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Advanced Optimization of Network Flows
Cabalka, Matouš ; Hrabec, Dušan (referee) ; Popela, Pavel (advisor)
The master’s thesis focuses on the optimization models in logistics with emphasis on the network interdiction problem. The brief introduction is followed by two overview chapters - graph theory and mathematical programming. Important definitions strongly related to network interdiction problems are introduced in the chapter named Basic concepts of graph theory. Necessary theorems used for solving problems are following the definitions. Next chapter named Introduction to mathematical programming firstly contains concepts from linear programming. Definitions and theorems are chosen with respect to the following maximum flow problem and the derived dual problem. Concepts of stochastic optimization follow. In the fifth chapter, we discuss deterministic models of the network interdiction. Stochastic models of the network interdiction follow in the next chapter. All models are implemented in programmes written in the programming language GAMS, the codes are attached.
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Network flows and their modifications
Bitara, Matúš ; Hošek, Jaromír (referee) ; Popela, Pavel (advisor)
The thesis deals with optimization models in transportation problems. Brief introduction to graph theory and linear programming is followed by transportation problem of waste transport. Then there is a part with real data applied to the territory of the Czech Republic. After that the user interface created in Visual Basic programming language is explained. In conclusion computational results are discussed as well as their possible improvement.
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Optimization of rail waste transportation
Ambrozková, Anna ; Hrabec, Dušan (referee) ; Pavlas, Martin (advisor)
The bachelor thesis focuses on optimization of rail waste transportation. Theoretical part is about graph theory and optimization, where is introduced for example representation of graphs, network flows or linear programming. Practical part deals with comparison of road and rail networks, motivational example and at least with the application on real data of whole Czech Republic.
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Traffic assignment optimization models
Holešovský, Jan ; Mrázková, Eva (referee) ; Popela, Pavel (advisor)
Optimalizace toku v síti je klasickou aplikací matematického programování. Tyto modely mají, mimo jiné, široké uplatnění také v logistice, kde se tak snažíme docílit optimálního rozdělení dopravy, např. vzhledem k maximalizaci zisku, či minimalizaci nákladů. Toto pojetí ovšem často problém idealizuje, poněvadž předpokládá existenci jediného rozhodovatele. Takový přístup je možný ve striktně organizovaných sítích jako např. v logistických sítích přepravních společností, železničních sítích či armádním zásobování. Úloha ''Traffic Assignment Problem'' (TAP) se zaměřuje na dopady teorie her na optimalizaci toku, tj. zkoumá vliv více rozhodovatelů na celkové využití sítě. V práci se zaobíráme úlohou TAP s působením náhodných vlivů, k čemuž využíváme metod stochastické a vícestupňové optimalizace. Dále zkoumáme možnosti zlepšení stávajícího využití sítě za rozhodnutí autoritativního rozhodovatele, kterému je umožněn zásah do samotné struktury sítě, k čemuž využíváme víceúrovňové programování.
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Selected optimization models in logistics
Málek, Martin ; Pavlas, Martin (referee) ; Popela, Pavel (advisor)
The bachelor thesis focuses on optimization models in logistics, which are solved by linear programming. Theoretical part introduces basic terms of graph theory, optimization, linear programming and network flows. Practical part contains mathematical models, their implementation, and obtained results. Furthermore, real-world application is solved at the end.
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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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Models for network flow identification
Smejkalová, Veronika ; Kůdela, Jakub (referee) ; Pavlas, Martin (advisor)
The bachelor thesis is focused on development of a mathematical model of network flow in waste managment. The theoretical part of thesis deals with graph theory, network flow and optimization. The next chapter introduces the mathematical model. The model was compiled with the use of Information systems of waste management. The data are very often burdened by error. The task of the model is revelation of those errors to make the data useful. This thesis also includes suggestions for further development.
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Optimization in transportation problems
Brandstetter, Matyáš ; Mrázková, Eva (referee) ; Popela, Pavel (advisor)
The thesis deals with optimization models in transportation problems. It begins with a brief introduction to graph theory, linear programming and network flows. The text is accompanied with pictures made in GeoGebra. The presented problems are explained with particular examples. Transportation problems in network flows and their Python implementation recieve more attention in throughout the thesis. Functions written in Python help with data preprocessing and preparation, that is needed in order to solve larger optimization problems.
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Navigation of Units in Video Games Using Flow Networks
Pacovský, Jan ; Gemrot, Jakub (advisor)
This thesis investigates the navigation of units in real-time strategy computer games and is focused on the task of navigating a bigger group of units through a game world that contains narrows passages. The narrow passages causes signi- ficant delays that could be avoided by splitting the group and taking some part of it through an alternative way. In this thesis, a solution using flow networks is proposed. The map is transformed into a flow network which then allows the planner to find an alternative route to the fully occupied narrow passage. The proposed method was tested in a simulator specifically designed for this task and compared with the conventional methods of navigation in computer games. The final evaluation shows that the navigation of units using flow networks can successfully solve this problem. 1
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Navigation of Units in Video Games Using Flow Networks
Pacovský, Jan ; Gemrot, Jakub (advisor) ; Chrpa, Lukáš (referee)
This thesis investigates the navigation of units in real-time strategy computer games and is focused on the task of navigating a bigger group of units through a game world that contains narrows passages. The narrow passages causes signi- ficant delays that could be avoided by splitting the group and taking some part of it through an alternative way. In this thesis, a solution using flow networks is proposed. The map is transformed into a flow network which then allows the planner to find an alternative route to the fully occupied narrow passage. The proposed method was tested in a simulator specifically designed for this task and compared with the conventional methods of navigation in computer games. The final evaluation shows that the navigation of units using flow networks can successfully solve this problem. 1
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