outperforms a state-of-the-art optimization software (CPLEX). We have also developed a tailored branch-and-bound algorithm that is better at improving the dual bound than a general branch-and-bound algorithm. This is a step towards the development of a method that can find proven optimal solutions to the combined problem within a reasonable time frame.
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Najafiazar, Bahador. "Mathematical Optimization in Reservoir Management." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for petroleumsteknologi og anvendt geofysikk, 2014. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-27058.
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Getting the most out of a hydrocarbon reservoir is not a trivial task. It takes plentyof interwoven decisions to make. There are many forms of tools that support engineersto make correct decisions. The simplest ones would only display measurementsin a suitable way, and appoint the rest of the decision making processto human knowledge and experience. Complex decision support tools may implementmodel-based estimation and optimization. This work targets methods foroptimization-based decision support.The objective of this study is to formulate, implement and test promising methodsof hydrocarbon production optimization through various test cases. To do this, avarious optimizations algorithm were applied to the simulated reservoir modelsusing the Matlab Reservoir Simulation Toolbox (MRST).
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Saunders, David. "Applications of optimization to mathematical finance." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp04/mq29265.pdf.
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Chang, Tyler Hunter. "Mathematical Software for Multiobjective Optimization Problems." Diss., Virginia Tech, 2020. http://hdl.handle.net/10919/98915.
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In this thesis, two distinct problems in data-driven computational science are considered. The main problem of interest is the multiobjective optimization problem, where the tradeoff surface (called the Pareto front) between multiple conflicting objectives must be approximated in order to identify designs that balance real-world tradeoffs. In order to solve multiobjective optimization problems that are derived from computationally expensive blackbox functions, such as engineering design optimization problems, several methodologies are combined, including surrogate modeling, trust region methods, and adaptive weighting. The result is a numerical software package that finds approximately Pareto optimal solutions that are evenly distributed across the Pareto front, using minimal cost function evaluations. The second problem of interest is the closely related problem of multivariate interpolation, where an unknown response surface representing an underlying phenomenon is approximated by finding a function that exactly matches available data. To solve the interpolation problem, a novel algorithm is proposed for computing only a sparse subset of the elements in the Delaunay triangulation, as needed to compute the Delaunay interpolant. For high-dimensional data, this reduces the time and space complexity of Delaunay interpolation from exponential time to polynomial time in practice. For each of the above problems, both serial and parallel implementations are described. Additionally, both solutions are demonstrated on real-world problems in computer system performance modeling.<br>Doctor of Philosophy<br>Science and engineering are full of multiobjective tradeoff problems. For example, a portfolio manager may seek to build a financial portfolio with low risk, high return rates, and minimal transaction fees; an aircraft engineer may seek a design that maximizes lift, minimizes drag force, and minimizes aircraft weight; a chemist may seek a catalyst with low viscosity, low production costs, and high effective yield; or a computational scientist may seek to fit a numerical model that minimizes the fit error while also minimizing a regularization term that leverages domain knowledge. Often, these criteria are conflicting, meaning that improved performance by one criterion must be at the expense of decreased performance in another criterion. The solution to a multiobjective optimization problem allows decision makers to balance the inherent tradeoff between conflicting objectives. A related problem is the multivariate interpolation problem, where the goal is to predict the outcome of an event based on a database of past observations, while exactly matching all observations in that database. Multivariate interpolation problems are equally as prevalent and impactful as multiobjective optimization problems. For example, a pharmaceutical company may seek a prediction for the costs and effects of a proposed drug; an aerospace engineer may seek a prediction for the lift and drag of a new aircraft design; or a search engine may seek a prediction for the classification of an unlabeled image. Delaunay interpolation offers a unique solution to this problem, backed by decades of rigorous theory and analytical error bounds, but does not scale to high-dimensional "big data" problems. In this thesis, novel algorithms and software are proposed for solving both of these extremely difficult problems.
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ROSSI, FILIPPO. "Mathematical models for selling process optimization." Doctoral thesis, Università degli studi di Genova, 2021. http://hdl.handle.net/11567/1050078.
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The work of the Thesis has been pursued in collaboration with an important company operating in the tourist sector.
The followed projects in the work can be seen as belonging to the Destination Management branch, that is the study and the implementation of actions aimed at better managing the company offer related to touristic experiences broadly. In particular, the first project has been related to Revenue Forecasting and has dealt with the definition of a methodology, based on mathematical and statistical techniques, aimed at forecasting the revenue streams linked to specific items of a company; the second project, Destination Discovery, instead aimed at the high-level analysis of tourism opportunities in different geographical areas, researching and evaluating new possibilities
for the company related to tourist interest. In the work, some preliminaries about what a forecast is will be provided and the many techniques aimed at accomplishing the task, giving a general theoretical framework for the topic will be discussed. Then some details about data and the set of more practical operations needed in order to extract information from them in a numerical manner, eventually building a forecasting model on it will be discussed. Later the application of the techniques previously introduced to the different projects will be discussed; for each one of them, the methodologies followed and the analyzes carried out will be provided, as well as the obtained results.
Finally an analysis of what has globally been done in the work along with different comments, the obtained results and some possible future work and improvements will conclude the work.
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Rossetti, Gaia. "Mathematical optimization techniques for cognitive radar networks." Thesis, Loughborough University, 2018. https://dspace.lboro.ac.uk/2134/33419.
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This thesis discusses mathematical optimization techniques for waveform design in cognitive radars. These techniques have been designed with an increasing level of sophistication, starting from a bistatic model (i.e. two transmitters and a single receiver) and ending with a cognitive network (i.e. multiple transmitting and multiple receiving radars). The environment under investigation always features strong signal-dependent clutter and noise. All algorithms are based on an iterative waveform-filter optimization. The waveform optimization is based on convex optimization techniques and the exploitation of initial radar waveforms characterized by desired auto and cross-correlation properties. Finally, robust optimization techniques are introduced to account for the assumptions made by cognitive radars on certain second order statistics such as the covariance matrix of the clutter. More specifically, initial optimization techniques were proposed for the case of bistatic radars. By maximizing the signal to interference and noise ratio (SINR) under certain constraints on the transmitted signals, it was possible to iteratively optimize both the orthogonal transmission waveforms and the receiver filter. Subsequently, the above work was extended to a convex optimization framework for a waveform design technique for bistatic radars where both radars transmit and receive to detect targets. The method exploited prior knowledge of the environment to maximize the accumulated target return signal power while keeping the disturbance power to unity at both radar receivers. The thesis further proposes convex optimization based waveform designs for multiple input multiple output (MIMO) based cognitive radars. All radars within the system are able to both transmit and receive signals for detecting targets. The proposed model investigated two complementary optimization techniques. The first one aims at optimizing the signal to interference and noise ratio (SINR) of a specific radar while keeping the SINR of the remaining radars at desired levels. The second approach optimizes the SINR of all radars using a max-min optimization criterion. To account for possible mismatches between actual parameters and estimated ones, this thesis includes robust optimization techniques. Initially, the multistatic, signal-dependent model was tested against existing worst-case and probabilistic methods. These methods appeared to be over conservative and generic for the considered signal-dependent clutter scenario. Therefore a new approach was derived where uncertainty was assumed directly on the radar cross-section and Doppler parameters of the clutters. Approximations based on Taylor series were invoked to make the optimization problem convex and {subsequently} determine robust waveforms with specific SINR outage constraints. Finally, this thesis introduces robust optimization techniques for through-the-wall radars. These are also cognitive but rely on different optimization techniques than the ones previously discussed. By noticing the similarities between the minimum variance distortionless response (MVDR) problem and the matched-illumination one, this thesis introduces robust optimization techniques that consider uncertainty on environment-related parameters. Various performance analyses demonstrate the effectiveness of all the above algorithms in providing a significant increase in SINR in an environment affected by very strong clutter and noise.
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Trescher, Saskia. "Estimating Gene Regulatory Activity using Mathematical Optimization." Doctoral thesis, Humboldt-Universität zu Berlin, 2020. http://dx.doi.org/10.18452/21900.
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Die Regulation der Genexpression ist einer der wichtigsten zellulären Prozesse und steht in Zusammenhang mit der Entstehung diverser Krankheiten. Regulationsmechanismen können mit einer Vielzahl von Methoden experimentell untersucht werden, zugleich erfordert die Integration der Datensätze in umfassende Modelle stringente rechnergestützte Methoden. Ein Teil dieser Methoden modelliert die genomweite Genexpression als (lineares) Gleichungssystem über die Aktivität und Beziehungen von Transkriptionsfaktoren (TF), Genen und anderen Faktoren und optimiert die Parameter, sodass die gemessenen Expressionsintensitäten möglichst genau wiedergegeben werden. Trotz ihrer gemeinsamen Wurzeln in der mathematischen Optimierung unterscheiden sich die Methoden stark in der Art der integrierten Daten, im für ihre Anwendung notwendigen Hintergrundwissen, der Granularität des Regulationsmodells, des konkreten Paradigmas zur Lösung des Optimierungsproblems, und der zur Evaluation verwendeten Datensätze.
In dieser Arbeit betrachten wir fünf solcher Methoden und stellen einen qualitativen und quantitativen Vergleich auf. Unsere Ergebnisse zeigen, dass die Überschneidungen der Ergebnisse sehr gering sind, was nicht auf die Stichprobengröße oder das regulatorische Netzwerk zurückgeführt werden kann. Ein Grund für die genannten Defizite könnten die vereinfachten Modelle zellulärer Prozesse sein, da diese vorhandene Rückkopplungsschleifen ignorieren. Wir schlagen eine neue Methode (Florae) mit Schwerpunkt auf die Berücksichtigung von Rückkopplungsschleifen vor und beurteilen deren Ergebnisse. Mit Floræ können wir die Identifizierung von Knockout- und Knockdown-TF in synthetischen Datensätzen verbessern. Unsere Ergebnisse und die vorgeschlagene Methode erweitern das Wissen über genregulatorische Aktivität können die Identifizierung von Ursachen und Mechanismen regulatorischer (Dys-)Funktionen und die Entwicklung von medizinischen Biomarkern und Therapien unterstützen.<br>Gene regulation is one of the most important cellular processes and closely interlinked pathogenesis. The elucidation of regulatory mechanisms can be approached by many experimental methods, yet integration of the resulting heterogeneous, large, and noisy data sets into comprehensive models requires rigorous computational methods. A prominent class of methods models genome-wide gene expression as sets of (linear) equations over the activity and relationships of transcription factors (TFs), genes and other factors and optimizes parameters to fit the measured expression intensities. Despite their common root in mathematical optimization, they vastly differ in the types of experimental data being integrated, the background knowledge necessary for their application, the granularity of their regulatory model, the concrete paradigm used for solving the optimization problem and the data sets used for evaluation.
We review five recent methods of this class and compare them qualitatively and quantitatively in a unified framework. Our results show that the result overlaps are very low, though sometimes statistically significant. This poor overall performance cannot be attributed to the sample size or to the specific regulatory network provided as background knowledge. We suggest that a reason for this deficiency might be the simplistic model of cellular processes in the presented methods, where TF self-regulation and feedback loops were not represented. We propose a new method for estimating transcriptional activity, named Florae, with a particular focus on the consideration of feedback loops and evaluate its results. Using Floræ, we are able to improve the identification of knockout and knockdown TFs in synthetic data sets. Our results and the proposed method extend the knowledge about gene regulatory activity and are a step towards the identification of causes and mechanisms of regulatory (dys)functions, supporting the development of medical biomarkers and therapies.
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Haddon, Antoine. "Mathematical Modeling and Optimization for Biogas Production." Thesis, Montpellier, 2019. http://www.theses.fr/2019MONTS047.
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La digestion anaérobique est un processus biologique au cours duquel des micro-organismes décomposent de la matière organique pour produire du biogaz (dioxyde de carbone et methane) qui peut être utilisé comme source d'énergie renouvelable. Cette thèse porte sur l'élaboration de stratégies de contrôle et la conception de bioréacteurs qui maximisent la production de biogaz.La première partie se concentre sur le problème de contrôle optimal de la maximisation de la production de biogaz dans un chemostat avec un modèle à une réaction, en contrôlant le taux de dilution. Pour le problème à horizon fini, nous étudions des commandes type feedback, similaires à ceux utilisés en pratique et consistant à conduire le réacteur vers un niveau de substrat donné et à le maintenir à ce niveau. Notre approche repose sur une estimation de la fonction de valeur inconnue en considérant différentes fonctions de coût pour lesquelles la solution optimale admet un feedback optimal explicite et autonome. En particulier, cette technique fournit une estimation de la sous-optimalité des régulateurs étudiés pour une large classe de fonctions de croissance dépendant du substrat et de la biomasse. À l'aide de simulations numériques, on montre que le choix du meilleur feedback dépend de l'horizon de temps et de la condition initiale.Ensuite, nous examinons le problème sur un horizon infini, pour les coûts moyen et actualisé. On montre que lorsque le taux d'actualisation tends vers à 0, la fonction de valeur du problème actualisé converge vers la fonction de valeur pour le coût moyen. On identifie un ensemble de solutions optimales pour le problème de limite et avec coût moyen comme étant les contrôles qui conduisent le système vers un état qui maximise le débit de biogaz sur un ensemble invariant.Nous revenons ensuite au problème sur à horizon fini fixe et avec le Principe du Maximum de Pontryagin, on montre que le contrôle optimal à une structure bang arc singulier. On construit une famille de contrôles extremal qui dépendent de la valeur constante du Hamiltonien. En utilisant l'équation de Hamilton-Jacobi-Bellman, on identifie le contrôle optimal comme étant celui associé à la valeur du Hamiltonien qui satisfait une équation de point fixe. On propose ensuite un algorithme pour calculer la commande optimale en résolvant cette équation de point fixe. On illustre enfin cette méthode avec les deux principales types de fonctions de croissance de Monod et Haldane.Dans la deuxième partie, on modélise et on étudie l'impact de l'hétérogénéité du milieu réactionnel sur la production de biogaz. Pour cela, on introduit un modèle de bioréacteur pilote qui décrit les caractéristiques spatiales. Ce modèle tire parti de la géométrie du réacteur pour réduire la dimension spatiale de la section contenant un lit fixe et, dans les autres sections, on considère les équations 3D de Navier-Stokes en régime permanent pour la dynamique des fluides. Pour représenter l'activité biologique, on utilise un modèle à deux réactions et pour les substrats, des équations advection-diffusion-réaction. On considère seulement les biomasses qui sont attachées au lit fixe et on modélise leur croissance avec une fonction densité dépendante. On montre que ce modèle peut reproduire le gradient spatial de données expérimentales et permet de mieux comprendre la dynamique interne du réacteur. En particulier, les simulations numériques indiquent qu'en mélangeant moins, le réacteur est plus efficace, élimine plus de matières organiques et produit plus de biogaz<br>Anaerobic digestion is a biological process in which organic compounds are degraded by different microbial populations into biogas (carbon dioxyde and methane), which can be used as a renewable energy source. This thesis works towards developing control strategies and bioreactor designs that maximize biogas production.The first part focuses on the optimal control problem of maximizing biogas production in a chemostat in several directions. We consider the single reaction model and the dilution rate is the controlled variable.For the finite horizon problem, we study feedback controllers similar to those used in practice and consisting in driving the reactor towards a given substrate level and maintaining it there. Our approach relies on establishing bounds of the unknown value function by considering different rewards for which the optimal solution has an explicit optimal feedback that is time-independent. In particular, this technique provides explicit bounds on the sub-optimality of the studied controllers for a broad class of substrate and biomass dependent growth rate functions. With numerical simulations, we show that the choice of the best feedback depends on the time horizon and initial condition.Next, we consider the problem over an infinite horizon, for averaged and discounted rewards. We show that, when the discount rate goes to 0, the value function of the discounted problem converges and that the limit is equal to the value function for the averaged reward. We identify a set of optimal solutions for the limit and averaged problems as the controls that drive the system towards a state that maximizes the biogas flow rate on an special invariant set.We then return to the problem over a fixed finite horizon and with the Pontryagin Maximum Principle, we show that the optimal control has a bang singular arc structure. We construct a one parameter family of extremal controls that depend on the constant value of the Hamiltonian. Using the Hamilton-Jacobi-Bellman equation, we identify the optimal control as the extremal associated with the value of the Hamiltonian which satisfies a fixed point equation. We then propose a numerical algorithm to compute the optimal control by solving this fixed point equation. We illustrate this method with the two major types of growth functions of Monod and Haldane.In the second part, we investigate the impact of mixing the reacting medium on biogas production. For this we introduce a model of a pilot scale upflow fixed bed bioreactor that offers a representation of spatial features. This model takes advantage of reactor geometry to reduce the spatial dimension of the section containing the fixed bed and in other sections, we consider the 3D steady-state Navier-Stokes equations for the fluid dynamics. To represent the biological activity, we use a 2 step model and for the substrates, advection-diffusion-reaction equations. We only consider the biomasses that are attached in the fixed bed section and we model their growth with a density dependent function. We show that this model can reproduce the spatial gradient of experimental data and helps to better understand the internal dynamics of the reactor. In particular, numerical simulations indicate that with less mixing, the reactor is more efficient, removing more organic matter and producing more biogas
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Persson, Mikael. "Cableharness selection for gearboxes using mathematical optimization." Thesis, KTH, Optimeringslära och systemteori, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-209929.
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The Scania modular product system enables the production of thousands of different versions of gearboxes. If each version use a unique cable harness, this leads to large costs for storage and production. It is desired to find a smaller set of cable harnesses to fit the needs of all gearboxes. In this report we present two mathematical programming models to accomplish this while minimizing cost for production and storage. We propose a procedure for partitioning the data into smaller subsets without loosing model accuracy. We also show how the solution to the first model may be used as a warm start solution for the second model. The report focuses on cables for gearbox control systems used in heavy trucks manufactured by Scania. Results from testing the models against data provided by Scania is presented. These results suggest that substantial reduction in production cost can be achieved. Findings from this project can be used in similar situations, for example engine control system cables and general vehicle electric wiring.<br>Scanias modulsystem gör att tusentals olika växellådsvarianter är möjliga att tillverka. Om varje växellådsvariant skall ha ett eget kablage leder detta till stora lagerhållnings- och produktionskostnader. Det är därför fördelaktigt om man kan hitta en mindre uppsättning kablage som uppfyller kraven för alla växellådor. Två modeller inom matematisk optimering presenteras för att uppnå målet samtidigt som kostnader för lagerhållning och produktion minimeras. Vidare föreslås en metod för att dela upp problemet i delproblem utan att noggrannheten minskar. Vi visar även hur lösningen från den första modellen kan användas som varmstart till den andra modellen. Fokus är på kablage för växellådor till Scanias lastbilar. Resultat från test av modellerna med data från Scanias produktion presenteras. Resultaten visar på att en betydande besparing är möjlig. Rapportens slutsatser kan även användas i liknande situationer, till exempel motorstyrsystem och andra elsystem i fordon.
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Andersson, Björn. "Mathematical Optimization of Radiation Therapy Goal Fulfillment." Thesis, Uppsala universitet, Institutionen för informationsteknologi, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-325396.
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Cancer is one of the deadliest diseases today, and with increasingly larger and older populations, cancer constitutes an enormous contemporary and future challenge. Luckily, advances in technology and medicine are continuously contributing to a decrease in cancer mortality, and to the reduction of treatment side effects. The aim of this Master's thesis is to be a part of these advances, thereby increasing the survival chances and well-being of future cancer patients. The thesis regards specifically the improvement of radiation therapy, a form of treatment utilized in both curative and palliative cancer care. In radiation therapy, ionizing radiation is directed at cancerous cells in the body. The radiation prevents the further proliferation of malignant cells by damaging their DNA. However, the radiation is also harmful to healthy cells. It is therefore of utmost importance that the irradiation of the patient is done in such a way to spare the critical organs in the vicinity of the tumor. To obtain the best possible treatment, mathematical optimization algorithms are utilized. Using physical models of how radiation travels in the body, it is possible to calculate what effect the irradiation of the patient will have. To quantify the quality of the treatment, mathematical functions are used, which evaluate the radiation dose under certain criteria. Once these functions are defined, algorithms can be applied that find the optimal treatment with regard to the given criteria. The formulation of these functions and their properties is the main focus of this thesis. Using clinical evaluation criteria previously used to assess treatments, a framework for optimizing functions that directly correlate to the clinical goals is constructed. The framework is examined and used to generate radiation therapy plans for three cancer patients. In each of the cases, the constructed treatment plans demonstrate high quality, often better than or comparable to the plans created by experienced dose planners using existing tools. A particularly interesting application of the developed framework is the automatic generation of treatments. This relies on the clinician giving the clinical goals as input to the algorithm. A plan is then generated with maximal goal fulfillment. This eliminates the tedious and time consuming process of parameter tuning to achieve a satisfactory plan. Several studies have demonstrated the ability of automatic planning to retain the plan quality while substantially improving planning efficiency.
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Gambella, Claudio <1988>. "Mathematical Optimization for Routing and Logistic Problems." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amsdottorato.unibo.it/7607/1/gambella_claudio_tesi.pdf.
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In this thesis, we focus on mathematical optimization models and algorithms for solving routing and logistic problems. The first contribution regards a path and mission planning problem, called Carrier-Vehicle Traveling Salesman Problem (CVTSP), for a system of heterogeneous vehicles. A Mixed-Integer Second Order Conic Programming (MISOCP) model and a Benders-like enumeration algorithm are presented for solving CVTSP. The second work concerns a class of routing problems, referred to as Interceptor Vehicle Routing Problems (IVRPs). They generalize VRPs in the sense that target points are allowed to move from their initial location according to a known motion. We present a novel MISOCP formulation and a Branch-and-Price algorithm based on a Lagrangian Relaxation of the vehicle-assignment constraints. Other two contributions focus on waste flow management problems: the former considers a deterministic setting in which a Mixed-Integer Linear Programming (MILP) formulation is used as a Decision Support System for a real-world waste operator, whereas the latter deals with the uncertainty of the waste generation amounts by means of Two-Stage Multiperiod Stochastic Mixed-Integer Programming formulations. Finally, we give an overview on the optimization challenges arising in electric car-sharing systems, both at strategic and tactical planning level.
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Gambella, Claudio <1988>. "Mathematical Optimization for Routing and Logistic Problems." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amsdottorato.unibo.it/7607/.
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In this thesis, we focus on mathematical optimization models and algorithms for solving routing and logistic problems. The first contribution regards a path and mission planning problem, called Carrier-Vehicle Traveling Salesman Problem (CVTSP), for a system of heterogeneous vehicles. A Mixed-Integer Second Order Conic Programming (MISOCP) model and a Benders-like enumeration algorithm are presented for solving CVTSP. The second work concerns a class of routing problems, referred to as Interceptor Vehicle Routing Problems (IVRPs). They generalize VRPs in the sense that target points are allowed to move from their initial location according to a known motion. We present a novel MISOCP formulation and a Branch-and-Price algorithm based on a Lagrangian Relaxation of the vehicle-assignment constraints. Other two contributions focus on waste flow management problems: the former considers a deterministic setting in which a Mixed-Integer Linear Programming (MILP) formulation is used as a Decision Support System for a real-world waste operator, whereas the latter deals with the uncertainty of the waste generation amounts by means of Two-Stage Multiperiod Stochastic Mixed-Integer Programming formulations. Finally, we give an overview on the optimization challenges arising in electric car-sharing systems, both at strategic and tactical planning level.
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Colombo, F. "MATHEMATICAL PROGRAMMING ALGORITHMS FOR NETWORK OPTIMIZATION PROBLEMS." Doctoral thesis, Università degli Studi di Milano, 2014. http://hdl.handle.net/2434/234164.
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In the thesis we consider combinatorial optimization problems that are defined by means of networks. These problems arise when we need to take effective decisions to build or manage network structures, both satisfying the design constraints and minimizing the costs.
In the thesis we focus our attention on the four following problems:
- The Multicast Routing and Wavelength Assignment with Delay Constraint in WDM networks with heterogeneous capabilities (MRWADC) problem: this problem arises in the telecommunications industry and it requires to define an efficient way to make multicast transmissions on a WDM optical network. In more formal terms, to solve the MRWADC problem we need to identify, in a given directed graph that models the WDM optical network, a set of arborescences that connect the source of the transmission to all its destinations. These arborescences need to satisfy several quality-of-service constraints and need to take into account the heterogeneity of the electronic devices belonging to the WDM network.
- The Homogeneous Area Problem (HAP): this problem arises from a particular requirement of an intermediate level of the Italian government called province. Each province needs to coordinate the common activities of the towns that belong to its territory. To practically perform its coordination role, the province of Milan created a customer care layer composed by a certain number of employees that have the task to support the towns of the province in their administrative works. For the sake of efficiency, the employees of this customer care layer have been partitioned in small groups and each group is assigned to a particular subset of towns that have in common a large number of activities. The HAP requires
to identify the set of towns assigned to each group in order to minimize the redundancies generated by the towns that, despite having some activities in common, have been assigned to different groups.
Since, for both historical and practical reasons, the towns in a particular subset need to be adjacent, the HAP can be effectively modeled as a particular graph partitioning problem that requires the connectivity of the obtained subgraphs and the satisfaction of nonlinear knapsack constraints.
- Knapsack Prize Collecting Steiner Tree Problem (KPCSTP): to implement a Column Generation algorithm for the MRWADC problem and for the HAP, we need also to solve the two corresponding pricing problems. These two problems are very similar, both of them require to find an arborescence, contained in a given directed weighted graph, that minimizes the difference between its cost and the prizes associated with the spanned nodes. The two problems differ in the side constraints that their feasible solutions need to satisfy and in the way in which the cost of an arborescence is defined. The ILP formulations and the resolution methods that we developed to tackle these two problems have many characteristics in common with the ones used to solve other similar problems.
To exemplify these similarities and to summarize and extend the techniques that we developed for the MRWADC problem and for the HAP, we also considered the KPCSTP. This problem requires to find a tree that minimizes the difference between the cost of the used arcs and the profits of the spanned nodes. However, not all trees are feasible: the sum of the weights of the nodes spanned by a feasible tree cannot exceed a given weight threshold. In the thesis we propose a computational comparison among several optimization methods for the KPCSTP that have been either already proposed in the literature or obtained modifying our ILP formulations for the two previous pricing problems.
- The Train Design Optimization (TDO) problem: this problem was the topic of the second problem solving competition, sponsored in 2011 by the Railway Application Section (RAS) of the Institute for Operations Research and the Management Sciences (INFORMS). We participated to the contest and we won the second prize. After the competition, we continued to work on the TDO problem and in the thesis we describe the improved method that we have obtained at the end of this work. The TDO problem arises in the freight railroad industry. Typically, a freight railroad company receives requests from customers to transport a set of railcars from an origin rail yard to a destination rail yard. To satisfy these requests, the company first aggregates the railcars having the same origin and the same destination in larger blocks, and then it defines a trip plan to transport the obtained blocks to their correct destinations. The TDO problem requires to identify a trip plan that efficiently uses the limited resources of the considered rail company. More formally, given a railway network, a set of blocks and the segments of the network in which a crew can legally drive a train, the TDO problem requires to define a set of trains and the way in which the given blocks can be transported to their destinations by these trains, both satisfying operational constraints and minimizing the transportation costs.
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Ramachandran, Selvaraj. "Hypoid gear optimization." PDXScholar, 1992. https://pdxscholar.library.pdx.edu/open_access_etds/4419.
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A hypoid gear optimization procedure using the method of feasible directions has been developed. The objective is to reduce the gear set weight with bending strength, contact strength and facewidth-diametral pitch ratio as constraints. The objective function weight, is calculated from the geometric approximation of the volume of the gear and pinion. The design variables selected are number of gear teeth, diametral pitch, and facewidth. The input parameters for starting the initial design phase are power to be transmitted, speed, gear ratio, type of application, mounting condition, type of loading, and the material to be used. In the initial design phase, design parameters are selected or calculated using the standard available procedures. These selected values of design parameters are passed on to the optimization routine as starting points.
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Gu, Fangqing. "Many objective optimization: objective reduction and weight design." HKBU Institutional Repository, 2016. https://repository.hkbu.edu.hk/etd_oa/315.
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Many-objective optimization problems (MaOPs), in which the number of objectives is greater than three, are common in various applications, and have drawn many scholars' attention. Evolutionary multiobjective optimization (EMO) algorithms have been successfully applied to solve bi- and tri-objective optimization problems. However, MaOPs are more challenging compared with the bi- and tri-objective optimization problems. The performances of most existing classical EMO algorithms generally deteriorate over the number of objectives. Thus, this thesis presents a weight design method to modify classical decomposition-based EMO algorithms for solving MaOPs, and a novel objective extraction method to transform the MaOP into a problem with few objectives.;Additionally, performance metrics play an important role in understanding the strengths and weaknesses of an algorithm. To the best of our knowledge, there is no direct performance metric for the objective reduction algorithms. Their performance can only be indirectly evaluated by the metrics, such as IGD-metric and H-metric, of the solutions obtained by an EMO algorithm equipped with the objective reduction method. This thesis presents a direct performance metric featuring the simplicity and usability of the objective reduction algorithms. Meanwhile, we propose a novel framework for many-objective test problems, which features both simple and complicated Pareto set shape, and is scalable in terms of the numbers of the objectives and the essential objectives. Also, we can control the importance of essential objectives.;As some MaOPs may have redundant or correlated objectives, it is desirable to reduce the number of the objectives in such circumstances. However, the Pareto solution of the reduced problem obtained by most existing objective reduction methods may not be the Pareto solution of the original MaOP. Thus, this thesis proposes an objective extraction method for MaOPs. It formulates the reduced objective as a linear combination of the original objectives to maximize the conflict between the reduced objectives. Subsequently, the Pareto solution of the reduced problem obtained by the proposed algorithm is that of the original MaOP, and the proposed algorithm can preserve the non-dominant relation as much as possible. We compare the proposed objective extraction method with three objective reduction methods, i.e., REDGA, L-PCA and NL-MVU-PCA. The numerical studies show the effectiveness and robustness of the proposed approach.;The decomposition-based EMO algorithms, e.g. MOEA/D, M2M, have demonstrated the effectiveness in dealing with MaOPs. Nevertheless, these algorithms need to design the weight vectors, which has significant effects on the algorithms' performance. Especially, when the Pareto front of the problem is incomplete, these algorithms cannot obtain a set of uniform solutions by using the conventional weight design methods. Not only can self-organizing map (SOM) preserve the topological properties of the input data by using the neighborhood function, but also its display is more uniform than the probability density of the input data. This phenomenon is advantageous to generate a set of uniform weight vectors based on the distribution of the individuals. Therefore, we propose a novel weight design method based on SOM, which can be integrated with most of the decomposition-based EMO algorithms. In this thesis, we choose the existing M2M algorithm as an example for such integration. This integrated algorithm is then compared with the original M2M and two state-of-the-art algorithms, i.e. MOEA/D and NSGA-II on eleven redundancy problems and eight non-redundancy problems. The experimental results show the effectiveness of the proposed approach.
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Zymolka, Adrian. "Design of survivable optical networks by mathematical optimization." Göttingen Cuvillier, 2007.
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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.<br>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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Craft, David (David Loren) 1973. "Local energy management through mathematical modeling and optimization." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/28858.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2004.<br>Includes bibliographical references (p. 217-223).<br>(cont.) Extensions to the core TOTEM model include a demand charge model, used for making daily optimal control decisions when the electric bill includes a charge based on the monthly maximum power draw. The problem of heating, ventilation, and air conditioning (HVAC) control is treated separately since it strongly violates TOTEM's linearity assumptions. Nonetheless, we describe a solution approach to the HVAC problem which operates in conjunction with TOTEM. We also provide an analysis of storage suitability in stochastic supply and demand networks. The node-based approach lends itself well to a software system that uses a drag- and-drop graphical network creation tool. We present a graphical user interface, the XML data representation, and the communication links to and from optimization software.<br>We develop an extensive yet tractable framework for analyzing and optimally controlling local energy networks. A local energy network is any set of generation, storage, and end-use devices existing to provide energy fulfillment to a building, a group of jointly operated buildings, or a village power system. The software developed is called TOTEM for Total Energy Management, and provides hourly (or sub-hourly) control over the flows in such energy networks. TOTEM manages multiple energy flows such as electricity, chilled water, heat, and steam together, since such energies are often coupled, particularly for networks containing cogeneration turbines (which produce electricity and steam) and absorption chillers (which use steam for driving refrigeration turbines). Due to the large number of interconnected devices in such networks, the model is kept as a linear mixed integer program, able to be solved rapidly with off-the-shelf mathematical optimization packages. Certain nonlinearities, for example input-output relationships for generators, are handled in this linear framework with piecewise linear approximations. Modeling flexibility is achieved by taking a node-centric approach. Each device in the network is represented as a node, and depending on each node's set membership, proper constraint and objective equations are written. Given the network, TOTEM uses hourly electricity and fuel pricing, weather, and demand projections to determine the optimal operating and scheduling strategy for the day, in both deterministic and stochastic settings. MIT's cogeneration plant is used as a case study, with other examples throughout the thesis demonstrate the use of TOTEM for assessing and controlling renewable resources, storage options, and<br>by David Craft.<br>Ph.D.
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Cubo, Rubén. "Mathematical modeling for optimization of Deep Brain Stimulation." Licentiate thesis, Uppsala universitet, Avdelningen för systemteknik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-284320.
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Deep Brain Stimulation (DBS) consists of sending mild electric stimuli to the brain via a chronically implanted lead. The therapy is used to alleviate the symptoms of different neurological diseases, such as Parkinson's Disease. However, its underlying biological mechanism is currently unknown. DBS patients undergo a lengthy trial-and-error procedure in order to tune the stimuli so that the treatment achieves maximal therapeutic benefits while limiting side effects that are often present with large stimulation values. The present licentiate thesis deals with mathematical modeling for DBS, extending it towards optimization. Mathematical modeling is motivated by the difficulty of obtaining in vivo measurements from the brain, especially in humans. It is expected to facilitate the optimization of the stimuli delivered to the brain and be instrumental in evaluating the performance of novel lead designs. Both topics are discussed in this thesis. First, an analysis of numerical accuracy is presented in order to verify the DBS models utilized in this study. Then a performance comparison between a state-of-the-art lead and a novel field-steering lead using clinical settings is provided. Afterwards, optimization schemes using intersection of volumes and electric field control are described, together with some simplification tools, in order to speed up the computations involved in the modeling.
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扇之介, 渡辺, and Sennosuke Watanabe. "Studies on mathematical structures of network optimization problems." Thesis, https://doors.doshisha.ac.jp/opac/opac_link/bibid/BB12863906/?lang=0, 2013. https://doors.doshisha.ac.jp/opac/opac_link/bibid/BB12863906/?lang=0.
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本論文は,様々なネットワーク最適化問題の数学的構造について様々な観点から調べたものである.主たる結果はネットワーク最適化問題の代表例である最大流問題に,関するいくつかの結果と,Min-Plus代数に値をもつ行列の固有値と固有ベクトルに関する特徴づけに関する結果からなっている.<br>博士(理学)<br>Doctor of Philosophy in Science<br>同志社大学<br>Doshisha University
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Romanko, O. "Mathematical modeling and optimization techniques in risk management." Thesis, Видавництво СумДУ, 2010. http://essuir.sumdu.edu.ua/handle/123456789/14411.
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Nowadays mathematical modeling and optimization techniques are used in many areas of science. The main challenge of practical models is minimizing risk in the presence of uncertainty. In the paper the examples of practical risk management problems that demonstrate how mathematical modeling combined with optimization algorithms are shown.
When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/14411
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Awunganyi, John. "A study of optimization in Hilbert Space." CSUSB ScholarWorks, 1998. https://scholarworks.lib.csusb.edu/etd-project/1459.
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Deligiannis, Anastasios. "Mathematical optimization and game theoretic methods for radar networks." Thesis, Loughborough University, 2016. https://dspace.lboro.ac.uk/2134/22732.
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Radar systems are undoubtedly included in the hall of the most momentous discoveries of the previous century. Although radars were initially used for ship and aircraft detection, nowadays these systems are used in highly diverse fields, expanding from civil aviation, marine navigation and air-defence to ocean surveillance, meteorology and medicine. Recent advances in signal processing and the constant development of computational capabilities led to radar systems with impressive surveillance and tracking characteristics but on the other hand the continuous growth of distributed networks made them susceptible to multisource interference. This thesis aims at addressing vulnerabilities of modern radar networks and further improving their characteristics through the design of signal processing algorithms and by utilizing convex optimization and game theoretic methods. In particular, the problems of beamforming, power allocation, jammer avoidance and uncertainty within the context of multiple-input multiple-output (MIMO) radar networks are addressed. In order to improve the beamforming performance of phased-array and MIMO radars employing two-dimensional arrays of antennas, a hybrid two-dimensional Phased-MIMO radar with fully overlapped subarrays is proposed. The work considers both adaptive (convex optimization, CAPON beamformer) and non-adaptive (conventional) beamforming techniques. The transmit, receive and overall beampatterns of the Phased-MIMO model are compared with the respective beampatterns of the phased-array and the MIMO schemes, proving that the hybrid model provides superior capabilities in beamforming. By incorporating game theoretic techniques in the radar field, various vulnerabilities and problems can be investigated. Hence, a game theoretic power allocation scheme is proposed and a Nash equilibrium analysis for a multistatic MIMO network is performed. A network of radars is considered, organized into multiple clusters, whose primary objective is to minimize their transmission power, while satisfying a certain detection criterion. Since no communication between the clusters is assumed, non-cooperative game theoretic techniques and convex optimization methods are utilized to tackle the power adaptation problem. During the proof of the existence and the uniqueness of the solution, which is also presented, important contributions on the SINR performance and the transmission power of the radars have been derived. Game theory can also been applied to mitigate jammer interference in a radar network. Hence, a competitive power allocation problem for a MIMO radar system in the presence of multiple jammers is investigated. The main objective of the radar network is to minimize the total power emitted by the radars while achieving a specific detection criterion for each of the targets-jammers, while the intelligent jammers have the ability to observe the radar transmission power and consequently decide its jamming power to maximize the interference to the radar system. In this context, convex optimization methods, noncooperative game theoretic techniques and hypothesis testing are incorporated to identify the jammers and to determine the optimal power allocation. Furthermore, a proof of the existence and the uniqueness of the solution is presented. Apart from resource allocation applications, game theory can also address distributed beamforming problems. More specifically, a distributed beamforming and power allocation technique for a radar system in the presence of multiple targets is considered. The primary goal of each radar is to minimize its transmission power while attaining an optimal beamforming strategy and satisfying a certain detection criterion for each of the targets. Initially, a strategic noncooperative game (SNG) is used, where there is no communication between the various radars of the system. Subsequently, a more coordinated game theoretic approach incorporating a pricing mechanism is adopted. Furthermore, a Stackelberg game is formulated by adding a surveillance radar to the system model, which will play the role of the leader, and thus the remaining radars will be the followers. For each one of these games, a proof of the existence and uniqueness of the solution is presented. In the aforementioned game theoretic applications, the radars are considered to know the exact radar cross section (RCS) parameters of the targets and thus the exact channel gains of all players, which may not be feasible in a real system. Therefore, in the last part of this thesis, uncertainty regarding the channel gains among the radars and the targets is introduced, which originates from the RCS fluctuations of the targets. Bayesian game theory provides a framework to address such problems of incomplete information. Hence, a Bayesian game is proposed, where each radar egotistically maximizes its SINR, under a predefined power constraint.
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Amankwah, Henry. "Mathematical Optimization Models and Methods for Open-Pit Mining." Doctoral thesis, Linköpings universitet, Optimeringslära, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-70844.
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Open-pit mining is an operation in which blocks from the ground are dug to extract the ore contained in them, and in this process a deeper and deeper pit is formed until the mining operation ends. Mining is often a highly complex industrial operation, with respect to both technological and planning aspects. The latter may involve decisions about which ore to mine and in which order. Furthermore, mining operations are typically capital intensive and long-term, and subject to uncertainties regarding ore grades, future mining costs, and the market prices of the precious metals contained in the ore. Today, most of the high-grade or low-cost ore deposits have already been depleted, and to obtain sufficient profitability in mining operations it is therefore today often a necessity to achieve operational efficiency with respect to both technological and planning issues. In this thesis, we study the open-pit design problem, the open-pit mining scheduling problem, and the open-pit design problem with geological and price uncertainty. These problems give rise to (mixed) discrete optimization models that in real-life settings are large scale and computationally challenging. The open-pit design problem is to find an optimal ultimate contour of the pit, given estimates of ore grades, that are typically obtained from samples in drill holes, estimates of costs for mining and processing ore, and physical constraints on mining precedence and maximal pit slope. As is well known, this problem can be solved as a maximum flow problem in a special network. In a first paper, we show that two well known parametric procedures for finding a sequence of intermediate contours leading to an ultimate one, can be interpreted as Lagrangian dual approaches to certain side-constrained design models. In a second paper, we give an alternative derivation of the maximum flow problem of the design problem. We also study the combined open-pit design and mining scheduling problem, which is the problem of simultaneously finding an ultimate pit contour and the sequence in which the parts of the orebody shall be removed, subject to mining capacity restrictions. The goal is to maximize the discounted net profit during the life-time of the mine. We show in a third paper that the combined problem can also be formulated as a maximum flow problem, if the mining capacity restrictions are relaxed; in this case the network however needs to be time-expanded. In a fourth paper, we provide some suggestions for Lagrangian dual heuristic and time aggregation approaches for the open-pit scheduling problem. Finally, we study the open-pit design problem under uncertainty, which is taken into account by using the concept of conditional value-atrisk. This concept enables us to incorporate a variety of possible uncertainties, especially regarding grades, costs and prices, in the planning process. In real-life situations, the resulting models would however become very computationally challenging.
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Jabeen, Zamrooda [Verfasser]. "Approaches to mathematical optimization and its applications / Zamrooda Jabeen." München : GRIN Verlag, 2019. http://d-nb.info/1181794331/34.
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Bonz, Justus [Verfasser]. "Essays of applied mathematical optimization in logistics / Justus Bonz." Hamburg : Staats- und Universitätsbibliothek Hamburg Carl von Ossietzky, 2021. http://d-nb.info/1229387293/34.
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Zhu, Ziming. "Mathematical optimization techniques for demand management in smart grids." Thesis, Loughborough University, 2014. https://dspace.lboro.ac.uk/2134/15107.
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The electricity supply industry has been facing significant challenges in terms of meeting the projected demand for energy, environmental issues, security, reliability and integration of renewable energy. Currently, most of the power grids are based on many decades old vertical hierarchical infrastructures where the electric power flows in one direction from the power generators to the consumer side and the grid monitoring information is handled only at the operation side. It is generally believed that a fundamental evolution in electric power generation and supply system is required to make the grids more reliable, secure and efficient. This is generally recognised as the development of smart grids. Demand management is the key to the operational efficiency and reliability of smart grids. Facilitated by the two-way information flow and various optimization mechanisms, operators benefit from real time dynamic load monitoring and control while consumers benefit from optimised use of energy. In this thesis, various mathematical optimization techniques and game theoretic frameworks have been proposed for demand management in order to achieve efficient home energy consumption scheduling and optimal electric vehicle (EV) charging. A consumption scheduling technique is proposed to minimise the peak consumption load. The proposed technique is able to schedule the optimal operation time for appliances according to the power consumption patterns of the individual appliances. A game theoretic consumption optimization framework is proposed to manage the scheduling of appliances of multiple residential consumers in a decentralised manner, with the aim of achieving minimum cost of energy for consumers. The optimization incorporates integration of locally generated and stored renewable energy in order to minimise dependency on conventional energy. In addition to the appliance scheduling, a mean field game theoretic optimization framework is proposed for electric vehicles to manage their charging. In particular, the optimization considers a charging station where a large number of EVs are charged simultaneously during a flexible period of time. The proposed technique provides the EVs an optimal charging strategy in order to minimise the cost of charging. The performances of all these new proposed techniques have been demonstrated using Matlab based simulation studies.
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Jadeja, Bhoopatsinh Udaysinh. "Mathematical model and optimization of an interleaving warehouse layout." Thesis, Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/91125.
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This research is devoted to the development of a mathematical model for an Interleaving Warehouse Layout. The space allocated to the items in the warehouse is most commonly determined on the basis of inventory cost of the items. Once the space requirements for the items are computed, the actual assignment of items to locations in the warehouse is carried out independently. An Interleaving Warehouse Layout is presented in this research to incorporate both reorder quantity and location of each item in a single comprehensive mathematical model of the warehouse. The advantage of this approach is that it considers the quantity and location problems encountered in a warehouse layout simultaneously.
The mathematical model developed for the warehouse layout is optimized utilizing the computer code GRG2.5. The numerical results for two warehouses are summarized, discussed and compared with the data available in the literature.<br>M.S.
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Wu, Yu. "Mathematical optimization and game theoretic techniques for multicell beamforming." Thesis, Loughborough University, 2016. https://dspace.lboro.ac.uk/2134/20039.
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The main challenge in mobile wireless communications is the incompatibility between limited wireless resources and increasing demand on wireless services. The employment of frequency reuse technique has effectively increased the capacity of the network and improved the efficiency of frequency utilization. However, with the emergence of smart phones and even more data hungry applications such as interactive multimedia, higher data rate is demanded by mobile users. On the other hand, the interference induced by spectrum sharing arrangement has severely degraded the quality of service for users and restricted further reduction of cell size and enhancement of frequency reuse factor. Beamforming technique has great potential to improve the network performance. With the employment of multiple antennas, a base station is capable of directionally transmitting signals to desired users through narrow beams rather than omnidirectional waves. This will result users suffer less interference from the signals transmitted to other co-channel users. In addition, with the combination of beamforming technique and appropriate power control schemes, the resources of the wireless networks can be used more efficiently. In this thesis, mathematical optimization and game theoretic techniques have been exploited for beamforming designs within the context of multicell wireless networks. Both the coordinated beamforming and the coalitional game theoretic based beamforming techniques have been proposed. Initially, coordinated multicell beamforming algorithms for mixed design criteria have been developed, in which some users are allowed to achieve target signal-to-interference- plus-noise ratios (SINRs) while the SINRs of rest of the users in all cells will be balanced to a maximum achievable SINR. An SINR balancing based coordinated multicell beamforming algorithm has then been proposed which is capable of balancing users in different cells to different SINR levels. Finally, a coalitional game based multicell beamforming has been considered, in which the proposed coalition formation algorithm can reach to stable coalition structures. The performances of all the proposed algorithms have been demonstrated using MATLAB based simulations.
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Trescher, Saskia [Verfasser]. "Estimating Gene Regulatory Activity using Mathematical Optimization / Saskia Trescher." Berlin : Humboldt-Universität zu Berlin, 2020. http://d-nb.info/1218529822/34.
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Bordin, Chiara <1983>. "Mathematical Optimization Applied to Thermal and Electrical Energy Systems." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amsdottorato.unibo.it/6915/1/Bordin_Chiara_tesi.pdf.
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This Thesis aims at building and discussing mathematical models applications focused on Energy problems, both on the thermal and electrical side.
The objective is to show how mathematical programming techniques developed within Operational Research can give useful answers in the Energy Sector, how they can provide tools to support decision making processes of Companies operating in the Energy production and distribution and how they can be successfully used to make simulations and sensitivity analyses to better understand the state of the art and convenience of a particular technology by comparing it with the available alternatives.
The first part discusses the fundamental mathematical background followed by a comprehensive literature review about mathematical modelling in the Energy Sector.
The second part presents mathematical models for the District Heating strategic network design and incremental network design. The objective is the selection of an optimal set of new users to be connected to an existing thermal network, maximizing revenues, minimizing infrastructure and operational costs and taking into account the main technical requirements of the real world application. Results on real and randomly generated benchmark networks are discussed with particular attention to instances characterized by big networks dimensions.
The third part is devoted to the development of linear programming models for optimal battery operation in off-grid solar power schemes, with consideration of battery degradation.
The key contribution of this work is the inclusion of battery degradation costs in the optimisation models. As available data on relating degradation costs to the nature of charge/discharge cycles are limited, we concentrate on investigating the sensitivity of operational patterns to the degradation cost structure. The objective is to investigate the combination of battery costs and performance at which such systems become economic. We also investigate how the system design should change when battery degradation is taken into account.
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Bordin, Chiara <1983>. "Mathematical Optimization Applied to Thermal and Electrical Energy Systems." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amsdottorato.unibo.it/6915/.
Full textAbstract:
This Thesis aims at building and discussing mathematical models applications focused on Energy problems, both on the thermal and electrical side.
The objective is to show how mathematical programming techniques developed within Operational Research can give useful answers in the Energy Sector, how they can provide tools to support decision making processes of Companies operating in the Energy production and distribution and how they can be successfully used to make simulations and sensitivity analyses to better understand the state of the art and convenience of a particular technology by comparing it with the available alternatives.
The first part discusses the fundamental mathematical background followed by a comprehensive literature review about mathematical modelling in the Energy Sector.
The second part presents mathematical models for the District Heating strategic network design and incremental network design. The objective is the selection of an optimal set of new users to be connected to an existing thermal network, maximizing revenues, minimizing infrastructure and operational costs and taking into account the main technical requirements of the real world application. Results on real and randomly generated benchmark networks are discussed with particular attention to instances characterized by big networks dimensions.
The third part is devoted to the development of linear programming models for optimal battery operation in off-grid solar power schemes, with consideration of battery degradation.
The key contribution of this work is the inclusion of battery degradation costs in the optimisation models. As available data on relating degradation costs to the nature of charge/discharge cycles are limited, we concentrate on investigating the sensitivity of operational patterns to the degradation cost structure. The objective is to investigate the combination of battery costs and performance at which such systems become economic. We also investigate how the system design should change when battery degradation is taken into account.
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Lear, John B. "The effects of uncertainty on the economics of optimising control." Phd thesis, Department of Chemical Engineering, 1992. http://hdl.handle.net/2123/5999.
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Greene, James J. "Global optimization of water distribution systems." Thesis, This resource online, 1992. http://scholar.lib.vt.edu/theses/available/etd-10062009-020212/.
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Vance, Bennet. "Join-order optimization with Cartesian products." Full text open access at:, 1998. http://content.ohsu.edu/u?/etd,586.
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Mohd, Ismail Bin. "Global optimization using interval arithmetic." Thesis, University of St Andrews, 1987. http://hdl.handle.net/10023/13824.
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This thesis contains a description of algorithm, MW, for bounding the global minimizers and globally minimum value of a twice continuously differentiable function f :Rn → R1 R1 in a compact sub-interval of Rn. The algorithm MW is similar to the algorithm of Hansen (Han-80a] in that interval arithmetic is used together with certain of Hansen's ideas, but is different from Hansen's algorithm in that MW bounds the Kuhn Tucker points corresponding to the global minimizers of f in the given sab-interval. The Kuhn Tucker points are bounded with prescribed precision by using either of the algorithms KMSW [SheW-85c] or MAP [SheW-85b]. Numerical results which are obtained from Triplex [BaCM-82a] [MorC-83a] implementations of H and MW axe presented.
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Zhao, Ying, and 趙穎. "Optimization of cooperative material handling systems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2006. http://hub.hku.hk/bib/B37837710.
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Manlove, David Francis. "Minimaximal and maximinimal optimisation problems a partial order-based approach /." Thesis, Connect to electronic version, 1998. http://hdl.handle.net/1905/164.
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Gattupalli, Rajeswar R. "Advances in global optimization /." View online ; access limited to URI, 2008. http://0-digitalcommons.uri.edu.helin.uri.edu/dissertations/AAI3314454.
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Battermann, Astrid. "Mathematical optimization methods for the remediation of ground water contaminations." [S.l.] : [s.n.], 2000. http://deposit.ddb.de/cgi-bin/dokserv?idn=963762184.
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Allende, Gemayqzel Bouza. "Mathematical programs with equilibrium constraints: solution techniques from parametric optimization." Enschede : University of Twente [Host], 2006. http://doc.utwente.nl/56164.
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Rahulamathavan, Yogachandran. "Mathematical optimization techniques for resource allocation in cognitive radio networks." Thesis, Loughborough University, 2011. https://dspace.lboro.ac.uk/2134/8982.
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Introduction of data intensive multimedia and interactive services together with exponential growth of wireless applications have created a spectrum crisis. Many spectrum occupancy measurements, however, have shown that most of the allocated spectrum are used inefficiently indicating that radically new approaches are required for better utilization of spectrum. This motivates the concept of opportunistic spectrum sharing or the so-called cognitive radio technology that has great potential to improve spectrum utilization. This technology allows the secondary users to access the spectrum which is allocated to the licensed users in order to transmit their own signal without harmfully affecting the licensed users' communications. In this thesis, an optimal radio resource allocation algorithm is proposed for an OFDM based underlay cognitive radio networks. The proposed algorithm optimally allocates transmission power and OFDM subchannels to the users at the basestation in order to satisfy the quality of services and interference leakage constraints based on integer linear programming. To reduce the computational complexity, a novel recursive suboptimal algorithm is proposed based on a linear optimization framework. To exploit the spatial diversity, the proposed algorithms are extended to a MIMO-OFDM based cognitive radio network. Finally, a novel spatial multiplexing technique is developed to allocate resources in a cognitive radio network which consists of both the real time and the non-real users. Conditions required for convergence of the proposed algorithm are analytically derived. The performance of all these new algorithms are verified using MATLAB simulation results.
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Rozgic, Marco [Verfasser]. "Mathematical Optimization of Industrial Sheet Metal Forming Processes / Marco Rozgic." Hamburg : Helmut-Schmidt-Universität, Bibliothek, 2018. http://d-nb.info/1165340658/34.
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Bournaka, Georgia. "Mathematical optimization and signal processing techniques for cooperative wireless networks." Thesis, Loughborough University, 2013. https://dspace.lboro.ac.uk/2134/13629.
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The rapid growth of mobile users and emergence of high data rate multimedia and interactive services have resulted in a shortage of the radio spectrum. Novel solutions are therefore required for future generations of wireless networks to enhance capacity and coverage. This thesis aims at addressing this issue through the design and analysis of signal processing algorithms. In particular various resource allocation and spatial diversity techniques have been proposed within the context of wireless peer-to-peer relays and coordinated base station (BS) processing. In order to enhance coverage while providing improvement in capacity, peer-to-peer relays that share the same frequency band have been considered and various techniques for designing relay coefficients and allocating powers optimally are proposed. Both one-way and two-way amplify and forward (AF) relays have been investigated. In order to maintain fairness, a signal-to-interference plus noise ratio (SINR) balancing criterion has been adopted. In order to improve the spectrum utilization further, the relays within the context of cognitive radio network are also considered. In this case, a cognitive peer-to-peer relay network is required to achieve SINR balancing while maintaining the interference leakage to primary receiver below a certain threshold. As the spatial diversity techniques in the form of multiple-input-multipleoutput (MIMO) systems have the potential to enhance capacity significantly, the above work has been extended to peer-to-peer MIMO relay networks. Transceiver and relay beamforming design based on minimum mean-square error (MSE) criterion has been proposed. Establishing uplink downlink MSE duality, an alternating algorithm has been developed. A scenario where multiple users are served by both the BS and a MIMO relay is considered and a joint beamforming technique for the BS and the MIMO relay is proposed. With the motivation of optimising the transmission power at both the BS and the relay, an interference precoding design is presented that takes into account the knowledge of the interference caused by the relay to the users served by the BS. Recognizing joint beamformer design for multiple BSs has the ability to reduce interference in the network significantly, cooperative multi-cell beamforming design is proposed. The aim is to design multi-cell beamformers to maximize the minimum SINR of users subject to individual BS power constraints. In contrast to all works available in the literature that aimed at balancing SINR of all users in all cells to the same level, the SINRs of users in each cell is balanced and maximized at different values. This new technique takes advantage of the fact that BSs may have different available transmission powers and/or channel conditions for their users.
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Sabillón, Antúnez Carlos Francisco. "Mathematical optimization of unbalanced networks operation with smart grid devices." Universidade Estadual Paulista (UNESP), 2018. http://hdl.handle.net/11449/154075.
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Previous issue date: 2018-03-26<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)<br>As redes de distribuição de energia elétrica devem estar preparadas para fornecer um serviço econômico e confiável a todos os clientes, bem como para integrar tecnologias relacionadas à geração distribuída, armazenamento de energia e veículos elétricos. Uma representação adequada da operação das redes de distribuição, considerando as tecnologias de redes inteligentes, é fundamental para atingir esses objetivos. Este trabalho apresenta formulações matemáticas para a operação em regime permanente das redes de distribuição, que consideram o desequilíbrio de redes trifásicas. Modelos matemáticos da operação de dispositivos relacionados à redes inteligentes presentes em redes de distribuição são desenvolvidos (e.g., dispositivos de controle volt-var, sistemas de armazenamento de energia e veículos elétricos). Além disso, características relacionadas à dependência da tensão das cargas, geração distribuída e limites térmico e de tensão também estão incluídos. Essas formulações constituem um marco matemático para a análise de otimização da operação das redes de distribuição de energia elétrica, o que possibilita modelar os processos de tomada de decisões. Objetivos diferentes relacionados a aspectos técnicos e/ou econômicos podem ser almejados dentro deste marco; Além disso, a extensão para otimização multi-período e multi-cenário é discutida. Os modelos apresentados são construídos com base em formulações de programação linear inteira mista, evitando o uso de formulações não-lineares inteiras mistas convencionais. A aplicação do marco apresentado é ilustrada em abordagens de controle para coordenação de carregamento de veículos elétricos, controle de magnitude de tensão e controle de geração distribuída renovável. Diversos métodos são desenvolvidos, com base no marco de otimização matemática, para otimizar a operação de sistemas de distribuição desbalanceados, considerando não apenas diferentes penetrações de veículos elétricos e fontes de energia renováveis, mas também a presença de sistemas de armazenamento e dispositivos de controle volt-var. A este respeito, o agendamento dinâmico e a otimização multi-período de janela rolante são frequentemente usados para alcançar uma operação ótima na rede. A eficácia e robustez das metodologias, bem como a confiabilidade do marco de otimização matemática, são verificados usando vários sistemas de teste (e.g., 123-node, 34-node e 178-node) com nós de média e baixa tensão, diferentes janelas de controle e várias disponibilidades de controle relacionadas aos dispositivos de rede inteligente.<br>Electric distribution networks should be prepared to provide an economic and reliable service to all customers, as well as to integrate technologies related to distributed generation, energy storage, and plug-in electric vehicles. A proper representation of the electric distribution network operation, taking into account smart grid technologies, is key to accomplish these goals. This work presents mathematical formulations for the steady-state operation of electric distribution networks, which consider the unbalance of three-phase grids. Mathematical models of the operation of smart grid-related devices present in electric distribution networks are developed (e.g., volt-var control devices, energy storage systems, and plug-in electric vehicles). Furthermore, features related to the voltage dependency of loads, distributed generation, and voltage and thermal limits are also included. These formulations constitute a mathematical framework for optimization analysis of the electric distribution network operation, which could assist planners in decision-making processes. Different objectives related to technical and/or economic aspects can be pursued within the framework; in addition, the extension to multi-period and multi-scenario optimization is discussed. The presented models are built based on mixed integer linear programming formulations, avoiding the use of conventional mixed integer nonlinear formulations. The application of the presented framework is illustrated throughout control approaches for plug-in electric vehicle charging coordination, voltage magnitude control, and renewable distributed generation control. Several methods are developed, based on this framework, to optimize the operation of unbalanced distribution systems considering not only different penetrations of electric vehicles and renewable energy sources but also the presence of storage systems and volt-var control devices. In this regard, dynamic scheduling and rolling multi-period optimization are often used to achieve optimal economic operation in the grid. The effective and robustness of the methodologies, as well as the reliability of the mathematical framework, are verified using many test systems (e.g., 123-node, 34-node, and 178-node) with medium and low voltage nodes, different operation control time frames, and several control availabilities related to the smart grid devices.
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Oremland, Matthew Scott. "Techniques for mathematical analysis and optimization of agent-based models." Diss., Virginia Tech, 2014. http://hdl.handle.net/10919/25138.
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Agent-based models are computer simulations in which entities (agents) interact with each other and their environment according to local update rules. Local interactions give rise to global dynamics. These models can be thought of as in silico laboratories that can be used to investigate the system being modeled. Optimization problems for agent-based models are problems concerning the optimal way of steering a particular model to a desired state. Given that agent-based models have no rigorous mathematical formulation, standard analysis is difficult, and traditional mathematical approaches are often intractable.
This work presents techniques for the analysis of agent-based models and for solving optimization problems with such models. Techniques include model reduction, simulation optimization, conversion to systems of discrete difference equations, and a variety of heuristic methods. The proposed strategies are novel in their application; results show that for a large class of models, these strategies are more effective than existing methods.<br>Ph. D.
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Rozgi`c, Marco [Verfasser]. "Mathematical Optimization of Industrial Sheet Metal Forming Processes / Marco Rozgic." Hamburg : Helmut-Schmidt-Universität, Bibliothek, 2018. http://d-nb.info/1165340658/34.
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Heymann, Benjamin. "Mathematical contributions for the optimization and regulation of electricity production." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLX052/document.
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Nous présentons notre contribution sur la régulation et l’optimisation de la production d’électricité.La première partie concerne l’optimisation de la gestion d’un micro réseau. Nous formulons le programme de gestion comme un problème de commande optimal en temps continu, puis nous résolvons ce problème par programmation dynamique à l’aide d’un solveur développé dans ce but : BocopHJB. Nous montrons que ce type de formulation peut s’étendre à une modélisation stochastique. Nous terminons cette partie par l’algorithme de poids adaptatifs, qui permet une gestion de la batterie du micro réseau intégrant le vieillissement de celle-ci. L’algorithme exploite la structure à deux échelles de temps du problème de commande.La seconde partie concerne des modèles de marchés en réseaux, et en particulier ceux de l’électricité. Nous introduisons un mécanisme d’incitation permettant de diminuer le pouvoir de marché des producteurs d’énergie, au profit du consommateur. Nous étudions quelques propriétés mathématiques des problèmes d’optimisation rencontrés par les agents du marché (producteurs et régulateur). Le dernier chapitre étudie l’existence et l’unicité des équilibres de Nash en stratégies pures d’une classe de jeux Bayésiens à laquelle certains modèles de marchés en réseaux se rattachent. Pour certains cas simples, un algorithme de calcul d’équilibre est proposé.Une annexe rassemble une documentation sur le solveur numérique BocopHJB<br>We present our contribution on the optimization and regulation of electricity produc- tion.The first part deals with a microgrid Energy Management System (EMS). We formulate the EMS program as a continuous time optimal control problem and then solve this problem by dynamic programming using BocopHJB, a solver developed for this application. We show that an extension of this formulation to a stochastic setting is possible. The last section of this part introduces the adaptative weights dynamic programming algorithm, an algorithm for optimization problems with different time scales. We use the algorithm to integrate the battery aging in the EMS.The second part is dedicated to network markets, and in particular wholesale electricity markets. We introduce a mechanism to deal with the market power exercised by electricity producers, and thus increase the consumer welfare. Then we study some mathematical properties of the agents’ optimization problems (producers and system operator). In the last chapter, we present some pure Nash equilibrium existence and uniqueness results for a class of Bayesian games to which some networks markets belong. In addition we introduce an algorithm to compute the equilibrium for some specific cases.We provide some additional information on BocopHJB (the numerical solver developed and used in the first part of the thesis) in the appendix