Scientific Journal of KubSAU

Polythematic online scientific journal
of Kuban State Agrarian University
ISSN 1990-4665
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Name

Pavlov Dmitriy Alekseevich

Scholastic degree


Academic rank

associated professor

Honorary rank

Organization, job position

Kuban State Agrarian University
   

Web site url

Email

7.779@mail.ru


Articles count: 6

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430 kb

MATHEMATICAL MODEL OF ORGANIZATION OF DISTRIBUTED CALCULATIONS IN A CORPORATE NETWORK ON PREFRACTAL GRAPHS IN VECTOR FORMULATION

abstract 1261702040 issue 126 pp. 564 – 581 28.02.2017 ru 138
In the article we investigate the multicriteria task arising at the organization of distributed calculations in a corporate network. As a mathematical tool to solve the problem we use prefractal graphs, which naturally reflect the structure of relationships in global and corporate networks. The corporate network with the distributed computing system at the solution of a particular task has to be reliable, quickly and qualitatively to make decisions. And every computer in the network should be a part in the solution of the problem, since it is fixed for a certain function. The problem is reduced to cover the prefractal graphs with disjoint simple paths along the edges and vertices. On the set of all admissible coverings we constructed a vector-target function with specific criteria. All these criteria have a specific meaningful interpretation, allowing organizing the calculation of maximum reliability, with minimum time information processing and loading balancing between the network elements. In the article we constructed polynomial algorithms for finding optimal solutions according to specific criteria. For the criteria which are not optimizing the allocated coverings, estimates of the lower and upper bounds are given. For all the algorithms we constructed and substantiated estimation of computational complexity, confirming the advantage of using algorithms on prefractal graphs to classical algorithms on graphs
621 kb

MATHEMATICAL MODEL OF THE PROBLEM OF ROUTE ORGANIZATION IN LARGE-SCALE TRANSPORT NETWORKS WITH THE APPLICATION OF MULTICRITERIAL OPTIMIZATION METHODS

abstract 1331709092 issue 133 pp. 1220 – 1230 30.11.2017 ru 52
Most of the tasks of planning and organizing transport routes are pointed to solving optimization problems on graphs in multi-criteria statements, for which the only optimal solution is missing. In conditions of multicriteria, it becomes necessary to search for a set of alternatives instead of an optimum. The quality of the admissible solutions is estimated by the vector objective function. The article proposes to investigate the problem using a special class of graphs - prefractal graphs, which allow describing in a natural way the structure of the hierarchy of territorial links, as well as enable to take into account structural dynamics in terms of system growth. A multicriteria mathematical formulation of the problem of covering a prefractal graph by simple intersecting chains is constructed, to which the investigated problem of organizing routes in large-scale transport networks reduces. The main social and economic requirements for the transport system are formulated and included in the model in the form of criteria
496 kb

MULTICRITERIА PROBLEM OF FINDING THE OPTIMAL PATHS FOR LARGE-SCALE TRANSPORT SYSTEM

abstract 1131509046 issue 113 pp. 618 – 635 30.11.2015 ru 398
This article explores the multicriteria problems arise in the organization of routes in large-scale transport management system. As a mathematical tool for constructing a model, we were using the prefractal graphs. Prefractal graphs naturally reflect structure of the device of communications of transport system, reflecting its important features – locality and differentiation. Locality is provided with creation of internal routes (city, raionwide, etc.). Differentiation is understood as division of routes on intra regional, interregional and international. The objective is reduced to a covering of prefractal graphs by the simple paths which are crossed on edges and nodes. On the set of feasible solutions, vector criterion function with certain criteria is based. In concepts of transport system, the given criteria have concrete substantial interpretation, the transport routes allowing to design considering features of system. In this article, we construct polynomial algorithms for finding optimal according to certain criteria decision. By the criteria which aren't optimizing the allocated routes their estimates of the lower and upper bounds are given. On all given algorithms the estimates of computing complexity confirming advantage of use of methods of prefractal and fractal graphs before classical methods of the theory of graphs are constructed and proved
527 kb

SIMULATION OF LARGE-SCALE TRANSPORT NETWORKS USING METHODS OF MULTICRITERIA OPTIMIZATION AND TAKING INTO ACCOUNT STRUCTURAL DYNAMICS

abstract 1201606111 issue 120 pp. 1686 – 1705 30.06.2016 ru 349
In the article we present a spatial structure of largescale transport systems. The model of a transport network can be presented in the form of a graph, with a set of the nodes corresponding to elements of a network and a set of edges – to sections of roads the connecting these nodes. As the model of a card of roads, it is offered to use prefractal graphs which naturally reflect structure of communications when reviewing a transport network in different scales (the states, regions, areas). Prefractal graphs allow describing structural dynamics of the studied system in the discrete time. One of the most widespread scenarios of structural dynamics is the growth of structure. The statement of tasks of the organization of transport routes contains requirements criteria to finding of optimal solutions. Often these requirements and criteria are contradicting each other. It leads to appearance of a multicriteria problem definition. The multicriteria problem definition on a class of prefractal graphs is considered. The optimum algorithm of separation of the greatest maximum paths by the given criterion is constructed and estimates by remaining criteria are given. In operation computing complexity of the constructed algorithm of separation of the greatest maximum paths on a prefractal graph is calculated and advantage of operation of algorithm on last before algorithm of separation of the greatest maximum paths on normal graphs is justified. The constructed algorithm on prefractal graphs has polynomial complexity
440 kb

SIMULATION OF THE LARGE-SCALE TRANSPORT NETWORK BY PREFRACTAL GRAPHS

abstract 1311707085 issue 131 pp. 1035 – 1045 29.09.2017 ru 62
This work is devoted to a new method for designing large-scale structures of transport networks. The model of a large-scale transport network is built on prefractal graphs. The model of a large-scale transport network is based on the principle of hierarchical organization of territories. A prefractal graph is a finite analogue of a fractal graph combining the properties of a fractal and a graph. Some problems of discrete optimization on prefractal graphs become polynomially solvable under certain conditions. Reducing the complexity of extreme problems on prefractal graphs is due to the fact that on these graphs for some problems, along with the selfsimilarity property, the property of heredity appears. Using this property, it is possible to construct parallel algorithms for problems on prefractal graphs, the complexity of which is orders of magnitude lower than for known successive algorithms
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