Kibernetika ta kompiuterni tekhnologiyi最新文献

{"title":"Predicting and Determining the Time Between Metrological Failures of Smart Systems for Precision Farming","authors":"V. Kondratov","doi":"10.34229/2707-451x.22.1.8","DOIUrl":"https://doi.org/10.34229/2707-451x.22.1.8","url":null,"abstract":"Introduction. Solving the problem of forecasting and determining the operating time for metrological failure and conducting the first calibration of smart systems of precision land use is possible by solving the problem of self-calibration of smart sensors that are part of these smart systems (SS). This problem is solved and described in [1].\u0000The purpose of the paper is the methodology for dynamic prediction and determination of the time between metrological failures (MF) and the first verification of SS designed for precision farming.\u0000Results. The article describes a method patented in Ukraine for measuring the SS operating time for a MF (dynamic prediction method) based on a synthesized probabilistic-physical model (PP-model) of SS MF described by a multi-parameter Kondratov – Weibull distribution function (DF) with controlled (flexible) parameters. The proposed model describes the relationship between the normalized error and the parameters of the metrological reliability (MR) of the SS.\u0000It is shown that the dynamic regression PP-models of MF are a combination of the capabilities of regression models using flexible multi-parameter DF, with the possibility of using dynamic (spatio-temporal) processes covering different trends in the change in the values of normalized errors and their uncertainty bands, confidence level, time frame, acceptable boundary conditions, etc.\u0000Dynamic regression models of MF SS make it possible to understand the relationship between DF variables and allow the possibility of studying metrological problems (“scenarios”) of the “what if …” type.\u0000The dynamic regression method is a set of techniques for reciprocating approximation of the values of the shift parameter of the dynamic PP-model of MF to the predicted value of the shift parameter of the static PP-model of MF SS, as well as methods for assessing the reliability and accuracy of forecasting and determination.\u0000The article describes the essence of a new method for determining the operating time of the SS in the MF using the PP-model of the MF based on the Kondratov – Weibull DF. For the first time, a graphical portrait of the PP-model of SS metrological failures in the combined system of scales (coordinates) has been developed and presented - with the scales \"probability of metrological failure Pξ\" and \"normalized error ξx\" and separate or combined scales of \"interval time scale tx \" and \"calendar time scale\".\u0000The procedure for determining the time of the first verification is described, the advantage of non-periodic verifications is noted in order to save costs for their implementation.\u0000The possibility of occurrence of \"conditional misses\" in determining the error and time of operation on the MF during one or another verification is shown. Their existence is established only after the subsequent verification, analysis of the obtained data, and drawing the curve of the DF on a graphical portrait.\u0000 It is recommended to choose the time between verifications as a multipl","PeriodicalId":34598,"journal":{"name":"Kibernetika ta kompiuterni tekhnologiyi","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42985767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Intelligent Processing of Data From Chlorophyll Fluorometric Sensors","authors":"V. Hrusha","doi":"10.34229/2707-451x.22.1.5","DOIUrl":"https://doi.org/10.34229/2707-451x.22.1.5","url":null,"abstract":"Introduction. Chlorophyll fluorescence induction (CFI) is a monitoring method of plant objects. CFI is a radiation of chlorophyll in red spectrum during a chlorophyll lighting of alive plant in blue spectrum. Chlorophyll fluorometers – the special devices that are used for measurement of CFI. Series of such devices were developed in V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine. In particular, fluorometer «Floratest» and a network of wireless sensors were developed for CFI measurement. An accumulation of massive amount of measurements resulted into possibility to use intellectual methods like neural networks.\u0000The purpose of the paper is to research the possibilities of machine learning methods (neural networks, support vector machine (SVM), XGBoost algorithm) for analysis of CFI curves that were measured by means of sensors developed in V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine.\u0000Results. Neural networks, SVM, XGboost ensure early detection of influence of stress factors on state of plants before appearance of external symptoms on plants that was showed on basis of data received during experiments with treatment of plants by herbicide. Analogically there was showed the possibility of using the machine learning methods for determination of soil humidity. The better methods for given tasks were determined. The study of possibilities to enhance the results of mentioned methods by means of normalization was conducted. The best results were demonstrated by z-score normalization and by minimax normalization to the range [-1;1].\u0000Conclusions. The application of different machine learning algorithm for processing CFI curves demonstrated that SVM and XGBoost better suit for task of classification plants treated by means of herbicide. Neural network demonstrated worst results. The application mentioned methods for task of determination of artificial watering necessity demonstrated that neural network shows better result, SVM shows worse result and XGBoost shows worst result. Keywords: Chlorophyll fluorescence induction, neural network, support vector machine, algorithm XGBoost.","PeriodicalId":34598,"journal":{"name":"Kibernetika ta kompiuterni tekhnologiyi","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44434258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Some Optimization Problems on Permutations","authors":"G. Donets, Vasyl Biletskyi","doi":"10.34229/2707-451x.22.1.1","DOIUrl":"https://doi.org/10.34229/2707-451x.22.1.1","url":null,"abstract":"Numerous studies consider combinatorial optimization problems and their solution methods, since a large number of practical problems are described by means of combinatorial optimization models. Among these problems, the most prominent ones are function optimization problems on combinatorial configurations. Many of the studies mentioned above propose approaches and describe methods to solve combinatorial optimization problems for linear and fractionally linear functions on combinatorial sets such as permutations and arrangements.\u0000This work describes new approaches and methods to solve some maximization problems for linear, fractionally linear and quadratic functions on permutation set. Algorithms for solving these problems are given.\u0000 For linear function, we provide a considerably easy method to find the permutation on which the function attains its maximum value.\u0000 We describe the general algorithm to find fractionally linear function maximum. We consider the cases in which variables of numerator and denominator do not intersect, and when the numerator function and the denominator function have one common variable. We also describe the case in which the numerator function and the denominator function in total have incomplete variable list, i.e. when the total quantity of variables is less than the quantity of numbers in the permutation set.\u0000As for solving the problem of finding quadratic function maximum on permutation set, it turned out that there is no universal algorithm to solve this problem for any quadratic function. In this paper, we describe a method of finding maximum on permutation set for quadratic function consisting of two items.\u0000We provide examples of solving the considered optimization problems.\u0000 Keywords: function, permutation, set, transposition, coefficients.","PeriodicalId":34598,"journal":{"name":"Kibernetika ta kompiuterni tekhnologiyi","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46350793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Magnetometric Investigations of Biomagnetic Signals: Magnetocardiography","authors":"Mykhailo Primin, I. Nedayvoda","doi":"10.34229/2707-451x.22.1.4","DOIUrl":"https://doi.org/10.34229/2707-451x.22.1.4","url":null,"abstract":"Introduction. Superconducting magnetometers based on SQUIDs (SQUID- Superconducting QUantum Interference Device) are currently used to register weak magnetic fields generated in various human organs and measured outside the body (in the environment). The creation of information technology, which is a set of methods and software tools combined into a technological chain that ensures registration, storage, pre-processing, analysis of measurement data and automatic diagnostic output, is an essential science-intensive component that determines the possibilities and success of the applied use of non-contact diagnostic systems of the human heart\u0000The purpose. Article presents new algorithms for spatial analysis of cardiomagnetic signal measurement results. The algorithms are based on the inverse problem solution, when the magnetic field source is matched to the spatial distribution of the magnetic signal and the parameters and spatial configuration of the source are determined. A model of the cardiomagnetic source was used in the form of a system of current density vectors, which are distributed in a plane that is parallel to the measurement plane and crosses the volume of the heart.\u0000Results. The inverse problem is solved using the apparatus of two-dimensional integral Fourier transformations. The data transformation algorithm allows to correctly take into account the design of the magnetic flux transformer (the dimensions of the pickup coils, their spatial location and the electrical connection scheme). Algorithm modifications have been developed for most of the known (implemented in existing magnetocardiographs) designs of magnetic flux transformers of the first and second order gradientometers. The operation of the algorithm is modeled on real data of magnetometric investigations of the human heart. Investigations have shown that the application of the proposed algorithms allows obtaining new information about the spatial configuration of the magnetic signal source in the human heart, which can be used in the future for the diagnosis of human heart diseases. Keywords: magnetocardiography, inverse problem of magnetostatics, Fourier transform, SQUID gradientometer.","PeriodicalId":34598,"journal":{"name":"Kibernetika ta kompiuterni tekhnologiyi","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42262769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Investigation of Natural Algorithms and Their Complex Application for Optimization of Logistics Tasks","authors":"V. Andriichuk, V. Tretynyk","doi":"10.34229/2707-451x.22.1.2","DOIUrl":"https://doi.org/10.34229/2707-451x.22.1.2","url":null,"abstract":"Introduction. At present, with the increase in the number of data and the complexity of various processes in many branches of the national economy, the classical methods of answering have ceased to meet the needs. So, for example, if you consider the logistics industry (this and transportation, and various cartographic services for consumers), we see how dynamically developing these areas. To construct optimal routes, if we continued to use old algorithms, we would have to spend a huge amount of computer resources and time to get results. Instead, the study finds new methods that make it possible to speed up and simplify the solution of problems. So, for example, for logistics problems, instead of classical combinatorial problems, algorithms are being replaced by environmental scientists. They were called natural algorithms. For example, scientists have noticed that ants find the shortest route to food using the iteration and intensity of a pheromone trace that leaves previous ants who are moving along the path. This idea formed the basis of the algorithm of the ant colony. Even if in reality ants find the optimal way more difficult than the simplified idea of researchers, it turned out that this simplification was enough to find an optimal route between some points of the type like ants looking for an optimal route food.\u0000To develop a complex meta-algorithm that would solve the problem of logistics network, the following methods are taken into account: natural algorithms, salesman problem, dynamic programming methods, combinatorial approaches, algorithms for complex data analysis.\u0000This paper considers the application of methods of natural algorithms to solve the problem of coordinated logistics.\u0000The purpose of the paper. The aim of the work is to increase the efficiency of using natural algorithms in logistics problems. In general, the main tasks of logistics are to forecast the amount of costs, products and resources under certain circumstances. However, the required amount of material, information, financial, service and other data flows is not always available in logistics tasks, many variables are unknown. Then heuristic methods of algorithms come to the rescue to solve such problems of an applied nature.\u0000Results. The software implementation of the model in the Python programming language was performed. Some methods of dynamic programming, fuzzy logic were used and the hyperopt library was used to implement the script. Keywords: natural algorithms, logistics, ant algorithm, meta-algorithm.","PeriodicalId":34598,"journal":{"name":"Kibernetika ta kompiuterni tekhnologiyi","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41541077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Formalization of the Problem of Optimization of Base Places and Routes of the UAV Group","authors":"L. Hulianytskyi, Oleg Rybalchenko","doi":"10.34229/2707-451x.21.4.2","DOIUrl":"https://doi.org/10.34229/2707-451x.21.4.2","url":null,"abstract":"Introduction. The problem of planning the mission of a set of heterogeneous unmanned aerial vehicles (UAVs)is considered, which is to survey and/or service a given set of targets in the field. A mathematical model of the problem and algorithms for its solving that is based on deterministic local search, as well as optimization by ant colonies are proposed. The efficiency of algorithms is investigated based on the results of solving problems with real objects in the field. The relative error of the results of each algorithm was obtained, which allowed to compare their efficiency.\u0000The purpose of the paper is to solve a routing problem in different ways to reduce overall mission cost and compare the efficiency. The problem statement considers multiple starting points and destinations (depots) for UAVs with determined capacity, so algorithms proposed in the paper are designed to optimize the initial placement. Each UAV has a maximum flight distance because of an energy limit, though vehicles can be recharged by visiting one of previously placed depots. The mission goal is to visit all the given targets while minimizing the overall cost, so fuel consumption over distance, depot placement, and resources needed to survey and/or service of the target by each UAV are considered as components of the final cost metric to be minimized considering a set of specific constraints.\u0000Results. To solve the given UAV routing problem, a max-min algorithm of ant systems was developed, which features step-by-step interaction of ants to form solutions, a hybrid taboo search algorithm and a deterministic local search algorithm - the decay vector method. The developed algorithms were tested both on the known travelling salesman problems, and on specially developed problems with multiple depots and additional restrictions. \u0000Conclusions. The proposed algorithms which are based on ant colony optimization are compared both in terms of accuracy and computation time. A hybrid algorithm achieved slightly better score, though computation time has increased. Keywords: routing, combinatorial optimization, UAV, local search, ant colony optimization algorithms.","PeriodicalId":34598,"journal":{"name":"Kibernetika ta kompiuterni tekhnologiyi","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48791877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Development of a Cluster with Cloud Computing Based on Neural Networks With Deep Learning for Modeling Multidimensional Fields","authors":"M. Kosovets, L. Tovstenko","doi":"10.34229/2707-451x.21.4.8","DOIUrl":"https://doi.org/10.34229/2707-451x.21.4.8","url":null,"abstract":"Introduction. The modeling of multidimensional fields on multiprocessors, with a neural network architecture, which is rebuilt in the process of solving the problem by means of deep learning, is considered. This architecture of the calculator allows the device to be used to solve the problems of passive location, monitoring station, active LPI location station, base telecommunications station at the same time. Particular attention is paid to the use of bionic principles in the processing of multidimensional signals. A cluster computer with cloud computing is proposed for creating a modeling complex for processing multidimensional signals and debugging the target system.\u0000The cluster is made in the form of a multiprocessor based on neural network technology with deep learning. Biomimetic principles are used in the architecture of the modeling complex.\u0000The purpose of the work. Creation of a modeling complex as a cluster with cloud computing using neural networks with deep learning. The cluster is a neuromultiprocessor that is rebuilt in the process.\u0000Results. In the process, we managed to create a multiprocessor, which in the process of computing is rebuilt, to simulate a terahertz 3D Imager scanner using cloud computing.\u0000Conclusions. In the process of performing the work a complex for modeling multidimensional signals was created. As the basis of the computer used a cluster that is rebuilt in the process. The computing base consists of neural networks with cloud computing. Keywords: cognitive space, deep learning, convolutional neural network, neural network architectures, cluster.","PeriodicalId":34598,"journal":{"name":"Kibernetika ta kompiuterni tekhnologiyi","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48748577","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Implementation of Multidigit Multiplication Basing on Discrete Cosine and Sine Transforms","authors":"A. Tereshchenko, V. Zadiraka","doi":"10.34229/2707-451x.21.4.7","DOIUrl":"https://doi.org/10.34229/2707-451x.21.4.7","url":null,"abstract":"Introduction. The emergence of new parallel computing systems such as multi-core processors, clusters, distributed systems, due to the solution of various applications in different spheres. Among such problems are the calculation of systems of linear algebraic equations with the number of unknown 33-35 million, the calculation of nuclear reactor shells, modeling of physical and chemical processes, aerodynamics, hydrodynamics, information security, and so on. This greatly expands the use of multidigit arithmetic, due to the fact that ignoring rounding errors leads to the fact that sometimes computer solutions are obtained that do not correspond to the physical content. Multidigit multiplication operation is an integral part of the exponentiation by module operation, the speed of which determines the speed of asymmetric cryptographic software and hardware complexes.\u0000This paper presents algorithms for implementing the multiplication operation of two N-digit numbers based on discrete cosine and sine transforms (DCT and DST) by separating the calculation for the real and imaginary parts of the DFT. Calculation of DCT and DST at the expense of additional bit shifts, additions and subtractions reduces the algorithm complexity to linear complexity by the number of integer multiplication operations.\u0000The purpose of the article is to reduce the number of multiplication operations to speed up the execution time of the multiplication operation of two N-bit numbers based on discrete transforms. Reduce the number of complex multiplication operations. Reduce the overall computational complexity and find a modification in which the calculation steps will correspond to DCT, DSP, IDCT and IDST. Use the coefficients to take into account the rounding errors to exclude multiplication operations on calculating DCT, DST, IDCT and IDST.\u0000Results. The relationship between DCT, DST and DFT of a real signal is considered, which allows to separate calculations for real and imaginary parts of DFT of real signals. The computational complexity is reduced almost twice at the expense of use of DFT properties of real signals. It is shown that after optimization steps of the algorithm calculation correspond to DCT, DST, IDCT and IDST. Using additional coefficients, which allow to take into account rounding errors at each step so that all calculations use integers. An analysis of the choice of word length in the calculation is given. For each algorithm, examples of calculation are given. Tables of dependence of the minimum lengths of the coefficients on the length of the multidigit number and the length of the digit (in bits) are given.\u0000Conclusions. Multiplication algorithms of two N-digit numbers based on discrete cosine and sine transforms (DCT and DST) are presented in this paper. Separating the calculation for the real and imaginary parts of the DFT allows to reduce the number of multiplication operations by 33%. The use of additional coefficients and calculation of DCT, DST, IDC","PeriodicalId":34598,"journal":{"name":"Kibernetika ta kompiuterni tekhnologiyi","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48486129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Vehicle Routing Problem When Using UAVs","authors":"Iryna Norba","doi":"10.34229/2707-451x.21.4.3","DOIUrl":"https://doi.org/10.34229/2707-451x.21.4.3","url":null,"abstract":"Introduction. In recent years, the use of unmanned aerial vehicles (UAVs) is growing rapidly. Initially introduced for military purposes, drones and related technologies have been successfully switched to a number of new civilian applications in the last few years, such as delivery, logistics, surveillance, entertainment, and more. They also opened up new opportunities, such as working in difficult or dangerous areas. The UAV has the potential to solve the problem of air mobility, allowing to change transport and logistics in the future. Combining UAVs with traditional land vehicles can solve the last-mile delivery problem by achieving significant improvements in distribution costs and speed of vehicle delivery. One of the biggest challenges is to plan UAV routes with a number of constraints, including time, distance or energy costs, cargo weight, environmental and environmental conditions (such as wind direction or obstacles), UAV battery life, and demand requirements. users you want to visit. Thus, it revealed the need to classify different types of research and study the general characteristics of the study area. This article aims to help identify the main topics and new areas of research, as well as provides a published overview of the current state and contribution to the problem of UAV routing, as well as a general categorization of the problem of vehicle routing (VRP).\u0000The purpose of the paper is to analyze the scientific contributions to the problem of UAV routing to determine the main characteristics of these problems, as well as trends in research and recent improvements.\u0000Results. Sources are classified according to the areas of application of UAVs; methods that include exact, heuristic, metaheuristic, and mixed algorithms are mentioned.\u0000Conclusions. An overview of the work on routing problems using UAVs and the tasks they generate, trends in research and recent developments. Keywords: Unmanned aerial vehicle, routing, vehicle, optimization.","PeriodicalId":34598,"journal":{"name":"Kibernetika ta kompiuterni tekhnologiyi","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45457943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Problem of Planning of Multi-Product Flows and Modernization of the Transportation Network","authors":"N. Zhurbenko, B. Chumakov","doi":"10.34229/2707-451x.21.4.1","DOIUrl":"https://doi.org/10.34229/2707-451x.21.4.1","url":null,"abstract":"Introduction. The problems of optimal planning of multi-product flows on transportation networks have a variety of important practical applications (transportation, logistics, communication networks). The mathematical models of these problems, as a rule, are characterized by a large dimension (hundreds of thousands of variables). Due to the specific features of multi-product transportation problems (pronounced block structure), the use of standard general-purpose optimization packages for their solution is not advisable. In this work of an applied nature, we propose a method for solving one class of such problems, taking into account their specificity. The method is based on the decomposition scheme with respect to a set of binding constraints. The corresponding dual problem is the nonsmooth optimization problem. To solve it, a new version of the subgradient algorithm with space dilation of variables is used. This approach to solving block optimization problems has been tested in solving a wide class of applied problems and, as experience shows, is characterized by a fairly high efficiency.\u0000Purpose of the article to develop a solution method and software for the problem of optimal planning of multi-product flows and modernization of the transportation system.\u0000Results. A mathematical model of the problem of optimal planning multi-product flows on the transportation network is proposed. The model is based on a variant transportation realization scheme. The software is developed in the C++ language in the style of object-oriented programming. The following algorithms are used as basic elements of the software: an algorithm for finding the shortest paths on a graph, an algorithm for solving a transportation problem on a graph, nonsmooth optimization algorithm.\u0000Conclusions. The output data of the developed software determines the following information: rational transportation scheme, critical by capacity sections of the transportation network, recommendations for the rational distribution of funds for the reconstruction of the transportation network. The software is designed to solve the problems of long-term planning of the functioning and development of the transportation system. Keywords: optimal planning, mathematical model, subgradient methods, dual problem, software.","PeriodicalId":34598,"journal":{"name":"Kibernetika ta kompiuterni tekhnologiyi","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48668769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}