Volodymyr Vasyanin

Introduction. The application of binary-reflected (mirror, reflexive) Gray codes for solving combinatorial problems with pseudo-Boolean functions (polynomials from Boolean variables) is considered. A recursive Ehrlich algorithm is given for generating a sequence of lines n-bit Gray codes, in which each subsequent line differs from the previous one...

The paper considers the network problem of optimizing the routing of groupage cargo flows in the transportation network with given tariffs for the transportation and handling of flows and constraints on the capacities of arcs, nodes, and the time of delivery of individual goods to a receiver. To compute the delivery time, the authors have proposed...

The article is devoted to the study of the optimization problem for the hierarchical structure of a multicommodity communication network with discrete flows and parameters when its density changes (the ratio of the number of network arcs to the maximum possible number of arcs for a given number of nodes in the network). The network has three levels...

UDC 519.854.3 Economic-mathematical models of flows distribution problem in multicommodity communication network / Trofymchuk O.M., Vasyanin V.A., Ushakova L.P. // Mathematical modeling in economy. — 2016. — N 2. — P. 5-21. The paper deals with the formulation of optimization problems of distribution flows with nonlinear functions of cost and buil...

Using numerical experiments, two implementations of Kruskal's algorithm based on the linked lists (the proposed algorithm) and tree (Tarjan's algorithm) data structures were compared with Prim's algorithm.

The method for computing the help matrix of merging the small packages of discrete flows during solving the optimization of packings problem in multicommodity networks with restrictions on the period of delivery or the number of merges of flows is proposed. On the basis of the proved statements, efficient computing algorithms for determining the no...

Gray codes in combinatorial optimization problems / Vasyanin V.A., Ushakova L.P. // Mathematical modeling in economy. – 2019. – № 1. – P. 63–69. The article provides useful information for developers of algorithms and programs on the use of Gray codes for solving combinatorial problems with pseudoBoolean functions (polynomials from Boolean variable...

Keywords: simulation, computer technology, multicommodity flows of correspondence, communications networks, hierarchical structures Introduction. The computer technology to modeling a hierarchical structure and a flow sorting scheme in communications network are considered. The computer program is the part of the software tools of automated informa...

UDC 519.854.2 Vehicle routing problems with simultaneous and split delivery and pickup of small-lot cargo in the internal service areas of trunk nodes of hierarchical transport network / Vasyanin V.A. // Mathematical modeling in economy. – 2017. – № 1-2. – P. 74–92. The paper presents mathematical formulations of the vehicle routing problems with s...

UDC 519.854.2 Vehicle routing problems with delivery and collection of small-lot cargo in the internal service areas of trunk nodes of hierarchical transport network / Vasyanin V.A., Ushakova L.P. // Mathematical modeling in economy. — 2016. — N 4. — P. The paper presents the basic principles and schemes of organization transportation of small-lot...

The authors consider the problem of choosing the capacity of arcs from a given set, which is important in flow distribution in multicommodity communication networks with constraint on flow delay time. Such problem is proved to be NP-hard. The algorithms for the approximate solution of the problem and results of their experimental comparison with ex...

V.A. Vasyanin Computer Simulation of the Distribution and Discrete Multicommodity Flows Routing in a Communication Network Keywords: simulation, computer technology, multicommodity flows of correspondence, communications networks, hierarchical structures. Introduction. We consider computer technology of modeling processes distribution and routing o...

The paper discusses algorithms to solve packing optimization problem, which arises in sorting and packing of small-lot cargo in containers in mainline transportation networks or in merging messages into virtual containers in backbone data transmission networks. A problem statement is proposed and its specific properties and approaches to the soluti...

The authors consider packing optimization for elements of a square matrix, which are given by positive integers, into blocks of fixed size. The problem is formulated and its combinatorial intractability is discussed. The problem is proved to be NP-complete. This is done by polynomial reduction of an NP-complete minimum-cost integer multicommodity f...

Consideration is given to the mathematical model of the nonlinear multiextreme discrete problem of distribution and routing in the multicommodity network of transport blocks with nested small packages flows of cargoes or messages with different addresses of destination. The special features of its solution for a transport network and data transmiss...

The techniques of solving the generalized problem of minimization of the nonlinear cost function on processing and distributing small-size lot discrete flows in a hierarchical multicommodity network is proposed. The technique makes it possible in the interactive regime to choose the hierarchic structure of a network and to determine the basic techn...

An algorithm for finding all shortest paths in an undirected network is considered. The following two criteria are used: the minimum number of arcs in a path and a minimum path length. The algorithm is analyzed for complexity, and it is empirically shown that, with increasing the network density, its computational efficiency becomes higher than tha...

The authors propose a technique to solve a packing problem for obtaining the initial data necessary to construct mathematical models of perspective development of nodes of multicommodity communication networks with discrete flows. The results of numerical modeling of the solution for a specific example for five stages of network development in fore...

We consider the rational organization of deliveries in optimization of a transportation work. An efficient computational algorithm based on the branch-and-bound method is proposed. This algorithm makes it possible to solve practical routing problems of rather high dimension.