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Optimal path planning for electric vehicles
Horák, Filip ; Šoustek, Petr (referee) ; Kůdela, Jakub (advisor)
This master’s thesis is about optimal route planning for electric vehicles. The first, theoretical part of this work introduces the issue and describes several heuristic methods that have been used to address optimization tasks. A practical part of the thesis is based around software implementation of the methods described earlier. Finally, several experiments and comparisons of obtained results are carried out.
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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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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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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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Integer Optimization for Transportation Problems
Cabalka, Matouš ; Žák, Libor (referee) ; Popela, Pavel (advisor)
The thesis deals with optimization models in transportation problems with emphasis on traveling salesman problem. Brief introduction to the history is followed by theoretical part describing linear programming, integer programming and formulation of traveling salesman problem. Description of data preprocessing is included. Finally computational results are discussed and evaluated.
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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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Optimal path planning for electric vehicles
Horák, Filip ; Šoustek, Petr (referee) ; Kůdela, Jakub (advisor)
This master’s thesis is about optimal route planning for electric vehicles. The first, theoretical part of this work introduces the issue and describes several heuristic methods that have been used to address optimization tasks. A practical part of the thesis is based around software implementation of the methods described earlier. Finally, several experiments and comparisons of obtained results are carried out.
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Assignment problem with application to heath service
Tlapák, Martin ; Kopa, Miloš (advisor) ; Lachout, Petr (referee)
This bachelor's thesis deals with the theory of the nurse scheduling problem using the theory of integer programming. That is why we define basic concepts and present basic theorem of integer programming. We present the algorithm made for solving integer programming. Next we define a basic concept of as- sigment problem. We show how to solve assigment problem by the Hungarian method. Finally we solve the real nurse scheduling problem. The nurse's pref- erences are included in our model. We are finding solution which is suitable for the labour code of the Czech Republic and the special requests of the stressful workplace. 1
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A knapsack problem
Piskačová, Nikola ; Kopa, Miloš (advisor) ; Lachout, Petr (referee)
This work deals with the theory of integer programming. In the first part, there are defined the basic concepts and there are mentioned the two most used methods for solving integer problems. Namely, it is the Branch and Bound method and the Cutting Plane method. In the second chapter, there is described the Knapsack Problem and its various formulations. This problem is a special case of integer optimalization. Next, there is a practical part, where a real problem is solved. The problem is how to place the products in shelves in equipment in the most effectively way. In this chapter is described how to process input data, create a model and solve the problem. In the second part of the practical part, the basics of stochastic optimalization and solution of these problems by the Scenario method are presented. This method is used to solve the previously mentioned problem if the delivery days are random. The aim of this work is to show the applicability of formulations of Knapsack Problem and to compare the obtained results. 1
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Scheduling optimization problems in education
Puček, Samuel ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
This work deals with the theory of integer programming. After defining the ba- sic concepts, it presents two algorithms suitable for solving integer problems. Firstly, it talks about the branch and bound algorithm and secondly, it talks about the cutting plane algorithm. Next, it presents an assignment problem, which is a special case of integer programming. The work describes the hungarian method and explains its usage on exemplary examples. The last part of the work solves the real problem from the practice. The aim of this section is to find an optimal schedule for classes one to seven of the selected elementary school. It introduces input data processing, creating a model and the solution. Obtained results are accompanied by a brief discussion. 1
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