Įvairūs grafo srautų minimizavimo arba maksimizavimo uždaviniai yra taikomi modeliuoti procesams logistikoje, kompiuteriniuose tinkluose, akcijų biržose, automobilių eisme ir t.t. Tokio uždavinio sprendimas esant dideliems grafams yra labai sudėtingas, todėl modelyje būna mažai kintančių parametrų arba modeliuojama tik dalis proceso. Tokio uždavinio pavyzdys (kuris ir bus nagrinėjamas) yra eismo modeliavimas keliuose. Kiekvienas vairuotojas bando pasiekti savo tikslą per minimalų galimą tuo metu esančiomis sąlygomis laiką. Tokiu būdu yra užimama „geriausia vieta“ kelyje, o kitiems vairuotojams užimtas kelias gali tapti neberacionalus ir bus pasirenkamas alternatyvus. Šioje vietoje atsispindi esminė tokio tipo uždavinio savybė: kiekvienas proceso dalyvis siekia maksimalios naudos sau, tokiu būdu tą naudą atimdamas iš kitų dalyvių. Šiu atveju „nauda“ yra vieta eisme. Darbe yra aprašytas eismo imitavimo sistemos modelis ir realizuotas tokia architektūra, kuri tinkama lygiagretiems skaičiavimams. Pateikta statistiniai gauto modelio analizavimo pavyzdžiai. Taip pat pasiūlyti keli algoritmai specifiniams uždaviniams spręsti, kaip dalinis modelio perskaičiavimas. / In this work we will try to apply various path search algorithm optimizations for solving traffic simulation problem. These optimizations are made on the basis of processes and patterns specific to car traffic. Other areas like logistics, money traffic and stocks should have their own specific optimizations. Primary selection criteria will be calculation time. Errors are also introduced by these optimizations, but benefits of solving more complex problems in much shorter time will outweigh those errors. Most of described algorithms are just modifications of traditional Dijkstra's algorithm. This allows to show step by step every optimization introduced, which we can split into 3 categories: Algorithms for finding shortest path in untouched graph, Algorithms for finding shorted path which need modified graph, Algorithms specific for traffic simulation. Algorithms up to graph transformations have been analyzed in previous works. These optimizations proved to be very perspective in point-to-point path search. Thou applying them to traffic modeling and introducing modeling specific optimizations is a relatively new research area. Also an algorithm imitating traffic laws has to be implemented. One of suggested optimizations could be called “fast partial recalculation”. This would allow a faster recalculation of main path loads. Assuming that traffic is the same and graph is slightly modified. A modified idea could be adapted for a recalculation with modified traffic loads. Vastly... [to full text]

Genetinių algoritmų panaudojimo galimybės ir paplitimas nuolat didėja. Daugelyje nagrinėtų mokslinių darbų, genetiniai algoritmai yra naudojami uždavinių optimizavimui. Optimizavimui naudojama daug skirtingų metodų. Sprendžiant konkretų uždavinį mokslinėje literatūroje paprastai pritaikoma keletas metodų tam, kad būtų pagerinti gauti rezultatai, t.y., išbandoma keletas strategijų. Deja, nepavyko rasti tyrimų, kaip tos pačios genetinės paieškos strategijos gali būti pritaikytos kitoms analogiškoms problemoms spręsti. Šiame darbe pateikiama probleminės srities apžvalga, tyrimo aprašymas bandymų rezultatai ir išvados. / The use of genetic algorithms considerably increases. In some research works GA‘s are investigated to optimize graph problems. There are many different strategies for GA optimization. Unfortunately, there are no investigations if a strategy, suitable for a particular graph problem, will be useful solving other graph problems. In this work I originated, described and developed some GA learning strategy elements. Also I developed some that are available in other research works. These elements are: generation of initial population, selection of individuals, mutation, crossover and some other parameters. All possible strategies (about 300) are tested in this work for three graph problems: shortest path, longest path and traveling salesman problem. Results are summarized and described.

In the research of the business IS development the business rules approach has achieved a lot of attention and already has a steady niche with a strong motivation behind. The usefulness of the approach and its advantages over the traditional IS development approaches call for the technology standards. Despite the work done towards standardization there is still a way to go – commercial products use their unique modeling languages for business rules, most of their rules processing and enforcement engines are stand-alone, even the embeddable ones use their unique rules representation format. In our research focusing on the business rules we have stepped towards employing the widely spread technology of active databases and have argued that it is feasible and possible to model business rules using conceptual graphs. Such a model having representations in visual and textual form (linear form and CGIF) and the possibility to translate the model to the near natural English language can be used both at conceptual and implementation levels. We have designed and implemented the automatic trigger generation component. Using the representative example from the real business organization (the representative example was comprised of structural domain knowledge and corresponding business rules) we have carried out the experiment during which the business rules model was transformed from visual notation to CGIF, then from CGIF to XML, and then from XML to MS SQL Server trigger. The... [to full text]

In the research of the business IS development the business rules approach has achieved a lot of attention and already has a steady niche with a strong motivation behind. The usefulness of the approach and its advantages over the traditional IS development approaches call for the technology standards. Despite the work done towards standardization there is still a way to go – commercial products use their unique modeling languages for business rules, most of their rules processing and enforcement engines are stand-alone, even the embeddable ones use their unique rules representation format. In our research focusing on the business rules we have stepped towards employing the widely spread technology of active databases and have argued that it is feasible and possible to model business rules using conceptual graphs. Such a model having representations in visual and textual form (linear form and CGIF) and the possibility to translate the model to the near natural English language can be used both at conceptual and implementation levels. We have designed and implemented the automatic trigger generation component. Using the representative example from the real business organization (the representative example was comprised of structural domain knowledge and corresponding business rules) we have carried out the experiment during which the business rules model was transformed from visual notation to CGIF, then from CGIF to XML, and then from XML to MS SQL Server trigger. The... [to full text]

Die Graphenwissennschaft vervendet man bei praktischem Bedarf in mehreren Gebieten der Wissenschaft (zum Beispiel: in der Chemie, in der Biologie, in der in der Psychologie, in der Informatik). Die Graphen vereinfachen viele kompliezierte Schemen, Probleme. Die Graphentheorie wird in der Schulmathematik bei der Kombinationslehre (die Baumgraphe, doppel Graph) benutzt. In der Diplomarbeit werden wichtige Arte und Eigenschaften der Gfaph verallgemeinert. Es wurde bewiesen: 1. Jeder vollständige Graph besitzt Verbindungen und der Graph ist gleichmäβig mit dem Grad r=p-1. 2. Jedem (p,q)-Graph und beliebigem v gehört der Menge V regelgerechte Ungleichheit 0≤deg v ≤p-1. 3. Wenn p≠8, dann G – kanten Graph Kp dann: 1) G hat Scheitel; 2) G – regelgerecht Graph mit Grad 2(p-2). 4. Jeden Naturzahlen m,n und vollständigem doppel Graph Km,n ist solche Gleichheit Km,n = regelgerecht. 5. Wenn m≠4 und n≠4, dann ist vollständiger doppel Graph Km,n kanten Graph L(Km,n): 1) hat Scheitel; 2) ist regelgerecht Graph mit Grad r=m+n-2.

The work presents a new low voltage electric network development method and a computer program implementing it. In the work is given analysis of the task actuality, review of CAD, electric circuit modeling – counting tools. It also explains the grounds why MS Visio programming environment was selected to implement the set tasks. In designed part of the system is presented systems specification, custom interface, data structure, data flow, systems functions and non functions requirements. Represented EJLPS smart shapes with graphics views and descriptions. Showed, how electric power network one-way circuit must be represented as oriented tree graph, and counting in them can be organized with searching algorithms. Made user case, static structure, component, deployment, activity and method models. Represented EJLPS subroutines and functions specification and shapes functions specification also. Systems testing was carried out using described testing methodology, tests descriptions and testing results. The work presents user documentation, with installation guide, system guide, system administrator guide and description of system functionality. In the final part of the work is presented system quality diagnosis, system development possibilities and information how the system was installed for a specific customer. Finally, a conclusion was made that MS Visio environment enabled to implement the EJLPS system specification in a cost-saving way and ensured effective searching... [to full text]

Šioje santraukoje trumpai aprašoma V. Kurausko disertacija. Pristatomos abi disertacijos dalys, įvedami atsitiktinių sankirtų grafų ir digrafų modeliai, apibrėžiamos minorinės grafų klasės, suformuluojami sprendžiami uždaviniai bei pateikiami pagrindiniai rezultatai. / This paper summarizes (in Lithuanian) the doctoral dissertation "On two models of random graphs" (in English) by V. Kurauskas. We introduce the random graph models (random intersection graphs, graphs with disjoint excluded minors) studied in the thesis, overview the problems and state the main results.

Disertacijoje nagrinėjami nestacionarių matematinių modelių nestandartinėse srityse skaitiniai sprendimo algoritmai. Uždavinio formulavimo sritis yra šakotosios struktūros (ang. branching structures), kurių išsišakojimo taškuose apibrėžiami tvermės dėsniai. Tvermės dėsnių skaitinė analizė ir nestandartinių kraštinių sąlygų analizė skiria nagrinėjamus uždavinius nuo klasikinių aprašytų literatūroje matematinės fizikos uždavinių. Disertacijoje suformuluoti uždaviniai apima skaitinių algoritmų šakotose struktūrose su skirtingais srautų tvermės dėsniais stabilumo ir konvergavimo tyrimą, lygiagrečiųjų algoritmų sudarymą ir taikymą, skaitinių schemų uždaviniams su nelokaliomis integralinėmis sąlygomis tyrimą. Disertacijoje sprendžiami taikomieji neurono sužadinimo ir impulso relaksacijos lazerio apšviestame puslaidininkyje uždaviniai, netiesinio modelio identifikavimo uždavinys. Disertaciją sudaro įvadas, penki skyriai, rezultatų apibendrinimas, literatūros šaltinių sąrašas ir autorės publikacijų disertacijos tema sąrašas. Įvadiniame skyriuje formuluojama problema, aprašytas tyrimų objektas, darbo aktualumas, formuluojami darbo tikslai ir uždaviniai, aprašoma tyrimų metodika, darbo mokslinis naujumas, darbo rezultatų praktinė reikšmė, pateikti ginamieji teiginiai ir disertacijos struktūra. Pabaigoje pristatomi pranešimai konferencijose disertacijos tema. Pirmajame skyriuje pateikta matematinių modelių nestandartinėse srityse arba su nestandartinėmis sąlygomis apžvalga. Antrajame... [toliau žr. visą tekstą] / The numerical algorithms for non-stationary mathematical models in non-standard domains are investigated in the dissertation. The problem definition domain is represented by branching structures with conjugation equations considered at the branching points. The numerical analysis of the conjugation equations and non-classical boundary conditions distinguish considered problems among the classical problems of mathematical physics presented in the literature. The scope of the dissertation covers the investigation of stability and convergence of the numerical algorithms on branching structures with different conjugation equations, the construction and implementation of parallel algorithms, the investigation of the numerical schemes for the problems with nonlocal integral conditions. The modeling of the excitation of neuron and photo-excited carrier decay in a semiconductor, also the problem of the identification of nonlinear model are considered in the dissertation. The dissertation consists of an introduction, five chapters, main conclusions, bibliography and the list of the author's publications on the topic of dissertation. Introductory chapter covers the problem formulation and the object of research, the topicality of the thesis, the aims and objectives of the dissertation, the methodology of research, scientific novelty and the practical value of the achieved results. The defended thesis and structure of the dissertation are given in this chapter. The first chapter... [to full text]

The numerical algorithms for non-stationary mathematical models in non-standard domains are investigated in the dissertation. The problem definition domain is represented by branching structures with conjugation equations considered at the branching points. The numerical analysis of the conjugation equations and non-classical boundary conditions distinguish considered problems among the classical problems of mathematical physics presented in the literature. The scope of the dissertation covers the investigation of stability and convergence of the numerical algorithms on branching structures with different conjugation equations, the construction and implementation of parallel algorithms, the investigation of the numerical schemes for the problems with nonlocal integral conditions. The modeling of the excitation of neuron and photoexcited carrier decay in a semiconductor, also the problem of the identification of nonlinear model are considered in the dissertation. / Disertacijoje nagrinėjami nestacionarių matematinių modelių nestandartinėse srityse skaitiniai sprendimo algoritmai. Uždavinio formulavimo sritis yra šakotosios strukturos (ang. branching structures), kurių išsišakojimo taškuose apibrežiami tvermės dėsniai. Tvermės dėsnių skaitinė analizė ir nestandartinių kraštinių sąlygų analizė skiria nagrinėjamus uždavinius nuo klasikinių aprašytų literatūroje matematinės fizikos uždaviniu. Disertacijoje suformuluoti uždaviniai apima skaitinių algoritmų šakotose struktūrose su skirtingais srautų tvermės dėsniais stabilumo ir konvergavimo tyrimą, lygiagrečiųjų algoritmų sudarymą ir taikymą, skaitinių schemų uždaviniams su nelokaliomis integralinėmis sąlygomis tyrimą. Disertacijoje sprendžiami taikomieji neurono sužadinimo ir impulso relaksacijos lazerio apšviestame puslaidininkyje uždaviniai, netiesinio modelio identifikavimo uždavinys.