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Comparison of Methods for Travelling Salesman Problem
Šušová, Lucia ; Janoušek, Vladimír (referee) ; Rozman, Jaroslav (advisor)
This work is about comparison of methods for solving the traveling salesman problem. There are many algorithms for finding solution of this NP complete problem but it is not easy to choose the right one. Main goal of this thesis is experimental methods comparison between each other. Reader is going to learn what result she can expect if she chooses certain algorithm for finding the path. First part is focused on theoretical basics where is described all needed information for understanding the problem. Second part describes single heuristics and methods for solving these problems. The methods are divided into groups by principle of working. Next part contains experimental comparison of methods. This comparison was done based on own implementation of single heuristics. The following part of this work contains information about this implementation and also describes comparison application. Next possible steps of this project are described in conclusion.
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Travelling Salesman Problem
Kolář, Adam ; Rozman, Jaroslav (referee) ; Zbořil, František (advisor)
The aim of this bachelor's thesis is to design a testing environment for the traveling salesman problem and compare the effectiveness of different approaches to the solution. The first part discussed the possibility of genetic algorithms, depending on the setting of a crossover, mutations and population size. In the second part, there is the same problem using two types of neural networks. The representative of the self-learning net was chosen Kohonen neural network. Hopfield neural network represents a method of minimizing the energy function with fixed coefficients. At both neural networks, there were described possible advantages and disadvantages. In the end, all the findings were interpreted in a global context.
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Construction of the Generalized Finite Automaton
Šoka, Martin ; Košař, Vlastimil (referee) ; Kaštil, Jan (advisor)
The thesis deals with the creation of an algorithm for the construction of the generalized finite automaton. This automaton differs from the conventional finite automaton by the fact that its transitions are defined by words, therefore it is possible to reduce the number of states of the generalized finite automaton. The introduction includes definitions of terms used later in the thesis. In the next chapters I describe the algorithm itself, including the comprehensive analysis of the heuristics for finding a maximal acyclic subgraph in the graph of the automaton. It also describes implementation of the algorithm and experimentation with automatons created by the algorithm.
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Evolutionary Algorithms in the Task of Boolean Satisfiability
Serédi, Silvester ; Vašíček, Zdeněk (referee) ; Sekanina, Lukáš (advisor)
The goal of this Master's Thesis is finding a SAT solving heuristic by the application of an evolutionary algorithm. This thesis surveys various approaches used in SAT solving and some variants of evolutionary algorithms that are relevant to this topic. Afterwards the implementation of a linear genetic programming system that searches for a suitable heuristic for SAT problem instances is described, together with the implementation of a custom SAT solver which expoloits the output of the genetic program. Finally, the achieved results are summarized.
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Graph Colouring, Graph Clique, Algorithms and Applications
Valachová, Alžbeta ; Dvořák, Jiří (referee) ; Šeda, Miloš (advisor)
This thesis deals with the problem of graph coloring and finding cliques in a graph, with a focus on the description of algorithms and their applications. Graph coloring is the process of assigning colors to individual vertices of a graph so that adjacent vertices have different colors. This issue is important for solving various optimization problems. The work also focuses on finding cliques in a graph, which is an important problem in social network analysis or image recognition. The aim of this thesis is to provide a complex overview of graph coloring, finding cliques in a graph, introduce and analyze existing algorithms and show their applications in practice.
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Travelling Salesman Problem
Kolář, Adam ; Rozman, Jaroslav (referee) ; Zbořil, František (advisor)
The aim of this bachelor's thesis is to design a testing environment for the traveling salesman problem and compare the effectiveness of different approaches to the solution. The first part discussed the possibility of genetic algorithms, depending on the setting of a crossover, mutations and population size. In the second part, there is the same problem using two types of neural networks. The representative of the self-learning net was chosen Kohonen neural network. Hopfield neural network represents a method of minimizing the energy function with fixed coefficients. At both neural networks, there were described possible advantages and disadvantages. In the end, all the findings were interpreted in a global context.
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Construction of the Generalized Finite Automaton
Šoka, Martin ; Košař, Vlastimil (referee) ; Kaštil, Jan (advisor)
The thesis deals with the creation of an algorithm for the construction of the generalized finite automaton. This automaton differs from the conventional finite automaton by the fact that its transitions are defined by words, therefore it is possible to reduce the number of states of the generalized finite automaton. The introduction includes definitions of terms used later in the thesis. In the next chapters I describe the algorithm itself, including the comprehensive analysis of the heuristics for finding a maximal acyclic subgraph in the graph of the automaton. It also describes implementation of the algorithm and experimentation with automatons created by the algorithm.
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Evolutionary Algorithms in the Task of Boolean Satisfiability
Serédi, Silvester ; Vašíček, Zdeněk (referee) ; Sekanina, Lukáš (advisor)
The goal of this Master's Thesis is finding a SAT solving heuristic by the application of an evolutionary algorithm. This thesis surveys various approaches used in SAT solving and some variants of evolutionary algorithms that are relevant to this topic. Afterwards the implementation of a linear genetic programming system that searches for a suitable heuristic for SAT problem instances is described, together with the implementation of a custom SAT solver which expoloits the output of the genetic program. Finally, the achieved results are summarized.
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