Browsing by Author "Miidla, Peep, juhendaja"

Now showing 1 - 11 of 11

Autonoomsete diferentsiaalvõrrandite süsteemide perioodilised lahendid
(Tartu Ülikool, 2002) Korobova, Evelin; Miidla, Peep, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
DEA meetodi rakendamine Kagu-Eesti gümnaasiumide efektiivsuse hindamisel
(Tartu Ülikool, 2013) Muru, Liina; Miidla, Peep, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
The aim of this Bachelor Thesis is to introduce Data Envelopment Analysis method and to apply it to the secondary schools of Southeastern Estonia. DEA method is a mathematical method that calculates the efficiency by solving linear programming problem. This method is special because it can calculate efficiency of non-profit organizations like hospitals, libraries and administrative units. This paper consists of four parts. The first part is the introduction of the DEA method. The second part is about choosing the inputs and outputs. DEA method needs different inputs and outputs and to find the best parameters, we contacted the County Governments of the three Southeastern Estonian counties, Põlva, Valga and Võru, which schools we analyzed in the paper. Every county government proposed a different set of inputs and outputs and so we got three sets to use in the DEA method. The fourth set was conducted using the information found in the earlier studies from all over the world. The third part is application of the method to the secondary schools of Southeastern Estonia and the fourth part is results. We analyzed 20 schools. To apply the method on the sets we used Data Envelopment Analysis (Computer) Program (DEAP) which is a DOS-program from the nineties, but inspite of the age is a very good program. It makes applying the DEA method easy. It only needs two .txt files, which consist of instructions and data. The program has many choices when it comes to the type of DEA. User can pick from output or input oriented method, one-, two- or multistage method, Malmquist or cost DEA. Results of the analyze depend on the inputs and outputs. With one set there were only three efficient schools and in another there were ten. The mean value of efficiency varied from 0,732 to 0,950. This study can be used by the profesionals to analyze the educational system. The most important part of the analyze is to find the right inputs and outputs to describe the educational system.
Karmarkari meetod
(Tartu Ülikool, 2016) Nurges, Dagmar; Miidla, Peep, juhendaja; Tartu Ülikool. Matemaatika ja statistika instituut; Tartu Ülikool. Loodus- ja täppisteaduste valdkond
Bakalaureusetöö eesmärk on tutvustada üht lineaarsete planeerimise ülesannete lahendusmeetodit – Karmarkari meetodit. Selleks antakse kõigepealt ülevaade lineaarse planeerimise ülesannetest ja nende laialdast rakendust leidnud lahendusmeetodist simpleksmeetodist. Seejärel kirjeldatakse duaalset lineaarse planeerimise ülesannet, mille abil saab suvalise lineaarse planeerimise ülesande viia Karmarkari meetodi rakendamiseks vajalikule kujule ning Karmarkari meetodi teooriat. Lõpetuseks tehakse näide Karmarkari meetodi ühe sammu kohta ja meetodi rakendamisest programmis Scilab.
Osakeste parvega optimeerimise rakendamine elektribörsil
(Tartu Ülikool, 2013) Rakaselg, Gerda; Miidla, Peep, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
This bachelor thesis consists of giving an overview of the electircity market in Estonia, introducing the method of particle swarm optimization (PSO) and implementing PSO on a problem associated with electricity market. Electricity market was opened only in the beginning of year 2013 in Estonia. Thus this subject is topical at the moment. We concentrate on power producers in the day-ahead market, specifically on submitting an offer curve to the day-ahead market. In order to maximize profit, power companies need appropriate bidding strategies. In this thesis one strategy is described and a method for calculating necessary prices and quantities for electricity is introduced. Particle swarm optimization is a computation technique, which is inspired by swarm behaviour such as fish schooling or bird flocking. PSO is initialized with a population of random particles and it searches for solution by updating generations. The particles fly through the n-dimensional problem space moving towards both current individual and current global optimum position. In last chapter of this thesis a theoretical example of finding an offer curve for two electricity generators is solved implementing particle swarm optimization. It is modelled using MATLAB.
Otsesuunatud tehisnärvivõrgud paketis R
(Tartu Ülikool, 2013) Liivoja, Merili; Miidla, Peep, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
Human brain is a complex and powerful system that is able to solve a wide variety of tasks. The aim of many scientists is to develop a computer simulation that mimics the brain functions and solves problems the way our brains do. Very simplified models of biological neural networks are artificial neural networks. There are two different types of artificial neural networks – feed forward neural networks and recurrent neural networks. This thesis gives an overview of feed-forward neural networks and their working principles. The thesis is divided into two main parts. The first part is the theory of feed-forward neural networks and the second part is a practical example of neural network with software R. The first part gives an overview of the artificial neuron and its history. Also different types of artificial neurons are introduced. The first part includes instructions of how feed-forward neural networks are composed and explains how they calculate the results. Separate chapter is devoted to training artificial neural networks. The chapter gives an overview of two main training algorithms – perceptron training algorithm and back-propagation algorithm. The first is designed to train perceptrons and the second is often used in training multi-layer feed-forward neural networks. The last topic explains how to construct feed-forward neural networks with software R. It includes a tutorial of how to build a neural network that calculates the square root. The tutorial will produce a neural network which takes a single input and produces a single output. Input is the number that we want square rooting and the output is the square root of the input.
Portfelli optimiseerimine kahel meetodil
(Tartu Ülikool, 2019) Käosaar, Kaisa; Miidla, Peep, juhendaja; Tartu Ülikool. Matemaatika ja statistika instituut; Tartu Ülikool. Loodus- ja täppisteaduste valdkond
Bakalaureusetöös uuritakse aktivaportfelli optimiseerimist kahel meetodil. Üks optimiseerimismeetod põhineb Harry Markowitzi portfelliteoorial ja teine Kiyoharu Tagawa artiklis „Chebyshev Inequality based Approach to Chance Constrained Portfolio Optimization” [14] välja pakutud meetodil, kus püstitatakse tõenäosusega tõkestatud optimiseerimisülesanne. Töö esimeses osas antakse ülevaade Markowitzi meetodist ja teises osas kirjeldatakse tõenäosusega tõkestatud meetodit. Kolmandas osas võrreldakse meetodeid omavahel arvulise näite abil.
Rändkaupleja ülesande lahendamine sipelgaalgoritmiga
(Tartu Ülikool, 2013) Laas, Teele; Miidla, Peep, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
Complex combinatorial optimization problems have arised in many different fields. However, often this kind of problems are very hard to solve in practice, scientists have worked out many algorithms for solving combinatorial optimization problems. Ant Algorithm is a recent metaheuristic method that is one of the applicable algorithms for solving optimization problems. The first chapter of this bachelor’s thesis gives an overview of Ant Algorithm. Ant Algorithm was first introduced by Dorigo and his colleagues in early 1990s and it is inspired by the behavior of real ants. People have explored the nature and have tried to understand different kinds of processes around us. A very interesting aspect of the behavior of several ant species is their ability to find shortest paths between the ant’s nest and the food sources. In the Ant Algorithm there are several artificial ants’ capabilities used to find solutions to the problem. Although the Ant Algorithm is quite new method, it is a well defined and good performing method that is more and more often applied to solve a variety of complex combinatorial problems. One of the Ant Algorithm’s successful applications is Travelling Salesman Problem, which was the first famous combinatorial problem solved by Ant Algorithm. Ant Algorithm is one of the most efficient algorithms for Travelling Salesman Problem. The second chapter of this bachelor’s thesis is dedicated to introducing the Travelling Salesman Problem. Travelling Salesman Problem is easy to describe but it is so difficult to solve. Travelling Salesman Problem is a well known and extensively studied problem and it has wide application background. We can’t imagine how many problems of our real life can be solved as Travelling Salesman Problems. In this chapter an overview of current applications is given. The last chapter of this thesis is a practical part of it. A certain Travelling Salesman Problem is solved with the Ant Algorithm there. The task was to find the shortest route between 15 different counties’ centers of Estonia. In this chapter the description and importance of different parameters in Ant Algorithm is given and the relationship between Ant Algorithm’s parameters is analyzed. Ant Algorithm is led by five parameters. The result of the task was a 948.79 km long tour through all these 15 cities which was found in 1.91 seconds. It was the fastest time to find the solution. Ant Algorithm showed good performance for solving this problem. Computings were realized in MATLAB environment. This thesis is interesting to read for those who would like to get some knowledge about mathematical optimization problems. It is interesting to know the practical side of math. In addition, this thesis is useful for those who want to solve different kinds of optimization problems using Ant Algorithm.
Riccati diferentsiaalvõrrand finantsmatemaatikas
(Tartu Ülikool, 2007) Kuld, Anu; Miidla, Peep, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
Singulaarse spektraalanalüüsi meetod
(2017) Riiner, Märt; Miidla, Peep, juhendaja; Tartu Ülikool. Matemaatika ja statistika instituut; Tartu Ülikool. Loodus- ja täppisteaduste valdkond
Käesolevas bakalaureusetöös antakse ülevaade singulaarse spektraalanalüüsi meetodist ja analüüsitakse aegrida, kasutades singulaarse spektraalanalüüsi meetodit(edaspidi SSA meetod). Selles bakalaureusetöös SSA meetodi numbriliseks rakendamiseks kasutatakse Tartu Ülikooli füüsika instituudi poolt kogutud ilmavaatluse andmeid ja neid analüüsitakse programmidega R ja Matlab.
Singular spectrum analysis forecasting for financial time series
(Tartu Ülikool, 2017) Osmanzade, Aytan; Miidla, Peep, juhendaja; Tartu Ülikool. Loodus- ja täppisteaduste valdkond; Tartu Ülikool. Matemaatika ja statistika instituut
SSA is a relatively new non-parametric data-driven technique in time series analysis, has been developed and applied to many practical problems across different fields. This paper focuses on the technique of Singular Spectrum Analysis (SSA), its application for financial time series, and also represents results of numerical experiments done by author. The main algorithm of SSA consists of two complementary stages: decomposition and reconstruction; both stages include two separate steps. The performance of the SSA technique is assessed by applying it to the close prices of “AS Tallink Grupp” stock. Results in this work are obtained from creation trajectory matrix of given time series and finding eigenvalues and eigenvectors; construction of the principal and reconstructed components of the time series; applying forecasting algorithm to the time series; interpretation of obtained results. In this thesis for numerical experiments we use the software Matlab.
Ülevaade metaheuristilistest meetoditest ja rändkaupmehe ülesande lahendamine GRASP meetodiga
(Tartu Ülikool, 2013) Loolaid, Indrek; Miidla, Peep, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
This bachelor thesis gives an overview of metaheuristics, what they are and what are they used for. Several metaheuristic algorithms are briefly examined which are divided into two groups based on how many solution candidates at a time a given algorithm operates with: trajectory methods, which operate with a single solution candidate at a time and population methods which operate with more than one solution candidates at a time. A brief criticism towards ”novel” metaheuristics is given which introduce new terminology to describe the algorithm but don’t offer new ideas. And finally a metaheuristic called GRASP is applied on the Travelling Salesman problem the size of 1000 ”cities”.