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Evolutionary computing
Popelka, Jan ; Smékal, Zdeněk (referee) ; Karásek, Jan (advisor)
The aim of this Bachelor's Thesis was to get acquainted with the Evolutionary Optimization Techniques, mainly with the Genetic Algorithm and Genetic Programming. It was subsequently described the role of optimization problem TSP solved using Genetic Algorithms and other Chapter solving Symbolic Regression using Genetic Programming. This optimalization problems were created in the programming JAVA and there are solved practical part of the thesis.
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Permutation Flip Processes
Hladký, Jan ; Řada, Hanka
We introduce a broad class of stochastic processes on permutations which we call flip processes. A single step in these processes is given by a local change on a randomly chosen fixed-sized tuple of the domain. We use the theory of permutons to describe the typical evolution of any such flip process started from any initial permutation. More specifically, we construct trajectories in the space of permutons with the property that if a finite permutation is close to a permuton then for any time it stays with high probability is close to this predicted trajectory. This view allows to study various questions inspired by dynamical systems.
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Evolutionary computing
Popelka, Jan ; Smékal, Zdeněk (referee) ; Karásek, Jan (advisor)
The aim of this Bachelor's Thesis was to get acquainted with the Evolutionary Optimization Techniques, mainly with the Genetic Algorithm and Genetic Programming. It was subsequently described the role of optimization problem TSP solved using Genetic Algorithms and other Chapter solving Symbolic Regression using Genetic Programming. This optimalization problems were created in the programming JAVA and there are solved practical part of the thesis.
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Why quintic polynomial equations are not solvable in radicals
Křížek, Michal ; Somer, L.
We illustrate the main idea of Galois theory, by which roots of a polynomial equation of at least fifth degree with rational coefficients cannot general be expressed bz radicals, i.e., by the operations +, -, ., :, and .... Therefore, higher order polynomial equations are usually solved by approximate methods. They can also be solved algebraically by means of ultraradicals.
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