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Optimization in selected engineering problems
Přikryl, Tomáš ; Popela, Pavel (referee) ; Mrázková, Eva (advisor)
The goal of this paper is a basic understanding of elementary concepts of the mathematical programming field and an aplication of such concepts for the optimization of machine design. The subject of nonlinear optimization is put under deeper scrutiny and so are solution methods of nonlinear problems. This paper also contains essential findings about shafts in the context of engineering components. In the practical part these findings are applied for an optimization of a shaft where the goal is to minimize the shaft’s weight.
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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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Pump station design optimization
Kunovský, Lukáš ; Klas, Roman (referee) ; Štigler, Jaroslav (advisor)
This diploma thesis summarizes the necessary knowledge for the design of the pump station. It focuses on the choice of suitable pumps and control valves. It also provides information on mathematical optimization methods. By combining these two disciplines a program was created that selects the most suitable combination of pumps and valves for the assigned requirements. These can vary over time. The goal of optimization is to minimize initial and operating costs. The phenomena considered are: time-varying flow and head height, serial and parallel co-operation of pumps, throttling control, a change of characteristics for variable speed and temperature, suction height control, maximum motor output, loss in connection piping.
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Optimization of Production Processes
Halas, David ; Dvořák, Jiří (referee) ; Popela, Pavel (advisor)
This thesis deals with modelling diffenrent types of production lines. Modeling is done by the mathematical programming and simulation methods. Optimization related computations are mostly implemented in program GAMS. Simulation is realized by using program Matlab/SimEvents. The results are presented by the Gantt diagrams.
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Optimization problems in AIMMS
Kůdela, Jakub ; Popela, Pavel (referee) ; Mrázková, Eva (advisor)
This bachelor's thesis deals with the usage of system AIMMS for solving and creating optimization models. After the introduction to theoretical background of optimization problems there is an example of modeling a selected problem and its implementation to AIMMS. Each of the selected problems has its graphical user interface where an end user can simply modify the data of the model. All the source codes of programs described above are attached.
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Advanced Networkflow Models for Circular Economy
Pluskal, Jaroslav ; Klimeš, Lubomír (referee) ; Šenkeřík, Roman (referee) ; Pavlas, Martin (advisor)
The dissertation thesis on "Advanced Network Models in the Field of Circular Economy" addresses a crucial topic concerning the need for efficient waste management from an environmental perspective and the achievement of stringent legislative goals. Circular economy represents a complex chain of processes, including waste collection, sorting, recycling, and final disposal. Analyzing and optimizing this intricate process pose challenges, particularly due to various stakeholders and variables involved. Hence, the development of supportive tools and models is imperative to conduct detailed analyses and gain insight into the addressed issues. This work introduces a set of novel mathematical models, utilizing optimization algorithms to plan the necessary infrastructure for waste processing and effectively work with reported data, aiming for sustainable solutions within the circular economy framework. The contributions of these models are further demonstrated through specific case studies, showcasing their ability to optimize processes within the circular economy. These case studies confirm that network flow-based tasks have the potential to significantly contribute to waste management planning, facilitating the transition towards a circular economy.
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Optimization in engineering problems
Klepáč, Jaromír ; Popela, Pavel (referee) ; Mrázková, Eva (advisor)
This bachelor thesis deals with optimization in engineering problems. In particular, it focuses on a task of optimal dimensions design of continuously loaded beam with specic requirements on nal beam weight and rigidity. For the purpose of well understanding of all the terms used during solving of an illustrative task, the thesis contains a brief introduction into the optimization problems, ordinary dierential equations, and theory of elasticity as well. Results obtained through optimization in the GAMS software will be checked by analytic solution and compared with an alternative calculation in the ANSYS software.
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Advanced Stochastic Programming Models in Power Engineering
Pavelka, Ondřej ; Štětina, Josef (referee) ; Popela, Pavel (advisor)
This diploma thesis applies stochastic optimization in the field of the power engineering. In the thesis first part, the needed mathematical theory is described, specifically mathematical, linear, nonlinear, integer and stochastic programming. The second part deals with the heating plant, in which heat is generated by gas and biomass boilers. The aim of this thesis is to design a model for the schedule planning of these boilers. The model is based on two stage stochastic programming with scenario approach. Then the model is solved by GAMS software. In the final part of the text, the focus is on the model sensitivity analysis and suggestions for future improvement.
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Optimization of the cooling of induction machines
Halfar, Ivo ; Dostál, Lukáš (referee) ; Janda, Marcel (advisor)
This master‘s thesis deals with problems of optimization of cooling in electrical machines. This work includes introduction to the theory of mathematical optimization and brief introduction to optimization problems. This thesis deals with using of program Ansys Workbench for the thermal analysis in electrical machines and optimization of their cooling. Thesis contains thermal analyse of specific asynchronous motor with the squirrel cage and optimization of its cooling.
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Transformations of optimization models with aplications
Rychtář, Adam ; Bednář, Josef (referee) ; Popela, Pavel (advisor)
The thesis deals with recent problems of waste management in the Czech Republic. In connection with the existing software implementation, the author focuses on the gradual development of advanced mathematical programming models, which generalize existing approaches. The author applies acquired knowledge in the areas of network flows, linear, integer, and stochastic programming. The important role is played by modifications and transformations of the discussed models. They are further used to obtain the experimental results for real-world input data by implementation in GAMS.
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