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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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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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Analysis of Impact of Covariates Entering Stochastic Optimization Problem
Volf, Petr
In the contribution we study consequences of imperfect information to precision of stochastic optimization solution. In particular, it is assumed that the characteristics of optimization problem are influenced by a set of covariates. This dependence is described via a regression model. Hence, the uncertainty is then caused by statistical estimation of regression parameters. The contribution will analyze several regression model cases, together with their application. Precision of results will be explored, both theoretically as well as with the aid of simulations.
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Stochastic optimization for electricity consumption control
Sekula, Jakub ; Popela, Pavel (referee) ; Kůdela, Jakub (advisor)
The aim of this work is to optimize charging of batteries used in an electric vehicle using electric charger control in order to decrease total costs. We will also count in scenario of using electric energy from vehicle’s batteries to run home demands because of different costs of energies during the day and night, when the batteries are usually charging. Given the uncertainty of events like the route, which will the vehicle cover, power demand of home or weather, we will use stochastic optimization, because we are able to tell with which probability would these events occur.
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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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Benchmarking of swarm optimization algorithms
Mittaš, Eduard ; Dosoudilová, Monika (referee) ; Kůdela, Jakub (advisor)
This thesis deals with benchmarking of swarm optimization algorithms. First part handles optimization problem and it’s meaning in testing of algorithm’s performances. Next chapter describes the very benchmarking itself, it’s tools and software platforms. Afterwards individual algorithms, which were selected for implementation are described. Following this part is a program realization of solution, selected algorithms, selected testing functions and the data, which is exported by the program. The last chapter deals with results of respective performance tests, in which algorithms solved given testing problems. Eventually these results are evaluated and from them an outcome of efficiency and performance of algorithms is formed.
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Stochastic activity networks
Sůva, Pavel ; Dupačová, Jitka (advisor) ; Kaňková, Vlasta (referee)
In the present work, stochastic network models representing a project as a set of activities are studied, as well as different approaches to these models. The critical path method, stochastic network models with probability constraints, finding a reference project duration, worst-case analysis in stochastic networks and optimization of the parameters of the probability distributions of the activity durations are studied. Use of stochastic network models in telecommunications networks is also briefly presented. In a numerical study, some of these models are implemented and the~related numerical results are analyzed.
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Optimization in energy problems
Fürst, Matouš ; Kopa, Miloš (advisor) ; Lachout, Petr (referee)
Title: Optimization in energy problems Author: Matouš Fürst Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Ing. Miloš Kopa, Ph.D., Department of Probability and Mathematical Statistics Abstract: In this thesis we present an optimization model of a semi-autonomous household, which aims to make energy management more efficient. The household is equipped with solar panels and an electric vehicle with a high-capacity battery. In the first part we summarize the basic properties of linear programming and two- stage stochastic linear programming. Subsequently, a two-stage stochastic linear program is formulated and solved in order to optimize the purchase, sale and storage of energy in the household during a single day. The program is formulated in two versions - with present and with departing vehicle. The final solution represents optimal decisions of the household and we discuss it with respect to the input data. In both versions the solution leads to a substantial reduction in costs compared to a household without a battery. Keywords: stochastic optimization, linear programming, domestic microgrid 1
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