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Stochastic Programming for Engineering Design
Hrabec, Dušan ; Roupec, Jan (referee) ; Popela, Pavel (advisor)
Stochastické programování a optimalizace jsou velmi užitečné nástroje pro řešení široké škály inženýrských úloh zahrnujících neurčitost. Diplomová práce se zabývá stochastickým programováním a jeho aplikací při řešení logistických úloh. Teoretická část práce je věnována jak základním pojmům z teorie grafů, tak pojmům souvisejících s matematickým, lineárním, celočíselným a stochastickým programováním. Pozornost je věnována také návaznosti zmíněných pojmů na logistiku. Druhá část se zabývá tvorbou vlastních úloh prezentujících stochastické logistické modely, jejich implementací a výsledky.
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Comparison of Methods for Travelling Salesman Problem
Šušová, Lucia ; Janoušek, Vladimír (referee) ; Rozman, Jaroslav (advisor)
This work is about comparison of methods for solving the traveling salesman problem. There are many algorithms for finding solution of this NP complete problem but it is not easy to choose the right one. Main goal of this thesis is experimental methods comparison between each other. Reader is going to learn what result she can expect if she chooses certain algorithm for finding the path. First part is focused on theoretical basics where is described all needed information for understanding the problem. Second part describes single heuristics and methods for solving these problems. The methods are divided into groups by principle of working. Next part contains experimental comparison of methods. This comparison was done based on own implementation of single heuristics. The following part of this work contains information about this implementation and also describes comparison application. Next possible steps of this project are described in conclusion.
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Mathematical models in logistics
Nevrlý, Vlastimír ; Holešovský, Jan (referee) ; Popela, Pavel (advisor)
The aim of the bachelor thesis is to model and generate test transportation networks, which are similar to real-world waste management networks. Several software tools (Mathematica, GAMS, Excel, VBA) are used to develop suitable procedures. The next task is to analyze dependence of computational complexity on the size of network by using statistical test computations. The existing original optimization model called NERUDA that supports decision-making in the eld of waste management is utilized. The obtained results are processed, analysed and interpreted in detail.
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Stochastic Optimization of Network Flows
Málek, Martin ; Holešovský, Jan (referee) ; Popela, Pavel (advisor)
Magisterská práce se zabývá stochastickou optimalizací síťových úloh. Teoretická část pokrývá tři témata - teorii grafů, optimalizaci a progressive hedging algoritmus. V rámci optimalizace je hlavní část věnována stochastickému programování a dvoustupňovému programování. Progressing hedging algoritmus zahrnuje také metodu přiřazování scénářů a modifikaci obecného algoritmu na dvou stupňové úlohy. Praktická část je věnována modelům na reálných datech z oblasti svozu odpadu v rámci České republiky. Data poskytl Ústav procesního inženýrství.
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The global optimalization methods
Dudová, Aneta ; Kozumplík, Jiří (referee) ; Mézl, Martin (advisor)
This bachelor work is dedicated to advanced methods of global optimization, and especially problem traveling salesman. It focuses on the description of the problem and its various options, including graph theory, heuristic algorithms, evolutionary algorithms, in which mainly genetic algorithms and optimization by ant colonies. In conclusion, the implementation of these methods and performed testing on different data sets of algorithms that approximately solve the traveling salesman problem.
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Models and methods for routing problems
Nevrlý, Vlastimír ; Žák, Libor (referee) ; Popela, Pavel (advisor)
This master's thesis deals with mathematical model building for routing problems and ways to solve them. There are discussed and implemented deterministic and heuristic approaches that are suitable to be utilized. A big effort is put into building of the mathematical model describing a real world problem from the field of waste management. Appropriate algorithms are developed and modified to solve a particular problem effectively. An original graphical environment is created to illustrate acquired results and perform testing computations.
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Software for automatic data extraction in analysis of brain connectivity
Bujnošková, Eva ; Schwarz, Daniel (referee) ; Jan, Jiří (advisor)
The brain; complex system people want to know about but still they are at the beginning of understanding it. There has been a lot of neuroimaging systems since developement of modern technologies and magnetic resonance imaging is one of them. In last days it isn't enough to examine only structural character of brain, the scientists are dealing with functional states more and more; the functional magnetic resonance imaging is perfectly good tool for this. There is a big amount of researches concerning individual brain regions but also a lot of them dealing with communication across the brain to clear up the causes of human behavior and functional failures. This thesis introduces the brain connectivity exploration, it uses the parcellation by anatomical atlases and it tries to use the knowledge of graph theory as one of the options to determine relations between brain centres and regions. The thesis introduces the software created for extraction of connectivity matrix resulting in graph processing and visualization.
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Graphics Graph Representation
Matula, Radek ; Goldefus, Filip (referee) ; Masopust, Tomáš (advisor)
This Master Thesis deals with the drawing algorithms of graphs known from the mathematical theory. These algorithms deals with an appropriate distribution of the graph vertices in order to obtain the most clear and readable graphs for human readers. The main objective of this work was also to implement the drawing algorithm in the application that would allow to edit the graph. This work deals also with graphs representation in computers.
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Lotka-Volterra competition model on graphs
Skácelová, Radka ; Šremr, Jiří (referee) ; Čermák, Jan (advisor)
This bachelor thesis analyzes several mathematical models describing the co-existence of two species, especially the classic Lotka-Volterra model and its extensions. These models are described by a system of non-linear differential equations. The goal of this thesis is to develop an extended predator-prey model using the graph theory, to find stationary states of this model and to analyze their stability. The thesis is furthermore focused on a comparison between the obtained results for this model with the existing results for the competition model on graphs.
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