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Numerické optimalizační metody
Lukšan, Ladislav
Tato zpráva popisuje teoretické i praktické vlastnosti numerických metod pro nepodmíněnou optimalizaci. Studují se metody pro obecné i speciální optimalizační úlohy, mezi které patří minimalizace součtu čtverců, součtu absolutních hodnot, maximní hodnoty a dalších nehladkých funkcí. Kromě metod pro standardní úlohy středních rozměrů jsou studovány i metody pro rozsáhlé řídké a strukturované úlohy. Velká pozornost je věnována soustavám nelineárních rovnic.\n
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Least squares method using genetic algorithm
Holec, Matúš ; Tichý, Vladimír (advisor) ; Šalamon, Tomáš (referee)
This thesis describes the design and implementation of genetic algorithm for approximation of non-linear mathematical functions using the least squares method. One objective of this work is to theoretically describe the basics of genetic algorithms. The second objective is to create a program that would be potentially used to approximate empirically measured data by the scientific institutions. Besides the theoretical description of the given subject, the text part of the work mainly deals with the design of the genetic algorithm and the whole application solving the given problem. Specific part of the assignment is that the developed application has to support approximation of points by various mathematical non-linear functions in several different intervals, and then it has to insure, that resulting functions are continuous throughout all the intervals. Described functionality is not offered by any available software.
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