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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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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 Model for Faculty Budget
Holá, Lucie ; Roupec, Jan (referee) ; Popela, Pavel (advisor)
The idea of this diploma thesis is an origin application of optimization models to solve a wage funds allocation problem on various institutes of each faculty. This diploma thesis includes an outline of linear programming models, nonlinear programming models, multiply programming models and parametric programming models. Studied questions are debating in wider context of distributing financial resources from the Budget of the Czech republic, through Ministry of education, youth and sports, universities, faculties after as much as various institutes. The accent is given on question of definition assessment scales of achievement criteria with general-purpose kvantification.
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Mathematical Programming Models for Optimal Control Problems
Dražka, Jan ; Mrázková, Eva (referee) ; Popela, Pavel (advisor)
This thesis deals with optimization of a vehicle’s (racing) drive on a track. The model of a vehicle and a track is built in this thesis. The first chapter is devoted to the fastest pass problem formulation. The problem optimizes (in the least time) the vehicle’s drive from a start line to a finish line. The problem is formulated as an optimal control theory problem. In the second chapter the optimal control theory problem is suitably discretised and transformed into a nonlinear programming problem. The transformation of the fastest pass problem into nonlinear programming problem, its detailed and illustrative derivation and reformulation form the main part of the thesis. Third chapter presents the implementation and solution of the problem using GAMS and MATLAB. This thesis is a part of a specific research project on which the author has participated. The main contribution of the author is an original formulation of the fastest pass problem as a nonlinear programming problem and its implementation and solving using GAMS.
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Optimization in Financial Applications
Večeřa, Tomáš ; Cabalka, Matouš (referee) ; Popela, Pavel (advisor)
The main purpose of this thesis is to create an efficient stock portfolio, specifically to optimize current distribution of stock index S&P 500. The building process consist of well-established mathematical-economical methods, which are then improved by applying mathematical models from statistics and optimization. Firstly, we define essential terms in order to reach deeper understanding of used methods. Afterwards, process of thorough selection of stocks and sectors comes to place. Data are then processed in program GAMS in three different ways, depending on investors preference. Although this approach was applied to current era, its principles are applicable to any given timeline.
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ADVANCED REGRESSION MODELS
Rosecký, Martin ; Popela, Pavel (referee) ; Bednář, Josef (advisor)
This thesis summarizes latest findings about municipal solid waste (MSW) modelling. These are used to solve multivariable version of inverse prediction problem. It is not possible to solve such problem analytically, so heuristic framework using regression models and data reconciliation was developed. As a side product, models for MSW modelling using PCA (Principal Component Analysis) and LM (Linear Model) were created. These were compared with heuristic model called RF (Random Forest). Both of these models were also used for per capita MSW modelling. Theoretical parts about generalized linear models, data reconciliation and nonlinear programming are also included.
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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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Budget Optimization
Golasowski, Martin ; Janíček, Ladislav (referee) ; Popela, Pavel (advisor)
The bachelor's thesis aims to approach the issue of creating a budget for a public university and the subsequent creation of a mathematical model. The thesis explains the rules and formulas for the distribution of funds for higher education to individual universities. Then, the formulas for the redistribution of these funds between individual faculties are given. Subsequently, a mathematical model of nonlinear programming in the GAMS system is built using real data and constraints. The model is then used to examine the change in the distribution of funds for various objective functions. The aim of compiling the model was not to offer a tool that will be automatically used for the distribution of funds at BUT, but to provide its users with a wider range of computational experiments and gain better insight into the problem.
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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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