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Optimization Models for Waste-to-Energy Problems
Hošek, Jaromír ; Bednář, Josef (referee) ; Popela, Pavel (advisor)
The main aim of this thesis is to create a sequence of mathematical optimization models with different levels of complexity for the efficient management and waste energy utilization. Stochastic programming approach was utilized to deal with random demand and uncertain heating values. Hence, more applicable model of the waste-to-energy plant has been developed. As the next step, the model is enhanced by heating plant extension. Computations are realized for real-world data and optimal solution is found by using GAMS implementation.
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Optimization of building constructions with probability constraints
Kokrda, Lukáš ; Mrázková, Eva (referee) ; Popela, Pavel (advisor)
The diploma thesis deals with penalty approach to stochastic optimization with chance constraints which are applied to structural mechanics. The problem of optimal design of beam dimensions is modeled and solved. The uncertainty is involved in the form of random load. The corresponding mathematical model contains a condition in the form of ordinary differencial equation that is solved by finite element method. The probability condition is approximated by several types of penalty functions. The results are obtained by computations in the MATLAB software.
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Software Support for Timetabling
Macků, Veronika ; Šeda, Miloš (referee) ; Roupec, Jan (advisor)
The aim of this thesis is the analysis of the current approaches to scheduling at BUT and other institutions of higher learning and the subsequent creation of a software for semiautomatic timetabling. The first part acts as an introduction to university timetabling problems, the analysis of the given problem and an overview of possible solving algorithms. The second part deals with the creation of the sofware itself and the implementation of the chosen heuristic method.
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Solving Canadian Traveller Problem
Filip, Sebastián ; Matoušek, Radomil (referee) ; Dvořák, Jiří (advisor)
This thesis deals with Canadian traveller problem (CTP), which can be defined as the shortest path problem in a stochastic environment. The overview of different CTP variants is presented in theoretical part of this thesis, as well as known solutions to these variants. In the next parts, the thesis focuses on the stochastic variation of CTP (SCTP). For this variant chosen solutions (strategies) are discussed more in depth. At the same time, the original strategies named UCTO and UCTP are presented. Further, the thesis deals with the description of a window application implemented in Java, which has been developed to validate and test the functionality of selected strategies. The final part contains experiments and comparison of selected strategies.
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Risk modelling in transportation
Lipovský, Tomáš ; Pavlas, Martin (referee) ; Popela, Pavel (advisor)
This thesis deals with theoretical basics of risk modelling in transportation and optimization using aggregated traffic data. In this thesis is suggested the procedure and implemented the application solving network problem of shortest path between geographical points. The thesis includes method for special paths evaluation depending on the frequency of traffic incidents based on real historical data. The thesis also includes a~graphical interface for presentation of the achieved results.
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Advanced Decomposition Methods in Stochastic Convex Optimization
Kůdela, Jakub ; Fabian, Csaba (referee) ; Šmíd,, Martin (referee) ; Popela, Pavel (advisor)
Při práci s úlohami stochastického programování se často setkáváme s optimalizačními problémy, které jsou příliš rozsáhlé na to, aby byly zpracovány pomocí rutinních metod matematického programování. Nicméně, v některých případech mají tyto problémy vhodnou strukturu, umožňující použití specializovaných dekompozičních metod, které lze použít při řešení rozsáhlých optimalizačních problémů. Tato práce se zabývá dvěma třídami úloh stochastického programování, které mají speciální strukturu, a to dvoustupňovými stochastickými úlohami a úlohami s pravděpodobnostním omezením, a pokročilými dekompozičními metodami, které lze použít k řešení problému v těchto dvou třídách. V práci popisujeme novou metodu pro tvorbu “warm-start” řezů pro metodu zvanou “Generalized Benders Decomposition”, která se používá při řešení dvoustupňových stochastických problémů. Pro třídu úloh s pravděpodobnostním omezením zde uvádíme originální dekompoziční metodu, kterou jsme nazvali “Pool & Discard algoritmus”. Užitečnost popsaných dekompozičních metod je ukázána na několika příkladech a inženýrských aplikacích.
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Analog Circuits Faults Diagnosis
Váško, Ondřej ; Kolka, Zdeněk (referee) ; Kincl, Zdeněk (advisor)
The main goal of this work is to present the issue of testing analogue linear circuits in terms of diagnosis of single components for which it is sought to prove their nominal values. It is necessary for the work to introduce methods of describing linear circuits via the node voltage method (MUN), and production of transmissive functions. The Matlab and PSpice programmes are used to do the diagnoses. The testing of single parameters of the circuit is carried out through proper placing of testing points in the circuit the way in which their number is as small as possible. Through transmissive functions we indirectly state the values of components operating on calculated frequencies. The set of frequencies for the components is figured out using the stochastic method.
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Optimization of Thermal Field with Phase Change
Pustějovský, Michal ; Klimeš, Lubomír (referee) ; Popela, Pavel (advisor)
This thesis deals with modelling of continuous casting of steel. This process of steel manufacturing has achieved dominant position not only in the Czech Republic but also worldwide. The solved casted bar cross-section shape is circular, because it is rarely studied in academical works nowadays. First part of thesis focuses on creating numerical model of thermal field, using finite difference method with cylindrical coordinates. This model is then employed in optimization part, which represents control problem of abrupt step change of casting speed. The main goal is to find out, whether the computation of numerical model and optimization both can be parallelized using spatial decomposition. To achieve that, Progressive Hedging Algorithm from the field of stochastic optimization has been used.
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Optimization models for resource allocation
Franěk, Jiří ; Šeda, Miloš (referee) ; Kůdela, Jakub (advisor)
The thesis presents an overview of the issue of resource allocation optimization and construction processing of two models for the given example describing an engineering production company. The first of the created models, which was conceived as deterministic, was transformed into a stochastic one using different demand scenarios. The solution of the models itself was implemented in the Julia programming language using available optimization libraries. An analysis of the solution including its graphic representation was carried out and a production plan for the company was successfully created.
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Software Support for Timetabling
Macků, Veronika ; Šeda, Miloš (referee) ; Roupec, Jan (advisor)
The aim of this thesis is the analysis of the current approaches to scheduling at BUT and other institutions of higher learning and the subsequent creation of a software for semiautomatic timetabling. The first part acts as an introduction to university timetabling problems, the analysis of the given problem and an overview of possible solving algorithms. The second part deals with the creation of the sofware itself and the implementation of the chosen heuristic method.
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