Kibernetika ta kompiuterni tekhnologiyi最新文献

{"title":"The Efficiency of Discrete Optimization Algorithm Portfolios","authors":"I. Sergienko, V. Shylo, V. Roshchyn, P. Shylo","doi":"10.34229/2707-451x.21.2.1","DOIUrl":"https://doi.org/10.34229/2707-451x.21.2.1","url":null,"abstract":"Introduction. Solving large-scale discrete optimization problems requires the processing of large-scale data in a reasonable time. Efficient solving is only possible by using multiprocessor computer systems. However, it is a daunting challenge to adapt existing optimization algorithms to get all the benefits of these parallel computing systems. The available computational resources are ineffective without efficient and scalable parallel methods. In this connection, the algorithm unions (portfolios and teams) play a crucial role in the parallel processing of discrete optimization problems.\u0000The purpose. The purpose of this paper is to research the efficiency of the algorithm portfolios by solving the weighted max-cut problem. The research is carried out in two stages using stochastic local search algorithms.\u0000Results. In this paper, we investigate homogeneous and non-homogeneous algorithm portfolios. We developed the homogeneous portfolios of two stochastic local optimization algorithms for the weighted max-cut problem, which has numerous applications. The results confirm the advantages of the proposed methods.\u0000Conclusions. Algorithm portfolios could be used to solve well-known discrete optimization problems of unprecedented scale and significantly improve their solving time. Further, we propose using communication between algorithms, namely teams and portfolios of algorithm teams. The algorithms in a team communicate with each other to boost overall performance. It is supposed that algorithm communication allows enhancing the best features of the developed algorithms and would improve the computational times and solution quality. The underlying algorithms should be able to utilize relevant data that is being communicated effectively to achieve any computational benefit from communication. Keywords: Discrete optimization, algorithm portfolios, computational experiment.","PeriodicalId":34598,"journal":{"name":"Kibernetika ta kompiuterni tekhnologiyi","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47188316","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":"Convex Polygonal Hull for a Pair of Irregular Objects","authors":"V.M. Dubynskyi, O. Pankratov, T. Romanova, B.S. Lysenko, R.V. Kayafyuk, O.O. Zhmud","doi":"10.34229/2707-451x.21.2.2","DOIUrl":"https://doi.org/10.34229/2707-451x.21.2.2","url":null,"abstract":"Introduction. Optimization placement problems are NP-hard. In most cases related to cutting and packing problems, heuristic approaches are used. The development of analytical methods for mathematical modeling of the problems is of paramount important for expanding the class of placement problems that can be solved optimally using state of the art NLP-solvers.\u0000The problem of placing two irregular two-dimensional objects in a convex polygonal region of the minimum size, which is a convex polygonal hull of the minimum area or perimeter, is considered. Continuous rotations and translations of non-overlapping objects are allowed.\u0000To solve the problem of optimal compaction of a pair of objects, two algorithms are proposed. The first is a sequentially search for local extrema on all feasible subdomains using a solution tree. The second algorithm searches for a locally optimal extremum on a single subdomain using a \"good\" feasible starting point.\u0000Purpose of the paper. Show how to construct a minimal convex polygonal hull for two continuously moving irregular objects bounded by circular arcs and line segments.\u0000Results. A mathematical model is constructed in the form of a nonlinear programming problem using the phi-function technique. Two algorithms are proposed for solving the problem of placing a pair of objects in order to minimize the area and perimeter of the enclosing polygonal area. The results of computational experiments are presented.\u0000Conclusions. The construction of a minimal convex polygonal hull for a pair of two-dimensional objects having an arbitrary spatial shape and allowing continuous rotations and translations makes it possible to speed up the process of finding feasible solutions for the problem of placing a large number of objects with complex geometry. Keywords: convex polygonal hull, irregular objects, phi-function technique, nonlinear optimization.","PeriodicalId":34598,"journal":{"name":"Kibernetika ta kompiuterni tekhnologiyi","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42500076","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":"Modification of the Use of Bayesian Recognition Procedures for Inflammatory Processes in Gliomas, Metastasis and Meningiomas by Indicators of Erythrocyte Sedimentation Rate","authors":"A. L. Tarasov, A. Gupal, N. Gridina","doi":"10.34229/2707-451x.21.2.5","DOIUrl":"https://doi.org/10.34229/2707-451x.21.2.5","url":null,"abstract":"Introduction. The article discusses the application of Bayesian recognition procedures with one independent feature in relation to the erythrocyte sedimentation rate data taken from patients with gliomas, metastases, meningiomas, traumatic brain injury and from a group of healthy people.\u0000Purpose of the article. Analysis of erythrocyte sedimentation rate indicators using optimal recognition procedures.\u0000Results. In earlier articles by the authors, a similar work was described, however, due to the fact that the erythrocyte sedimentation rate was measured in different concentrations of pharmaceuticals and due to the receipt of new data structures, it was possible to increase the efficiency of the recognition procedures by 3-4%. The maximum recognition efficiency of almost 90% was achieved in the differential diagnosis of gliomas in relation to traumatic brain injury and the use of a substance supplemented with chlorpromazine. When recognizing inflammatory processes in patients with metatsases in relation to a group of healthy people, the efficiency of the recognition procedure was 88% using NaATF with a dilution of 1:10. We also note a 4% increase in the recognition efficiency of conditionally benign grade II gliomas, i.e. the efficiency of recognition of the development of gliomas in the early stages increased. Also in this work, it was possible to identify inflammatory processes in benign extracerebral tumors - meningiomas. The effectiveness of this recognition in relation to a group of healthy people was 83%.\u0000Conclusions. New results of recognition of inflammatory processes in brain gliomas have been obtained, on the basis of which an auxiliary diagnostic tool has been improved in gliomas, metastases and meningiomas. This diagnostic method becomes especially valuable in cases where modern imaging diagnostic methods are not able to determine the presence of a tumor in a patient, as well as in the postoperative period with indulgent tumor growth. Keywords: Bayesian recognition procedure, gliomas, metastases, meningiomas, erythrocyte sedimentation rate, complex parameter.","PeriodicalId":34598,"journal":{"name":"Kibernetika ta kompiuterni tekhnologiyi","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46028761","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":"Methods of Numeration of Discrete Sequences","authors":"N. Gupal","doi":"10.34229/2707-451x.21.2.6","DOIUrl":"https://doi.org/10.34229/2707-451x.21.2.6","url":null,"abstract":"Introduction. Numeration, or code, discrete sequences act fundamental part in the theory of recognition and estimation. By the code get codes or indexes of the programs and calculated functions. It is set that the universal programs are that programs which will realize all other programs. This one of basic results in the theory of estimation. On the basis of numeration of discrete sequences of Godel proved a famous theorem about incompleteness of arithmetic.\u0000Purpose of the article. To develop synonymous numerations by the natural numbers of eventual discrete sequences programs and calculable functions mutually.\u0000Results. On the basis of numerations of eventual discrete sequences numerations are built for four commands of machine with unlimited registers (MUR) in the natural numbers of type of 4u, 4u +1, 4u+2, 4u+3 accordingly. Every program consists of complete list of commands. On the basis of bijection for four commands of MUR certainly mutually synonymous numerations for all programs of MUR. Thus, on the basis of the set program it is possible effectively to find its code number, and vice versa, on the basis of the set number it is possible effectively to find the program.\u0000Conclusions. Synonymous numerations by the natural numbers of complete discrete sequences are developed mutually, programs for MUR and calculable functions. Leaning against numeration of the programs it is set in the theory of calculable functions, that the universal programs are, that programs which will realize all other programs. By application of the calculated functions and s-m-n theorem are got to operation on the calculated functions: combination φx and φy, giving work φxφy, operation of conversion of functions, effective operation of recursion. Thus, the index of function φxφy is on the indexes of x and y [2]. Keywords: numeration, Godel code number, diagonal method.","PeriodicalId":34598,"journal":{"name":"Kibernetika ta kompiuterni tekhnologiyi","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42597006","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":"Progress in Determination of Protein Spatial Structure Based on Machine Learning","authors":"B. Biletskyy","doi":"10.34229/2707-451X.21.1.5","DOIUrl":"https://doi.org/10.34229/2707-451X.21.1.5","url":null,"abstract":"Introduction. The task of determining the spatial structure of proteins is one of the most important unsolved problems of mankind. Life on the planet Earth is called protein, because protein molecules are the drivers of life processes in living organisms. Proteins make up about 80% of the dry mass of the cell and coordinate the processes of metabolism. The functions of proteins are defined by its spatial structure.\u0000\u0000The results of recent competitions in methods for determining protein structures have shown significant progress in this important area. One of the research groups presented the AlphaFold 2 method, the accuracy of which reached the accuracy of experimental methods.\u0000\u0000Purpose of the article. The aim of the work is to consider and analyze the basic principles of the AlphaFold software package for determining the spatial structure of proteins.\u0000\u0000Results. We consider the main stages in the process of recognizing the structure of a protein using the AlphaFold program complex. The stages and corresponding methods include: search for homologous proteins based on multiple alignment methods, construction of protein-specific differentiated potential using artificial neural networks and protein structure energy optimization using gradient descent and limited sampling. We discuss how combination of various bioinformatics techniques powered by data from open data sources can lead to significant improvements in accuracy of protein structure prediction. Special attention is paid to the use of artificial neural networks for building the smooth protein-specific potential and following energy minimization based on constructed potential.\u0000\u0000Conclusions. The combination of a number of methods and the use of information from protein and genetic data banks allows us to make significant progress in solving the extremely important task of determining the structure of a protein.\u0000\u0000 \u0000\u0000Keywords: protein spatial structure, Machine Learning, AlphaFold.","PeriodicalId":34598,"journal":{"name":"Kibernetika ta kompiuterni tekhnologiyi","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46483938","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":"Twofold Addressing of Microinstructions in CMCU with Common Memory","authors":"A. Barkalov, L. Titarenko, O. Golovin, A. Matvienko","doi":"10.34229/2707-451X.21.1.9","DOIUrl":"https://doi.org/10.34229/2707-451X.21.1.9","url":null,"abstract":"Introduction. Control unit (CU) is one of the most important blocks of practically any digital system. Its characteristics largely determine the characteristics of a system as a whole. As a rule, to synthesize CUs, the models of Mealy and Moore finite state machines (FSMs) are used.\u0000\u0000The article is devoted to compositional microprogram control units (CMCUs). A CMCU is a Moore FSM in which a state register is replaced by a microinstruction address counter. The choice of CMCU is an optimal solution for implementing linear control algorithms. When developing FSM circuits, it is necessary to optimize such characteristics as the performance and hardware amount. The methods of optimization depend strongly on logic elements used. Nowadays, FPGA chips are one of the most common logic elements for implementing digital systems. To implement the CMCU circuit, it is enough to use look-up table (LUT) elements, programmable flip-flops, embedded memory blocks, and programmable interconnections. \u0000\u0000The purpose of the article. In the article, there is proposed a CMCU design method improving such characteristics of CU as the number of logic levels and regularity of programmable interconnections.\u0000\u0000The main drawback of LUT is a small number of inputs. Modern digital systems can generate signals of logical conditions entering the control unit, the number of which is tens of times greater than the number of LUT inputs. Such a discrepancy between the characteristics of the control algorithm and the number of inputs of the LUT elements leads to multi-level control circuits with an irregular structure of programmable interconnections, and is the reason for a decrease in performance and an increase in chip area and power consumption.\u0000\u0000Results. A method for double addressing of microinstructions in CMCU with shared memory is proposed. The method is an adaptation of the two-fold state assignment of Mealy FSMs, the circuits of which are implemented with FPGAs. The proposed method makes it possible to obtain a microinstruction addressing circuit with two logic levels and a regular interconnection system. The paper considers an example of the synthesis of the CMCU circuit and analyzes the proposed method.\u0000\u0000Conclusions. The proposed method allows reducing hardware amount (the number of LUTs and their interconnections), time of delay and power consumption. Moreover, the more complex the control algorithm, the greater the benefit the proposed method gives.\u0000\u0000 \u0000\u0000Keywords: compositional microprogram control unit, microinstruction, LUT, EMB, synthesis.","PeriodicalId":34598,"journal":{"name":"Kibernetika ta kompiuterni tekhnologiyi","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49255609","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":"About the Development of a High-Speed Simplified Image Codec","authors":"Yа. Luts, V. Luts","doi":"10.34229/2707-451X.21.1.6","DOIUrl":"https://doi.org/10.34229/2707-451X.21.1.6","url":null,"abstract":"In order to develop a high-speed simplified image codec, an analysis of the influence of known image compression algorithms and other parameters on performance was done. The relevance and expediency of developing a high-speed simplified image codec for the Internet of Things in order to increase the level of autonomy of IoT devices, reduce the cost of construction and dissemination of IoT infrastructure were substantiated. The efficiency coefficient of image compression algorithms was introduced, which is determined by the ratio between the computational complexity of the algorithms and their contribution to the final result. Simplification and reduction of the number of algorithms for predicting pixel values ​​were proposed and substantiated, because at this stage a significant number of computational operations is added by the procedure of comparing different prediction algorithms with each other. It is proposed to use only one block integer transformation with fast low complexity algorithms of calculating, which will significantly reduce the complexity of the block transformation stage, including due to the lack of high computational complexity of the algorithm for comparing the quality of block transformations. At the stage of entropy coding, it is also proposed to use simplified algorithms, because the contribution of this stage to the overall result in the general background is quite small, and the computational complexity is high (50 – 70 % of all calculations). A new algorithm for progressive image transfer was proposed - the transfer of a reduced image followed by the transfer of the original image on demand. The considered approaches and algorithms for the development of high-speed simplified image codec can be applied to further development of high-speed simplified video codec.\u0000\u0000 \u0000\u0000Keywords: computational complexity, fast transforms, computational efficiency, progressive data transfer, intra-prediction algorithms, simplified image codec, IoT.","PeriodicalId":34598,"journal":{"name":"Kibernetika ta kompiuterni tekhnologiyi","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49392330","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":"The Mathematical Safe Problem and Its Solution (Part 2)","authors":"S. Kryvyi, H. Hoherchak","doi":"10.34229/2707-451X.21.1.2","DOIUrl":"https://doi.org/10.34229/2707-451X.21.1.2","url":null,"abstract":"Introduction. The problem of mathematical safe arises in the theory of computer games and cryptographic applications. The article considers numerous variations of the mathematical safe problem and examples of its solution using systems of linear Diophantine equations in finite rings and fields.\u0000\u0000The purpose of the article. To present methods for solving the problem of a mathematical safe for its various variations, which are related both to the domain over which the problem is considered and to the structure of systems of linear equations over these domains. To consider the problem of a mathematical safe (in matrix and graph forms) in different variations over different finite domains and to demonstrate the work of methods for solving this problem and their efficiency (systems over finite simple fields, finite fields, ghost rings and finite associative-commutative rings).\u0000\u0000Results. Examples of solving the problem of a mathematical safe, the conditions for the existence of solutions in different areas, over which this problem is considered. The choice of the appropriate area over which the problem of the mathematical safe is considered, and the appropriate algorithm for solving it depends on the number of positions of the latches of the safe. All these algorithms are accompanied by estimates of their time complexity, which were considered in the first part of this paper.\u0000\u0000Conclusions. The considered methods and algorithms for solving linear equations and systems of linear equations in finite rings and fields allow to solve the problem of a mathematical safe in a large number of variations of its formulation (over finite prime field, finite field, primary associative-commutative ring and finite associative-commutative ring with unit).\u0000\u0000 \u0000\u0000Keywords: mathematical safe, finite rings, finite fields, method, algorithm.","PeriodicalId":34598,"journal":{"name":"Kibernetika ta kompiuterni tekhnologiyi","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46556876","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":"Optimized Layout of Spherical Objects in a Polyhedral Domain","authors":"T. Romanova, G. Yaskov, A. Chugay, Y. Stoian","doi":"10.34229/2707-451X.20.4.3","DOIUrl":"https://doi.org/10.34229/2707-451X.20.4.3","url":null,"abstract":"Introduction. The article studies the problem of arranging spherical objects in a bounded polyhedral domain in order to maximize the packing factor. The spherical objects have variable placement parameters and variable radii within the given upper and lower bounds. The constraints on the allowable distance between each pair of spherical objects are taken into account.\u0000\u0000The phi-function technique is used for analytical description of the placement constraints, involving object non-overlapping and containment conditions.\u0000\u0000The problem is considered as a nonlinear programming problem. The feasible region is described by a system of inequalities with differentiable functions.\u0000\u0000To find the local maximum of the problem the decomposition algorithm is used. We employ the strategy of active set of inequalities for reducing the computational complexity of the algorithm. IPOPT solver for solving nonlinear programming subproblems is used.\u0000\u0000The multistart strategy allows selecting the best local maximum point.\u0000\u0000Numerical results and the appropriate graphic illustration are given.\u0000\u0000The purpose of the article is presenting a mathematical model and developing a solution algorithm for arranging spherical objects in a polyhedral region with the maximum packing factor. It allows obtaining a locally optimal solution in a reasonable time.\u0000\u0000Results. A new formulation of the problem of arranging spherical objects in a polyhedral domain is considered, where both the placement parameters and the radii of the spherical objects are variable. A mathematical model in the form of nonlinear programming problem is derived. A solution approach based on the decomposition algorithm and multistart strategy is developed. The numerical results combined with the graphical illustration are given.\u0000\u0000Conclusions. The proposed approach allows modeling optimized layouts of spherical objects into a polyhedral domain.\u0000\u0000 \u0000\u0000Keywords: layout, spherical objects, polyhedral domain, phi-function.","PeriodicalId":34598,"journal":{"name":"Kibernetika ta kompiuterni tekhnologiyi","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46839140","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 Linear and Quadratic Two-Stage Transportation Problem","authors":"P. Stetsyuk, O. Lykhovyd, A. Suprun","doi":"10.34229/2707-451X.20.4.1","DOIUrl":"https://doi.org/10.34229/2707-451X.20.4.1","url":null,"abstract":"Introduction. When formulating the classical two-stage transportation problem, it is assumed that the product is transported from suppliers to consumers through intermediate points. Intermediary firms and various kinds of storage facilities (warehouses) can act as intermediate points.\u0000\u0000The article discusses two mathematical models for two-stage transportation problem (linear programming problem and quadratic programming problem) and a fairly universal way to solve them using modern software. It uses the description of the problem in the modeling language AMPL (A Mathematical Programming Language) and depends on which of the known programs is chosen to solve the problem of linear or quadratic programming.\u0000\u0000The purpose of the article is to propose the use of AMPL code for solving a linear programming two-stage transportation problem using modern software for linear programming problems, to formulate a mathematical model of a quadratic programming two-stage transportation problem and to investigate its properties.\u0000\u0000Results. The properties of two variants of a two-stage transportation problem are described: a linear programming problem and a quadratic programming problem. An AMPL code for solving a linear programming two-stage transportation problem using modern software for linear programming problems is given. The results of the calculation using Gurobi program for a linear programming two-stage transportation problem, which has many solutions, are presented and analyzed. A quadratic programming two-stage transportation problem was formulated and conditions were found under which it has unique solution.\u0000\u0000Conclusions. The developed AMPL-code for a linear programming two-stage transportation problem and its modification for a quadratic programming two-stage transportation problem can be used to solve various logistics transportation problems using modern software for solving mathematical programming problems. The developed AMPL code can be easily adapted to take into account the lower and upper bounds for the quantity of products transported from suppliers to intermediate points and from intermediate points to consumers.\u0000\u0000Keywords: transportation problem, linear programming problem, AMPL modeling language, Gurobi program, quadratic programming problem.","PeriodicalId":34598,"journal":{"name":"Kibernetika ta kompiuterni tekhnologiyi","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41444851","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}