Browsing Doctoral Dissertations by Title
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Levajković, Tijana (Novi Sad , 2011)[more][less]
Abstract: In this dissertation we study the main properties of the operators of Malliavin calculus de ned on a set of singular generalized stochastic processes, which admit chaos expansion representation form in terms of orthogonal polynomial basis and having values in a certain weighted space of stochastic distributions in white noise framework. In the rst part of the dissertation we focus on white noise spaces and introduce the fractional Poissonian white noise space. All four types of white noise spaces obtained (Gaussian, Poissonian, fractional Gaussian and fractional Poissonian) can be identi ed through unitary mappings. As a contribution to the Malliavin di erential theory, theorems which characterize the operators of Malliavin calculus, extended from the space of square integrable random variables to the space of generalized stochastic processes were obtained. Moreover the connections with the corresponding fractional versions of these operators are emphasized and proved. Several examples of stochastic di erential equations involving the operators of the Malliavin calculus, solved by use of the chaos expansion method, have found place in the last part of the dissertation. Particularly, obtained results are applied to solving a generalized eigenvalue problem with the Malliavin derivative and a stochastic Dirichlet problem with a perturbation term driven by the Ornstein-Uhlenbeck operator. URI: http://hdl.handle.net/123456789/3824 Files in this item: 1
DR_Tijana.pdf ( 1.518Mb ) -
Anokić, Ana (Beograd , 2017)[more][less]
Abstract: Optimization problems arise from many real-life situations. The development of adequate mathematical models of optimization problems and appropriate solution methods are of great importance for performance of real systems. The subject of this doctoral dissertation is a novel vehicle scheduling problem (VSP) that arises from optimizing the transport of agricultural raw materials. The organization of transport of raw materials is of great importance in the initial phase of production. This is particularly evident in the case of agricultural raw materials, because their price in the market is very low, and therefore, the costs of their transport represent the largest part of the total production cost. For this reason, any reduction of time and money spent in this early production stage directly increases the company’s profitability. The considered variant of VSP arises from optimizing the transport of sugar beet in a factory for sugar production in Serbia, but it can also be applied in a wider context, i.e., to optimize the transport of raw materials or goods in large companies under the same or similar conditions. The considered problem involves a number of specific constraints that distinguish it from existing variants of the vehicle scheduling problem. Therefore, mathematical models proposed in the literature for other variants of VSP do not describe adequately the considered problem. The complexity of the newly introduced VSP is analyzed. It is proven that the introduced VSP belongs to the class of NP-hard problems by comparing its relaxation with the Parallel Machine Scheduling Problem (PMSP). PMSP is known to be NP-hard, as it is equivalent to the Partitioning problem. From the established analogy between the relaxation of the considered VSP and PMSP, it is concluded that the VSP introduced in this dissertation is NP-hard. New mathematical models of the considered problem that involve all problem specific properties, are developed. The proposed mathematical models are compared in sense of efficiency by using Lingo 17 and CPLEX MIP 12.6.2 solvers. Experimental results showed that both exact solvers provided optimal or feasible solutions only for small-size real-life problem instances. However, this was expectable, having in mind the NP-hardness of the considered problem. Therefore, heuristic and metaheuristic method seem to be appropriate approaches for solving problem instances of larger dimension. Due to specific properties of the considered problem, the existing implementations of heuristic and metaheuristic methods for vehicle routing and scheduling problems can not be directly applied. For this reason, different variants of well-known Variable Neighborhood Search (VNS) metaheuristic, as well as Greedy Randomized Adaptive Search Procedure (GRASP), are designed. The constructive elements of the proposed VNS and GRASP implementations are adapted to the characteristics of the considered vehicle scheduling problem. A subproblem of the proposed variant of vehicle scheduling problem, denoted as VSP-P is considered first. VSP-P is obtained from the initial VSP by excluding problem specific constraints regarding vehicle arriving times to each location and to the factory area. Two metaheuristic algorithms are designed as solution methods for this subproblem: Basic Variable Neighborhood Search - BVNS, and Greedy Randomized Adaptive Search Procedure - GRASP. Both proposed approaches were tested on instances based on real-life data and on the set of generated instances of lager dimensions. Experimental results show that BVNS and GRASP reached all optimal solutions obtained by exact solvers on small-size real-life problem instances. On medium-size real-life instances, BVNS reached or improved upper bounds obtained by CPLEX solver under time limit of 5 hours. BVNS showed to be superior compared to GRASP in the sense of solution quality on medium size real-life instances, as well as on generated large-size problem instances. However, general conclusion is that both proposed methods represent adequate solution approaches for the subproblem VSP-P. BVNS provides solutions of better quality compared to GRASP, while GRASP outperforms BVNS regarding the average CPU time required to produce its best solutions. For the initial vehicle scheduling problem (VSP) that includes all problem specific constraints, three VNS-based metaheuristic methods are designed and implemented: Basic Variable Neighborhood Search - BVNS, Skewed Variable Neighborhood Search - SVNS, and Improved Basic Variable Neighborhood Search - BVNSi. BVNS and SVNS use the same neighborhood structures, but different search strategies in local search phase: BVNS uses Best improvement strategy, while SVNS uses First improvement strategy. All three VNS-based methods are tested on real-life and generated problem instances. As it was expected, experimental results showed that BVNS outperformed SVNS regarding solution quality, while SVNS running time was significantly shorter compared to BVNS. The third designed algorithm BVNSi represents a variant of BVNS that uses more general neighborhood structures compared to the ones used in BVNS and SVNS. The use of such neighborhood structures lead to the simplicity of BVNSi and shorter running times compared to BVNS. Two variants of BVNSi method that exploit different strategies in Local search phase are designed: BVNSiB with best improvement strategy and BVNSiF with First improvement strategy. The results of computational experiments for all proposed VNS-based methods for VSP are analyzed and compared. Regarding the quality of the obtained solutions, BVNS method shows the best performance, while SVNS needed the shortest average running times to produce its best solutions. Two variants of BVNSi method succeeded to find new best solutions on two medium size real life instances and to solve large size instances in shorter running time compared to BVNS and SVNS, respectively. However, both BVNSiB and BVNSiF turn out to be less stabile than BVNS and SVNS on real-life and generated inatances. In the case of one large-size generated instance, both BVNSi variants had significantly worse performance compared to BVNS and SVNS, which had negative impact on their average objective values and average running times. The proposed vehicle scheduling problem is of great practical importance for optimizing the transport of agricultural raw materials. It is planned to use the obtained results in practice (partially or completely), as a support to decision makers who organize transportation of in the early production phase. From the theoretical point of view, the developed mathematical models represent a scientific contribution to the fields of optimization and mathematical modeling. The variants of VNS methods that are developed and adapted to the problem, as well as comparison of their performances, represent a scientific contribution to the field of metaheuristic methods for solving NP-hard optimization problems. URI: http://hdl.handle.net/123456789/4664 Files in this item: 1
Anokic_Ana_disertacija.pdf ( 2.688Mb ) -
Stakić, Đorđe (Beograd , 2022)[more][less]
Abstract: Intermodal transport involves traffic with more than one type of trans port. Its presence in practice has become very significant. Bearing in mind that these are mostly long distances, optimization has become important in this area. By default, three standard types of containers of different sizes are used for the transport. In accordance with the given criteria adequate mathematical models have been developed. Based on the model, the exact solver CPLEX was programmed, which succeeds to find the optimal solutions for lesser values of the input parameters. For a number of models, solutions have been implemented in the C programming language. The input data for smaller instances was taken from the practice. To test instances of larger size, the input data is randomly generated from the selected domain. In the first part of this work the main focus is the search for the optimal route in transportation, according to the given criteria, which includes ocean and mainland transport. The problem becomes more complex by increasing the number of shipping companies, the number of side ports, as well as the number of modes of transport on land. In the second part of the paper, additional problems related to the optimization of intermodal transport are considered. More attention is paid to the individual packages by considering the mass and volume of the package, and sub sequently the limits of mass and volume of the containers. One of solved problems is related to the deployment of a large pack in several containers, then the selection of optimal allocation in accordance with the set criteria. The second solved problem is from the aggregate container transport and it is related to the deployment of a large number of packages into containers, taking the constraints of mass and volume into consideration. Here we also seek an optimal allocation in accordance with the set criteria, eg. the total minimum price. The problem thus considered to belong to the heterogeneous and homogeneous vector bin packing. The numerous com puter implementations of exact and approximate methods for the different models are made. Variant methods of Variable Neighborhood Search (VNS) and GRASP (Greedy Randomized Adaptive Search Procedures) have been designed to optimize the aggregate container transport. These approximation methods were compared with each other as well as with solutions obtained by exact solver CPLEX. URI: http://hdl.handle.net/123456789/5377 Files in this item: 1
DjordjeStakicDisertacija.pdf ( 1.629Mb ) -
MEASURING BLACK HOLE MASSES IN ACTIVE GALACTIC NUCLEI USING THE POLARIZATION OF BROAD EMISSION LINESSavić, Đorđe (Beograd , 2019)[more][less]
Abstract: Supermassive black holes (SMBHs) reside in the heart of nearly every massive galaxy in the Universe. Most of them lie dormant, but when the nearby gas is abundant, it will enter an active phase and form an active galactic nucleus (AGN). In their active phase, SMBHs have a profound effect on the host galaxy evolution and its environment. Reliable SMBH mass measuring is therefore an important task in modern astronomy. For that purpose, a method has been recently proposed by Afanasiev & Popović (2015) that uses the rotation of the polarization plane position angle across the broad emission line profile in order to trace the Keplerian motion and determine the SMBH mass. This method assumes that broad lines are emitted from a flattened disk-like region undergoing Keplerian motion, while the polarization is mainly due to the light scattering of the inner side of the coplanar dusty torus – the equatorial scattering. The goal of the thesis is to theoretically explore the possibilities of this method. We performed numerous Monte Carlo simulations for modeling equatorial scattering in AGNs using the radiative transfer code stokes (Goosmann & Gaskell 2007). We included complex motion of the emitting region in the form of radial inflows, vertical outflows, or due to the presence of the supermassive binary black holes (SMBBHs). We also selected fourwell known AGNs for observations: NGC4051, NGC4151, 3C273 and PG0844+349. Spectropolarimetry was done with the 6m telescope BTA of the Special Astrophysical Observatory of the Russian Academy of Science (SAO RAS) with the focal reducer SCORPIO. We modeled each of these AGNs using observational data available from the literature, and we compared the results of our models with observational data. We find that this method can be used as a new independent way to measure the SMBH masses in AGNs. The influence of the inflows and the outflows can be ignored if they are much lower than the Keplerian velocity. Additionally, when the scattering region is close to the broad line region, this method becomes independent of the viewing inclination. For SMBBHs, this method cannot be used, however, we obtained unique polarization profiles which are not common for a single SMBH, which could be used for identifying possible SMBBH candidates. SMBH mass estimates for the four observed AGNs are in good agreement with the masses obtained using other methods, such as the method of reverberation mapping. Method for independent SMBH mass measurements has been theoretically and experimentally verified in this work, which is very important for the future research that is dealing with the SMBH influence on its immediate environment. URI: http://hdl.handle.net/123456789/4821 Files in this item: 1
teza_Djordje_Savic.pdf ( 13.41Mb ) -
Zejnullahu, Abdullah (Priština)[more][less]
URI: http://hdl.handle.net/123456789/136 Files in this item: 1
phdAbdullahZejnullahu.pdf ( 1.513Mb ) -
Lazović, Zlatko (Beograd , 2019)[more][less]
Abstract: In the first section we present the theory on uniform spaces and measures of noncompactness in metric and uniform spaces. Next, we recall the basic concepts and properties of C∗ and W∗-algebras and Hilbert modules over these algebras with some known topologies on Hilbert W∗-module. In the second section we construct a local convex topology on the standard Hilbert module l2(A), such that any compact” operator (i.e., any operator in the norm closure of the linear span of the operators of the form maps bounded sets into totally bounded sets. In the biginning A presents unital W∗-algebra, leter on A presents unital C∗-algebra. The converse is true in the special case where A = B(H) is the full algebra of all bounded linear operators on a Hilbert space H. In the third section we define a measure of noncompactness λ on the standard Hilbert C∗-module l2(A) over a unital C∗-algebra, such that λ(E) = 0 if and only if E is A-precompact (i.e. it is ε-close to a finitely generated projective submodule for any ε > 0) and derive its properties. Further, we consider the known, Kuratowski, Hausdorff and Istratescu measure of noncompactnes on l2(A) regarded as a locally convex space with respect to a suitable topology. We obtain their properties as well as some relationships between them and above introduced measure of noncompactness. In the forth section we generalize the notion of a Fredholm operator to an arbitrary C∗-algebra. Namely, we define finite type elements in an axiomatic way, and also we define a Fredholm type element a as such an element of a given C∗-algebra for which there are finite type elements p and q such that (1−q)a(1−p) is invertible. We derive an index theorem for such operators. In subsection Corollaries we show that many well-known operators are special cases of our theory. Those include: classical Fredholm operators on a Hilbert space, Fredholm operators in the sense of Breuer, Atiyah and Singer on a properly infinite von Neumann algebra, and Fredholm operators on Hilbert C∗-modules over a unital C∗-algebra in the sense of Mishchenko and Fomenko. URI: http://hdl.handle.net/123456789/4819 Files in this item: 1
dr_Zlatko_Lazovic.pdf ( 2.019Mb ) -
Kovač, Nataša (Beograd , 2018)[more][less]
Abstract: Dissertation title : Metaheuristic approach for solving one class of optimization problems in transp ort Abstract : Berth Allo cation Problem incorp orates some of the most imp ortant de- cisions that have to b e made in order to achieve maximum e ciency in a p ort. Terminal manager of a p ort has to assign incoming vessels to the available b erths, where they will b e loaded/unloaded in such a way that some ob jective function is optimized. It is well known that even the simpler variants of Berth Allo cation Problem are NP-hard, and thus, metaheuristic approaches are more convenient than exact metho ds, b ecause they provide high quality solutions in reasonable compu- tational time. This study considers two variants of the Berth Allo cation Problem: Minimum Cost Hybrid Berth Allo cationProblem (MCHBAP) and Dynamic Mini- mum Cost Hybrid Berth Allo cationProblem (DMCHBAP), b oth with xed handling times of vessels. Ob jective function to b e minimized consists of the following com- p onents: costs of p ositioning, sp eeding up or waiting of vessels, and tardiness of completion for all vessels. Having in mind that the sp eed of nding high-quality solutions is of crucial imp ortance for designing an e cient and reliable decision supp ort system in container terminal, metaheuristic metho ds represent the natural choice when dealing with MCHBAP and DMCHBAP. This study examines the fol- lowing metaheuristic approaches for b oth typ es of a given problem: two variants of the Bee Colony Optimization (BCO), two variants of the Evolutionary Algorithm (EA), and four variants of Variable Neighb orho o d Search (VNS). All metaheuristics are evaluated and compared against each other and against exact metho ds inte- grated in commercial CPLEX solver on real-life instances from the literature and randomly generated instances of higher dimensions. The analysis of the obtained results shows that on real-life instances all metaheuristics were able to nd optimal solutions in short execution times. Randomly generated instances were out of reach for exact solver due to time or memory limits, while metaheuristics easily provided high-quality solutions in short CPU time in each run. The conducted computational analysis indicates that metaheuristics represent a promising approach for MCHBAP and similar problems in maritime transp ortation. The results presented in this pap er represent a contribution to the elds of combinatorial optimization, op erational research, metaheuristic metho ds, and b erth allo cation problem in the container terminals. URI: http://hdl.handle.net/123456789/4747 Files in this item: 1
N_Kovac-doktorska_disertacija.pdf ( 3.540Mb ) -
Putnik, Stanimir (Belgrade)[more][less]
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Vrdoljak, Božo (Belgrade)[more][less]
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Đurić, Milan (Belgrade , 1965)[more][less]
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Ašković, Tomislav (Belgrade , 1976)[more][less]
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Cijan, Boris (Belgrade)[more][less]
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Čanak, Miloš (Belgrade)[more][less]
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Hotomski, Petar (Belgrade , 1982)[more][less]
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Rizvanolli, Fuat (Belgrade , 1982)[more][less]
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Kordić, Stevan (Beograd , 2016)[more][less]
Abstract: Constrain satisfaction problems including the optimisation problems are among the most important problems of discrete mathematics with wide area of application in mathematics itself and in the applied mathematics. Dissertation study optimisation problem and presents an original method for finding its exact solution. The name of the method is Sedimentation Algorithm, which is introduced together with two heuristics. It belongs to the class of branch-and-bound algorithms, which uses backtracking and forward checking techniques. The Sedimentation Algorithm is proven to be totally correct. Ability of the Sedimentation Algorithm to solve different type of problems is demonstrated in dissertation by its application on the Boolean satisfiability problems, the Whitehead Minimisation Problem and the Berth Allocation Problem in container port. The best results are obtained for Berth Allocation Problem, because its modelling for Sedimentation Algorithm includes all available optimisation techniques of the method. The precise complexity estimation of the Sedimentation Algorithm for the Berth Allocation Problem is established. Experimental results verify that the Sedimentation Algorithm is capable to solve the Berth Allocation Problem on the state of art level. URI: http://hdl.handle.net/123456789/4413 Files in this item: 1
StevanKordic.pdf ( 2.477Mb ) -
Kapetanović, Miodrag (Belgrade)[more][less]
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Cvetković, Predrag (Belgrade , 1976)[more][less]
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Arbutina, Bojan (Faculty of Mathematics, University of Belgrade , 2009)[more][less]
Abstract: The main research topic of this dissertation are extreme mass ratio contact close binary systems, q 0.1, of W Ursae Majoris (W UMa) type. These close binaries (CBs) represent an interesting class of objects in which ”normal”, approximately one solar mass main-sequence star is in contact with a significantly less massive companion, M2 ∼ 0.1 M . Earlier theoretical investigations of these systems found that there is a minimum mass ratio qmin = M2/M1 ≈ 0.085 − 0.095 (obtained for n = 3 polytrope - fully radiative primary) above which these CBs are stable and could be observed. If the mass ratio is lower than qmin, or, equivalently, if orbital angular momentum is only about three times larger than the spin angular momentum of a massive primary, a tidal instability develops (Darwin’s instability) forcing eventually the stars to merge into a single, rapidly rotating object (such as FK Com-type stars or blue stragglers). However, there appear to be some W UMa-type CBs with empirically obtained values for the mass ratio below the theoretical limit for stability. The aim of this dissertation is to try to resolve the discrepancy between theory and observations by considering rotating polytropes. By including in theory the effects of higher central condensation due to rotation we were able to reduce qmin to the new theoretical value qmin = 0.070 − 0.074, for the overcontact degree f = 0 − 1, which is more consistent with the observed population. Other candidate systems for stellar mergers such as AM CVn-type stars have also been discussed in the dissertation. URI: http://hdl.handle.net/123456789/716 Files in this item: 1
phdBojanArbutina.pdf ( 6.326Mb ) -
Ćelić, Momir (Banjaluka , 1986)[more][less]