 

Bimodal distributions
Došlá, Šárka ; Anděl, Jiří (advisor) ; Dupač, Václav (referee)
We study the bimodality of the mixture of two unimodal distributions. In the special cases we give necessary and su±cient conditions ensuring the bimodality of such mixtures. We study the probability of the event that the histogram of a random sample from unimodal distribution indicates two peaks. For some types of unimodal distributions it is possible to simplify this problem and we can study histograms of samples from uniform distribution instead. We show that for increasing number of observations the probability that histogram with N classes has two peaks tends to the probability that the random permutation of numbers 1;...;N is bimodal.


Genetical algorithms and their use in optimization
Krtek, Jiří ; Antoch, Jaromír (advisor) ; Dupač, Václav (referee)
In the present work we deal with a branch of stochastic optimization algorithms, so called genetic algorithms. In the first chapter we can find description of a run of the genetic algorithm and the main operations which route searching of a feasible solution set, i.e. crossover and mutation. There is not absent a simple example, whereon reader can make sense of the presented operations. There is a short chapter devoted to theory of genetic algorithms which follows section describing various improvements of the basic algorithm, e.g. the Gray code. A real optimization problem is introduced in the third and also the last chapter. We have solved it using the theory of Markov decision processes for modeling a queuing system and by using genetic algorithms for finding optimum. We have also looked for optimum via a specialized algorithm. Both approaches are compared in the end of this chapter. All calculations have been implemented in the Fortran language.


Genetical algorithms and their use in optimization
Krtek, Jiří ; Dupač, Václav (referee) ; Antoch, Jaromír (advisor)
In the present work we deal with a branch of stochastic optimization algorithms, so called genetic algorithms. In the first chapter we can find description of a run of the genetic algorithm and the main operations which route searching of a feasible solution set, i.e. crossover and mutation. There is not absent a simple example, whereon reader can make sense of the presented operations. There is a short chapter devoted to theory of genetic algorithms which follows section describing various improvements of the basic algorithm, e.g. the Gray code. A real optimization problem is introduced in the third and also the last chapter. We have solved it using the theory of Markov decision processes for modeling a queuing system and by using genetic algorithms for finding optimum. We have also looked for optimum via a specialized algorithm. Both approaches are compared in the end of this chapter. All calculations have been implemented in the Fortran language.

 

Bimodal distributions
Došlá, Šárka ; Dupač, Václav (referee) ; Anděl, Jiří (advisor)
We study the bimodality of the mixture of two unimodal distributions. In the special cases we give necessary and su±cient conditions ensuring the bimodality of such mixtures. We study the probability of the event that the histogram of a random sample from unimodal distribution indicates two peaks. For some types of unimodal distributions it is possible to simplify this problem and we can study histograms of samples from uniform distribution instead. We show that for increasing number of observations the probability that histogram with N classes has two peaks tends to the probability that the random permutation of numbers 1;...;N is bimodal.

 