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Nešić, Ivana (Beograd , 2014)[more][less]

Mišković, Stefan (Beograd , 2016)[more][less]
Abstract: In this dissertation, three NPhard minmax discrete optimization problems are considered. The rst considered problem is multiperiod emergency service location problem, the second one is dynamic maximal covering location problem with multiple covering radii, and the third one is uncapacitated multiple allocation phub center problem. In many practical situations, input parameters (such as user demands, transportation time or cost) often vary with unknown distributions. Therefore, it is necessary to involve these uncertainties in the deterministic variants of the problems by applying robust optimization approach. Mathematical models for the deterministic and nondeterministic variants of all three problems are developed, except for the deterministic uncapacitated multiple allocation phub center problem, which has already been addressed in the literature. In addition, for the rst time in the literature, it was proven that the emergency service location problem is NPhard. The considered problems and their robust variants have numerous applications, due to the fact that in reallife situations input parameters are often subject to uncertainty. Multiperiod emergency service location problem may be used when determining optimal locations for police stations, re brigades, ambulances, and other emergency units in the given region. The dynamic maximal covering location problem with multiple covering radii is useful when choosing the optimal strategy for establishing resources (service centers, suppliers, facilities, etc.) with maximal satisfaction of customer demands in a certain region, by assuming that the service e ciency directly depends on the distance between customer and service center (i.e., the selected coverage radius). The uncapacitated multiple allocation phub center problem has signi cant applications in designing telecommunication and transportation networks, postal delivery systems, emergency systems, supply networks, etc. Since exact methods provide optimal solutions only for problem instances of small dimensions, hybrid metaheuristic algorithms are developed to solve both deterministic and robust variants of the considered problems. The proposed hybrid algorithms are obtained by combining particle swarm optimization, with local search heuristic { classical local search or variable neighborhood search method. For dynamic maximal covering location problem with multiple covering radii, a hybridization of metaheuristic algorithm with exact method based on linear programming is developed. All elements of the proposed algorithms are adopted to the problems under consideration. Di erent strategies are implemented for improving the e ciency of proposed algorithms, especially for the calculation of the objective function value and the local search part. The in uence of di erent parameters of hybrid algorithms on the solution quality is analyzed in detail. All parameters are adjusted by using analysis of variance. For all considered problems (both deterministic and robust variant), the performance of the proposed hybrid algorithms is evaluated on adequate test data sets. The proposed algorithms are compared with existing heuristic from the literature and exact methods incorporated in commercial CPLEX solver. The obtained experimental results indicate the e ciency of proposed algorithms in obtaining high quality solutions for all considered test instances. The presented comparative analysis indicates the advantages of the proposed hybrid algorithms over existing methods in the sense of solution quality and/or required computational time, especially in the case of large problem dimensions. The results presented in this paper represent a contribution to the eld of discrete optimization, robust optimization and metaheuristic methods. URI: http://hdl.handle.net/123456789/4423 Files in this item: 1
Miskovic_Stefan_teza.pdf ( 1.773Mb ) 
Simić, Ana (Beograd , 2014)[more][less]

Perić, Miloš (Beograd , 2015)[more][less]

Urošević, Jovanka (Beograd , 2016)[more][less]

Stanimirović, Zorica (Faculty of Mathematics, Belgrade, Serbia , 2004)[more][less]
Abstract: In this work a genetic algorithm (GA) for solving Uncapacitated Multiple Allocaton phub Median Problem (UMApHMP), Uncapacitated Multiple Allocaton phub Center Problem (UMApHCP) and Discrete Ordered Median Problem (DOMP) is described. These NPhard problems have many applications in practice. Binary representation is used, genetic operators adopted to the problems are constructed and hybridization GA with modified interchange heuristic for solving DOMP is applied. Proposed algorithm is tested on the corresponding instances from the literature. For both hub location problems GA reaches all solutions that are proved to be optimal so far in a reasonable computational time, even for problem instances of higher dimensions. In this paper the solutions for the largescaled problem instances (n=200, p=20) that are not reported in the literature yet are also presented. Significant results are also obtained on DOMP instances with dimensions n≤900, p≤200. For all problems GA solutions are comparable or better than ones obtained by existing methods. URI: http://hdl.handle.net/123456789/412 Files in this item: 1
mscZoricaStanimirovic.pdf ( 457.9Kb ) 
Lepović, Mirko (Beograd , 1991)[more][less]
URI: http://hdl.handle.net/123456789/4138 Files in this item: 1
Spektralna_teorija_grafova.PDF ( 4.283Mb ) 
Marić, Miroslav (Belgrade)[more][less]

Radojičić, Nina (MATEMATIČKI FAKULTET UNIVERZITETA U BEOGRADU , 2011)[more][less]
URI: http://hdl.handle.net/123456789/1849 Files in this item: 1
MASTER Nina Radojicic.pdf ( 1.247Mb ) 
Stanković, Miloš (Beograd , 2013)[more][less]
URI: http://hdl.handle.net/123456789/2563 Files in this item: 1
Milos Stankovic  master rad.pdf ( 1.414Mb ) 
Lazić, Mirjana (Kragujevac, Serbia , 2011)[more][less]
Abstract: This doctoral dissertation belongs to the Spectral theory of finite and infinite graphs, which joins elements of Graph theory and Linear algebra. The dissertation, beside Preface and References with 24 items, consists of four chapters divided in sections and Appendix. In Chapter 1 some results on the reduced energy of graphs are given. All connected graphs whose reduced energy does not exceed 3 are described. In Chapter 2 all finite and infinite graphs with seven nonzero eigenvalues are determined. Some results on integral graphs are given in Chapter 3. Finally, Chapter 4 contains some results on symmetric double starlike trees. The definitions of starlike tree and double starlike tree are given and we proved that there exist no two cospectral nonisomorphic symmetric double starlike trees. URI: http://hdl.handle.net/123456789/1879 Files in this item: 1
dokdis.pdf ( 713.4Kb ) 
Matić, Dragan (Beograd , 2013)[more][less]
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 pary 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 pary 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 Files in this item: 1
phd_matic_dragan.pdf ( 1.438Mb ) 
Matić, Dragan (Beograd , 2013)[more][less]
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 pary 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 pary 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/123456789/3050 Files in this item: 1
phd_matic_dragan.pdf ( 1.438Mb ) 
Djenić, Aleksandar (MATEMATIČKI FAKULTET UNIVERZITETA U BEOGRADU , 2011)[more][less]

Zeljić, Aleksandar (MATEMATIČKI FAKULTET UNIVERZITETA U BEOGRADU , 2011)[more][less]

Stojadinović, Mirko (Beograd , 2016)[more][less]
Abstract: Many realworld 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 stateoftheart 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 stateoftheart 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 Files in this item: 1
MirkoStojadinovicTeza.pdf ( 2.030Mb ) 
Jovanović, Dragana (MATEMATIČKI FAKULTET UNIVERZITETA U BEOGRADU , 2012)[more][less]

Stamenov, Ivana (Beograd , 2016)[more][less]

Mrkela, Lazar (Beograd , 2016)[more][less]

Džamić, Dušan (Beograd , 2014)[more][less]