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Now showing items 3972-3991 of 5066

REŠAVANJE NEKIH PROBLEMA U NASTAVI PRIMENOM METODA KOMBINATORNE OPTIMIZACIJE

Matić, Dragan (Beograd , 2013)

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Abstract:

In this work some actual combinatorial optimization problems are investigated. Several di erent methods are suggested for solving the following NP hard problems: maximally balanced connected partition problem in graph, general maximally balanced problem with q partitions (q ≥ 2), maximum set splitting problem and p-ary transitive reduction problem in digraphs. Together with investigation of combinatorial optimization methods for solving these problems, the applying of these problems in education is also considered in the dissertation. For solving each of these problems, metaheuristics are developed: variable neighborhood search is developed for each problem and genetic algorithm is used for solving p-ary transitive reduction problem in digraphs. For maximally balanced connected partition problem a mixed linear programming model is established, which enables to solve the problem exactly for the instances of lower dimensions. Achieved numerical results indicate the high level of reliability and usability of the proposed methods. Problems solved in this research are of a great interest both in theoretical and practical points of view. They are used in production, computer networks, engineering, image processing, biology, social sciences and also in various elds of applied mathematics and computer science. In this work the applying of some problems in educational issues is also considered. It is shown that approaches of nding maximally balanced connected partition in graph and nding maximum splitting of the set can be successfully used in course organization, which is veri ed on the concrete examples. Based on the objective indicators and professor's assessment, the techniques for the identifying the connections between the lessons, as well as the weights of the lessons are developed. Thus, whole course can be represented as a connected weighted graph, enabling the resolving of the lesson partition problem by mathematical approaches. By assigning the lessons into the appropriate categories (topics area) inside a iv course, a collection of subsets (corresponding to the topics) of the set of lessons is created. If we set the requirement that lessons should be split into two disjoint subsets (e.g. into the winter and summer semesters), in a way that corresponding topics are processed in both subsets, then the mathematical model of the requirement and its solution corresponds to the set splitting problem. By the developed models of course organization, from which the NP hard problems arise, in addition to the scienti c contributions in the elds of mathematical programming and operational research, contributions in educational aspects are added, especially in the methodology of teaching mathematics and computer science.

URI:

http://hdl.handle.net/123456789/4229

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phd_matic_dragan.pdf ( 1.438Mb )

Rešavanje nekih problema u nastavi primenom metoda kombinatorne optimizacije

Matić, Dragan (Beograd , 2013)

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Abstract:

URI:

http://hdl.handle.net/123456789/3050

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phd_matic_dragan.pdf ( 1.438Mb )

Rešavanje nekih problema zadovoljenja ograničenja primenom egzaktnih i heruističkih metoda

Djenić, Aleksandar (MATEMATIČKI FAKULTET UNIVERZITETA U BEOGRADU , 2011)

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URI: http://hdl.handle.net/123456789/1967

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MasterRad.pdf ( 1.312Mb )
Rešavanje NP - kompletnih problema svodjenjem

Zeljić, Aleksandar (MATEMATIČKI FAKULTET UNIVERZITETA U BEOGRADU , 2011)

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URI: http://hdl.handle.net/123456789/1832

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AZ_tekst.pdf ( 1.268Mb )

REŠAVANJE PROBLEMA CSP TEHNIKAMA SVOÐENJA NA PROBLEM SAT

Stojadinović, Mirko (Beograd , 2016)

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Abstract:

Many real-world problems can be modeled as constraint satisfaction problems (CSPs) and then solved by one of many available techniques for solving these problems. One of the techniques is reduction to SAT, i.e. Boolean Satisfiability Problem. Variables and constraints of CSP are translated (encoded) to SAT instance, that is then solved by state-of-the-art SAT solvers and solution, if exists, is translated to the solution of the original CSP. The main aim of this thesis is to improve CSP solving techniques that are using reduction to SAT. Two new hybrid encodings of CSPs to SAT are presented and they combine good sides of the existing encodings. We give the proof of correctness of one encoding that did not exist in literature. We developed system meSAT that enables reduction of CSPs to SAT by using 4 basic and 2 hybrid encodings. The system also enables solving of CSPs by reduction to two problems related to SAT, SMT and PB. We developed a portfolio for automated selection of encoding/solver to be used on some new instance that needs to be solved. The developed portfolio is comparable with the state-of-the-art portfolios. We developed a hybrid approach based on short solving timeouts with the aim of significantly reducing the preparation time of a portfolio. By using this approach, we got results comparable to the ones obtained by using preparation time of usual length. We made comparison between several machine learning techniques with the aim to find out which one is the best suited for the short training approach. The problem of assigning air traffic controllers to shifts is described and three models of this problem are presented. We used a large number of different solving methods and a diverse set of solvers for solving this problem. We developed optimization techniques that aim to find optimal solutions of the problem. A hybrid technique combining reduction to SAT and local search is shown to be the most efficient one. We also considered sudoku puzzles and the existing techniques of solving the puzzles of greater size than 9 9. Amongst the used techniques, the existing reduction to SAT is the most efficient in solving these puzzles. We improved the existing algorithm for generating large sudoku puzzles. It is shown that simple preprocessing rules additionally improve speed of generating large sudokus.

URI:

http://hdl.handle.net/123456789/4427

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MirkoStojadinovicTeza.pdf ( 2.030Mb )

REŠAVANJE PROBLEMA ISPITIVANJA PRIPADNOSTI INTERVALIMA

Ivanišević, Anja (Beograd , 2021)

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URI: http://hdl.handle.net/123456789/5262

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IvanisevicAnja.pdf ( 1.350Mb )
REŠAVANJE PROBLEMA KLASTEROVANJA KORIŠĆENJEM AUTOENKODERA I METODA GLOBALNE OPTIMIZACIJE

Aličić, Denis (Beograd , 2021)

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URI: http://hdl.handle.net/123456789/5286

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AlicicDenis.pdf ( 1.593Mb )
REŠAVANJE PROBLEMA MINIMALNOG ZBIRNOG BOJENJA GRAFA EGZAKTNIM I HEURISTIČKIM METODAMA

Ðorđević, Aleksandra (Beograd , 2022)

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URI: http://hdl.handle.net/123456789/5459

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DjordjevicAleksandra.pdf ( 987.3Kb )
REŠAVANJE PROBLEMA MULTIDIMENZIONALNOG RANCA PRIMENOM GENETSKOG ALGORITMA

Jovanović, Dragana (Beograd , 2012)

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URI: http://hdl.handle.net/123456789/5149

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MDKSP_DJovanovic.pdf ( 504.0Kb )
REŠAVANJE PROBLEMA MULTIDIMENZIONALNOG RANCA PRIMENOM GENETSKOG ALGORITMA

Jovanović, Dragana (MATEMATIČKI FAKULTET UNIVERZITETA U BEOGRADU , 2012)

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URI: http://hdl.handle.net/123456789/1963

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MDKSP_DJovanovic.pdf ( 504.0Kb )
REŠAVANJE PROBLEMA ODREĐIVANJA TRASA LINIJA GRADSKOG SAOBRAĆAJA PRIMENOM RAZNIH METAHEURISTIČKIH METODA

Stamenov, Ivana (Beograd , 2016)

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URI: http://hdl.handle.net/123456789/4396

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Stamenov_Ivana.pdf ( 2.762Mb )
Rešavanje problema optimalnog planiranja bežicnih meš mreža primenom metaheuristickih metoda

Mrkela, Lazar (Beograd , 2016)

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URI: http://hdl.handle.net/123456789/4355

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Mrkela_Lazar.pdf ( 957.7Kb )
Rešavanje problema raspoređivanja časova primenom optimizacionih tehnika na predloženi model 0-1 celobrojnog linearnog programiranja

Kaznovac, Marko (Beograd , 2012)

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URI: http://hdl.handle.net/123456789/4930

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mstr.pdf ( 622.9Kb )
Re savanje problema rasporedivanja poslova u vi sefaznoj proizvodnji sa paralelnim ma sinama primenom hibridnih metaheuristi ckih metoda

Džamić, Dušan (Beograd , 2014)

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URI: http://hdl.handle.net/123456789/3896

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masterDusanDzamic.pdf ( 1.841Mb )
REŠAVANJE PROBLEMA R-CENTRA SA POUZDANOM MREŽOM PRIMENOM METODE PROMENLJIVIH OKOLINA

Rađenović, Jovana (Beograd , 2022)

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URI: http://hdl.handle.net/123456789/5529

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Radjenovic_Jovana.pdf ( 1.671Mb )
REŠAVANJE PROBLEMA r-HAB MEDIJANE NEOGRANIČENIH KAPACITETA SA VIŠESTRUKIM ALOKACIJAMA METODOM PROMENLJIVIH OKOLINA

Katić, Marija (Beograd , 2023)

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URI: http://hdl.handle.net/123456789/5640

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v1_masterMarijaKatic.pdf ( 1.215Mb )
Rešavanje problema uspostavljanja uslužnih objekata primenom heurističkih metoda

Jordanski, Miloš (Beograd , 2014)

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URI: http://hdl.handle.net/123456789/3905

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masterMilosJordanski.pdf ( 2.189Mb )
REŠAVANJE RUBIKOVE KOCKE

Đurić, Miloš (Beograd , 2023)

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URI: http://hdl.handle.net/123456789/5659

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v1_masterMilosDjuric.pdf ( 1.218Mb )
Rešavanje sistema linearnih nejednačina pomoću linearne funkcije u osmom razredu osnovne škole

Pavlović, Milica (Beograd , 2018)

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URI: http://hdl.handle.net/123456789/4774

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masPavlovic_Milica.pdf ( 1.175Mb )
REŠAVANJE ŠTURM-LUIVILOVIH PROBLEMA KORIŠĆENJEM METODA KONAČNIH RAZLIKA I KONAČNIH ELEMENATA U MATLAB-U

Pajić, Lucija (Beograd , 2010)

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URI: http://hdl.handle.net/123456789/2587

Files in this item: 1

Lucija Pajic-Master_rad.PDF ( 848.5Kb )

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