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Evolutionary algorithms
Haupt, Daniel ; Polách, Petr (referee) ; Honzík, Petr (advisor)
The first part of this work deals with the optimization and evolutionary algorithms which are used as a tool to solve complex optimization problems. The discussed algorithms are Differential Evolution, Genetic Algorithm, Simulated Annealing and deterministic non-evolutionary algorithm Taboo Search.. Consequently the discussion is held on the issue of testing the optimization algorithms through the use of the test function gallery and comparison solution all algorithms on Travelling salesman problem. In the second part of this work all above mentioned optimization algorithms are tested on 11 test functions and on three models of placement cities in Travelling salesman problem. Firstly, the experiments are carried out with unlimited number of accesses to the fitness function and secondly with limited number of accesses to the fitness function. All the data are processed statistically and graphically.
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Cross_section and reinforcement optimization of roof truss
Odvárka, Miroslav ; Šimůnek, Petr (referee) ; Laníková, Ivana (advisor)
The thesis is focused on optimization of cross-section shape of reinforced concrete truss. An optimization algorithm was created in Microsoft Office Excel which optimizes the shape and reinforcement of the reinforced concrete truss. The truss is as cheap as possible while complying with the ultimate limit state and serviceability limit state - deflection. The algorithm uses the Solver tool which is a supplement program Microsoft Office Excel. Two truss variants were created. One has a cross-sectional shape of a truss designed according to empirical relationships and the second comprises an optimized cross-sectional shape using the algorithm formed. The internal truss forces were detected using Scia Engineer. Both options were statically assessed. When comparing the variants, that a considerable part of the material cost can be saved when optimizing the cross-sectional shape.
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Mathematical models for transportation problems
Brzobohatý, Jan ; Hrabec, Dušan (referee) ; Popela, Pavel (advisor)
This bachelor's thesis deals with stochastic dominance. The goal is to lay the foundations for defining stochastic dominance, to describe its properties and to explain this term on simple examples. Another goal is to apply this term to network problems with random transport price. Examples in this thesis also contain solutions and code to find these solutions written in GAMS language.
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Using Optimization's Algorithms by Designing of Structures
Fedorik, Filip ; Keršner, Zbyněk (referee) ; Haapala,, Antti (referee) ; Dický,, Jozef (referee) ; Kala, Jiří (advisor)
The application of optimization algorithms in the design of many economical and industrial problems currently represents a significant assignment. The development of high-powered computers allows an application of difficult mathematical techniques and physical phenomena to simulate real problems with sufficient accuracy. The optimization techniques used in engineering designs are mostly represented by modified mathematical programming methods with extension of their usability. The aim of the presented thesis "Using Optimization´s Algorithms by Designing of Structures" is to analyze the applicability of optimization procedures which are available in the widely used computing system ANSYS in civil and mechanical engineering practice. The numerical analyses were performed within the frame of multi-extreme, one to three dimensional optimization problems, multi-dimensional problems expressed by minimizing the weight of a truss beam and efficient design of air gap location in wooden studs from the point of view of thermal features of the structure. The analyzed optimization processes are in plurality verified with accurate manual computing and graphical solutions and the accent is put on optimization methods´ possibilities to improve robustness, efficiency and accuracy of the optimization algorithms in civil engineering problems´ designs. The optimization methods represent a suitable approach to improve the efficient design of a wide range of civil and mechanical engineering structures and elements. By combination of their advantages and FEM/FEA method it is possible to achieve very good results, although robustness of the solutions is not guaranteed. The robustness and accuracy of the procedure could be increased by competent exploration of design space and suitable selections of optimization methods´ features.
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Optimization of cogeneration system
Stacha, Radek ; Turek, Vojtěch (referee) ; Jegla, Zdeněk (advisor)
Master thesis is focused on optimization of cogeneration system for purpose of rating optimization methods and evaluating properties of these methods. For each method there is description together with block schemes. First part of thesis is devoted to description of methods and their comparison. Second part consists of development of hybrid algorithm, which is used to optimize cogeneration systém model. Each algorithm compared is together with hybrid algorithms included in annexes.
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Fuzzy Preference Structures in Multicriterial Decision Making
Majer, Tomáš ; Stryka, Lukáš (referee) ; Hliněná, Dana (advisor)
V mnohých rozhodovacích problémech evaluujeme akce z různých pohledů, které nazýváme kritéria. Například při ohodnocovaní auta uvažujeme kritéria jako maximální rychlost, cena, zrychlení a spotřeba. V obecnosti při rozhodování s ohledem na různá kritéria se setkáváme s problémem preferencí. Jedním z nejjednodušších řešení je vážený průměr uvažovaných kritérií. V této práci aplikujeme výsledky řešení jednoho multiriteriálního problému, přičemž porovnávání kritérií realizujeme použitím fuzzy preferenčních struktur. Naše řešení je ilustrováno na praktickém příkladě.
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Mathematical models for transportation problems
Brzobohatý, Jan ; Hrabec, Dušan (referee) ; Popela, Pavel (advisor)
This bachelor's thesis deals with stochastic dominance. The goal is to lay the foundations for defining stochastic dominance, to describe its properties and to explain this term on simple examples. Another goal is to apply this term to network problems with random transport price. Examples in this thesis also contain solutions and code to find these solutions written in GAMS language.
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Cross_section and reinforcement optimization of roof truss
Odvárka, Miroslav ; Šimůnek, Petr (referee) ; Laníková, Ivana (advisor)
The thesis is focused on optimization of cross-section shape of reinforced concrete truss. An optimization algorithm was created in Microsoft Office Excel which optimizes the shape and reinforcement of the reinforced concrete truss. The truss is as cheap as possible while complying with the ultimate limit state and serviceability limit state - deflection. The algorithm uses the Solver tool which is a supplement program Microsoft Office Excel. Two truss variants were created. One has a cross-sectional shape of a truss designed according to empirical relationships and the second comprises an optimized cross-sectional shape using the algorithm formed. The internal truss forces were detected using Scia Engineer. Both options were statically assessed. When comparing the variants, that a considerable part of the material cost can be saved when optimizing the cross-sectional shape.
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Fuzzy Preference Structures in Multicriterial Decision Making
Majer, Tomáš ; Stryka, Lukáš (referee) ; Hliněná, Dana (advisor)
V mnohých rozhodovacích problémech evaluujeme akce z různých pohledů, které nazýváme kritéria. Například při ohodnocovaní auta uvažujeme kritéria jako maximální rychlost, cena, zrychlení a spotřeba. V obecnosti při rozhodování s ohledem na různá kritéria se setkáváme s problémem preferencí. Jedním z nejjednodušších řešení je vážený průměr uvažovaných kritérií. V této práci aplikujeme výsledky řešení jednoho multiriteriálního problému, přičemž porovnávání kritérií realizujeme použitím fuzzy preferenčních struktur. Naše řešení je ilustrováno na praktickém příkladě.
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Using Optimization's Algorithms by Designing of Structures
Fedorik, Filip ; Keršner, Zbyněk (referee) ; Haapala,, Antti (referee) ; Dický,, Jozef (referee) ; Kala, Jiří (advisor)
The application of optimization algorithms in the design of many economical and industrial problems currently represents a significant assignment. The development of high-powered computers allows an application of difficult mathematical techniques and physical phenomena to simulate real problems with sufficient accuracy. The optimization techniques used in engineering designs are mostly represented by modified mathematical programming methods with extension of their usability. The aim of the presented thesis "Using Optimization´s Algorithms by Designing of Structures" is to analyze the applicability of optimization procedures which are available in the widely used computing system ANSYS in civil and mechanical engineering practice. The numerical analyses were performed within the frame of multi-extreme, one to three dimensional optimization problems, multi-dimensional problems expressed by minimizing the weight of a truss beam and efficient design of air gap location in wooden studs from the point of view of thermal features of the structure. The analyzed optimization processes are in plurality verified with accurate manual computing and graphical solutions and the accent is put on optimization methods´ possibilities to improve robustness, efficiency and accuracy of the optimization algorithms in civil engineering problems´ designs. The optimization methods represent a suitable approach to improve the efficient design of a wide range of civil and mechanical engineering structures and elements. By combination of their advantages and FEM/FEA method it is possible to achieve very good results, although robustness of the solutions is not guaranteed. The robustness and accuracy of the procedure could be increased by competent exploration of design space and suitable selections of optimization methods´ features.
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