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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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Mathematical models for transportation problems
Votavová, Helena ; Novotný, Jan (referee) ; Popela, Pavel (advisor)
The thesis deals with modelling and solution techniques for the selected transportation problems. Firstly, historical remarks and application-related comments are introduced. Then the selected transportation problems are defined and mathematical programming and graph theory concepts are utilised to model them. The travelling salesman problem and suitable algorithms are under focus. The original implementation in GAMS and Python is discussed. Algorithms have been tested for the instance based on the set of 73 towns in the Czech Republic. Finally, the test results are evaluated and compared.
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Optimization Methods for Compensation of Shooting Inaccuracy
Horníček, Jan ; Novotný, Jan (referee) ; Popela, Pavel (advisor)
In this work there is performed analysis of inaccuracy shooting and its optimum corrections especially for playing darts. At rst the model describing inaccurate shooting is made. Using this model we received prerequisites for numerical solving of our problem. Computing algorithm was made and than was proven that our problem can be solved with arbitrary precision by this algorithm. The algorithm was implemented in MATLAB and modied using functional Analysis to minimize computing time. Our problem was solved by this algorithm and in conclusion was made simple application for visualization of received data.
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Process Optimization
Vilém, Jan ; Hrabec, Dušan (referee) ; Popela, Pavel (advisor)
This bachelor's thesis examine the problem of the process optimization in mechanical engineering. It contains optimization model to optimize cutting conditions in turning. The problem was programmed in the GAMS system as linear and nonlinear problem. Limiting conditions are generally defined for several types of technological processes.
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Mathematical Modelling of Vehicle Fuel Consumption
Dražka, Jan ; Novotný, Jan (referee) ; Popela, Pavel (advisor)
This bachelor’s thesis deals with a model building of vehlicle’s model based on real data and with a modelling of it’s movement and it’s fuel consumption. The thesis includes a preparation of input data as well as model building. The main aim of the thesis is the comparison among selected driving modes from the point of fuel consumption and it’s optimization. This comparison is simulated in MATLAB environement and GAMS with the use of selected optimization algorithms.
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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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Optimization in engineering problems
Čepl, Ondřej ; Popela, Pavel (referee) ; Mrázková, Eva (advisor)
This bachelor's work engages optimization and its improvement in engineering cases. There are defined basic terms and optimization's cases, basic characteristics of the optimization case are accounted and basic methods of their solutions are understated. These teoretic findings are availed by optimization of the measurements of three-bar truss, whereas there are solved two options of optimization's case. Mathematical models are implemented to programm GAMS and at the conclusion is accomplished disccusion of accomplishments.
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Optimization Modelling Languages
Molliková, Eva ; Škapa, Stanislav (referee) ; Popela, Pavel (advisor)
The goal of the thesis is to introduce readers into the use of the GAMS modelling language that is an important tool for optimization model building. The overview of useful mathematical concepts introduces the text. The main part of thesis contains four examples presented in detail. Firstly, the basic GAMS related concepts, statements and techniques involving analysis of results are described. The second example illustrates development of model description beginning from quite specific instance towards general and flexible one. Two examples solved at the end show further use of the GAMS and can motivate reader to enhance their konwledge and apply optimization in his areas of specialization.
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Optimization in Engineering Design
Hrabec, Dušan ; Mrázková, Eva (referee) ; Popela, Pavel (advisor)
The aim of present work is to show possibilities of optimization for special basic examples of engineering design. The discussed models have been implemented in GAMS and the corresponding calculations have been performed. The knowledge of linear and non-linear programming is utilized.
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Engineering optimization models
Tydlačka, Martin ; Plšek, Jan (referee) ; Popela, Pavel (advisor)
A cross-section of a girder made out of profile I is designed with respect to random loads, to which a girder will face during life time. Because the random loads are there, we need another aaproach to solving this exercise. Acceptable aproach is usage of optimisation and four choosen models, solving random loads. The cross-section has been to optimize with respect to minimal weight subject the safety constraint. Goal of this thesis is to present method of transfer structural exercise to exercise of mathematical optimisation, present four choosen models and apply this to exercise with random loads.
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