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The article examines modern approaches to improve the efficiency of logistics processes in natural gas distribution. The main objective of the article is to develop and justify a combined approach for optimising these processes, including the use of graph theory and multi-criteria genetic algorithms to minimise the transportation costs and to maximise the revenue. The study demonstrates that the proposed approach can significantly reduce transaction costs and increase revenue through more efficient management of transport and resource allocation. The paper emphasises the importance of adaptability and flexibility of the logistics system in a dynamically changing external environment. Particular attention is paid to multi-criteria optimisation, which takes into account such important aspects as minimising transport costs, maximising revenue and ensuring security of supply. The proposed approach can be applied both at the national and international level, which is especially relevant in the context of current geopolitical changes and sanctions risks. The author also points out the need for further research to utilise data on available capacity in underground gas storage facilities and the possibility of booking additional transport capacity. The proposed approach is a powerful tool for improving the competitiveness of the Russian gas industry and ensuring the country's economic stability.

The article describes the problems of developing neurocontrollers for controlling dynamic objects, including the complexity of forming training data sets. It is indicated that one of the known methods for training an artificial neural network controlling an object is the neuroevolutionary approach, which involves using a genetic algorithm to adjust the synaptic weighting coefficients of an artificial neural network. The idea of using a means of demonstrating the evolutionary approach to adjusting the weighting coefficients of an artificial neural network for practical training of students in the basics of the neuroevolutionary approach is proposed. Software has been developed to demonstrate the neuroevolutionary approach using the example of the evolution of an artificial neural network of a given structure intended to control a simplified computer model of an autonomous vehicle. A method for resolving the problem of stagnation when using the evolutionary approach to training an artificial neural network is described. Options for using the developed software in teaching students the basics of artificial intelligence technologies and evolutionary methods of multicriteria optimization are proposed.

Over the last decade, our world exposed to many types of unpredictable disasters (recently Coronavirus). These disasters have clearly shown the uncertainty and vulnerability of supply chain systems. Also, it confirmed that adopting Just-in-Time (JIT) strategy to reduce the logistic chain cost may lead to inbuilt complexity and risks. Efficient tools are therefore needed to make complexity optimized supply chain decisions. Evolutionary algorithms, including genetic algorithms (GA), have proven effective in identifying optimal solutions that address the trade-offs between total supply chain cost and carbon emissions regulatory policy represented by carbon tax charges. These solutions pertain to the design challenges of supply networks exposed to potential disruption risks. However, GA have a set of parameters must be chosen for effective and robust performance of the algorithms. This paper aims to set the most suitable values of these parameters that used via GA – ased optimization cost and risk reduction model in firms using a JIT as a delivery system. The model has been conceptualized for addressing the design complexities of the supply chain, referred to as SCRRJITS (Simultaneous Cost and Risk Reduction in a Just-in-Time System). A complete analysis of the different parameters and operators of the algorithm is carried out using design of experiments approach. The algorithm performance measure used in this study is convergence of solutions. The results show the extent to which the quality of solution can be changed depending on selection of these parameters.

Relevance. Aluminum production is one of the most important industries all over the world. It has a high environmental load, resource and energy intensity. To reduce the negative impact of aluminum production, efforts are underway to improve its technological processes, aimed at increasing aluminum recovery rates, reducing waste volumes, and lowering energy consumption. The reduction of energy consumption can be achieved, among others, through implementing control systems that provide energy management. Due to the complexity and multiplicity of technological processes in aluminum production, the use of traditional linear approaches for such control systems is ineffective, and adequate mathematical models are required. At the same time, for the production level, the use of mathematical models based on a phenomenological description of the ongoing physical processes overly complicates the control task. As a result, the use of intelligent and adaptive approaches to both the mathematical description of technological processes and the optimal energy consumption management is relevant. Objects. Technological complexes of aluminum production, which have the properties of inertia, nonlinearity, and closedness; and the control system based on artificial intelligence methods. Alumina production is chosen as an illustration. Aim. To develop mathematical models capable of adequately describing the interrelated processes in the technological complexes under consideration, as well as the control system that allows optimal energy consumption management. Methods. For the mathematical model based on balance equations under uncertainty, the fuzzy-set theory was used along with the gradient descent method to identify the model parameters; for the optimization task, the genetic algorithm method was used. Results. The mass balance model and the process conditions changing model have been developed to determine the energy consumption for the technological complexes of aluminum production with continuous inertial nonlinear closed production. Based on these models, the dynamic characteristics of energy consumption and the parameters of technological processes were determined depending on the main controlled parameters, allowing us to predict emergencies. Considering technological parameters and cost factors, the optimization task for energy consumption management was solved.

This paper presents a genetic approach for optimizing intra coding in H.266/VVC. The proposed algorithm efficiently selects coding tools and Multi-Type Tree (MTT) partitions to achieve a balance between encoding time and video quality. The fitness evaluation function, which combines perceptual metrics and coding efficiency metrics, is used to assess the quality of each candidate solution. The results demonstrate a significant reduction in encoding time without compromising video quality. The proposed algorithm selects coding tools from a set of available tools in H.266/VVC. These tools include intra prediction modes, transform units, quantization parameters, and entropy coding modes. The MTT partitioning scheme includes four types of partitions: quadtree, binary tree, ternary tree, and quad-binary tree. Perceptual metrics are used to evaluate the visual quality of the encoded video. Coding efficiency metrics are used to evaluate the coding efficiency of the encoded video. The fitness evaluation function combines perceptual metrics and coding efficiency metrics to assess the quality of each candidate solution.

Objective. Comprehensive integrated circuit (IC) verification plays a crucial role in preventing costly errors and delays in product development cycle. It includes testing interaction and compatibility of different system elements, such as central processing unit, memory and various peripheral devices. Validating IC’s compliance to the functional requirements list may take up to 70% of the design process duration. This proportion grows with complexity and size of the device under development. Consequently, the essential tasks that integrated circuit developers face are research and development of methods for cutting design complexity and reducing implementation time.Method. Conducted research regarding usage of genetic algorithm for error discovery, which could lead to a failure in the end product.Result. Collected data regarding the amounts of victims and target errors for each fault of types stuck-at-0 and stuck-at-1 for circuits from ISCAS’85 and ISCAS’89 benchmarks. It has been discovered that the proposed method is more effective in comparison to random vector generation to an extent of target errors amount for every benchmark.Conclusions. Accumulated results allow for the algorithm usage during IC design in order to reduce time consumption for circuitry validation and improve on test kits quality.

The design of optimal seismic protection systems on bearings with hysteresis behavior leads to a conditional multidimensional global optimization problem with a nonlinear and non-differentiable objective function. In this paper, bearings with bilinear characteristic with hysteresis are considered, i.e. for each nonlinear bearing there are four parameters to optimize: ultimate elastic displacement and stiffness for the elastic mode and ultimate displacement and stiff-ness for the inelastic mode. We study the seismic response of an elastic beam on four nonlinear bearings under vertical seismic ground motion. The perturbation functional as an integral of the quadratic form of the state vector with a weight matrix formed from the stiffness and inertia matrices of the system on equivalent elastic supports is considered as the objective function. Minimization of the functional means the minimum of the total energy of the system on equivalent elastic bearings. Genetic algorithm is used to solve the optimization problem.

Introduction. The current practice of pile foundation selection is a time-consuming, incoherent and non-standardized process. The aim of the study is to develop a methodology for optimizing structural calculations on the example of a pile field, based on cone penetration test data. For this purpose it is necessary: to prepare an algorithm for processing data from engineering-geological surveys; to develop a strictly deterministic process of justification of the best option depending on the cost of the pile foundation; to obtain a visual representation of the data for the possibility of verification of the selected solution.Materials and methods. A genetic algorithm is used to optimize structural calculations of the pile field, which is implemented using the Galapagos plug-in based on the Grasshopper visual programming language. Python programming language is used to prepare initial data of geotechnical engineering surveys.Results. Linked algorithms for cone penetration test data processing and preliminary estimation of the optimal pile foundation configuration based on its total cost, on the bearing capacity of the pile foundation soil were developed.Conclusions. The developed algorithms can be used for preliminary calculation and rapid evaluation of pile foundation options. The required input data can be generated from calculation programmes. Alternatively, selection and optimization can be performed directly in Python code, using Grasshopper and Rhino only for force extraction and subsequent visualization of the results. Areas for further research and development include: consideration of layered geotechnical elements; estimation of the bearing capacity of each foundation footing independently and according to the underlying geotechnical elements; grouping of piles according to their position in the pile field and loads; consideration of the non-linear behaviour of the soil mass.

To study the mechanisms of growth and development, it is necessary to analyze the dynamics of the tissue patterning regulators in time and space and to take into account their effect on the cellular dynamics within a tissue. Plant hormones are the main regulators of the cell dynamics in plant tissues; they form gradients and maxima and control molecular processes in a concentration-dependent manner. Here, we present DyCeModel, a software tool implemented in MATLAB for one-dimensional simulation of tissue with a dynamic cellular ensemble, where changes in hormone (or other active substance) concentration in the cells are described by ordinary differential equations (ODEs). We applied DyCeModel to simulate cell dynamics in plant meristems with different cellular structures and demonstrated that DyCeModel helps to identify the relationships between hormone concentration and cellular behaviors. The tool visualizes the simulation progress and presents a video obtained during the calculation. Importantly, the tool is capable of automatically adjusting the parameters by fitting the distribution of the substance concentrations predicted in the model to experimental data taken from the microscopic images. Noteworthy, DyCeModel makes it possible to build models for distinct types of plant meristems with the same ODEs, recruiting specific input characteristics for each meristem. We demonstrate the tool’s efficiency by simulation of the effect of auxin and cytokinin distributions on tissue patterning in two types of Arabidopsis thaliana stem cell niches: the root and shoot apical meristems. The resulting models represent a promising framework for further study of the role of hormone-controlled gene regulatory networks in cell dynamics.

The Special Region of Yogyakarta is one of the most popular tourist destinations in Indonesia and offers a wide range of cultural wealth. Consequently, it is interesting to explore the many tourist attractions. A tour taking the optimal route can, of course, provide efficiency in terms of distance and travel time while also providing a quality experience to the traveler. Ignoring these factors can lead to a failed trip. To determine the optimal route, we spread a questionnaire to travelers (n = 507) and obtained their preferences when traveling to be used in designing the optimum route. We present two scenarios in this paper for comparison: the first is the common way tourists determine travel routes, and the second uses a genetic algorithm approach. We found that determining the optimal route of travel using methods of genetic algorithms can shorten the total travel distance of tourists by 68.8 kilometers (29.20%), reduce the travel time by 137.60 minutes (8.87%), and at the same time maintain tourist preferences during their tour. We also propose efforts to improve the optimization of cultural tourist travel routes, focusing on the travel aspects between tourist destinations and on the aspects of the tourist destination itself.

Objective. The article proposes ways to modify genetic algorithms used to automate the process of scheduling.Method. The methods of evolutionary calculations, the theory of schedules, genetic algorithms, the developed software product are used in the work.Result. It is established that the construction of the initial GA population for solving the problem is an extremely important criterion for the convergence of the result. It has been established that the two-stage mutation also allows individuals to be adjusted in the right direction, thereby reducing the time required to perform GA work.Conclusion. Studies show that the developed methods of GA modification can greatly affect the performance of software in the automated scheduling of educational institutions, a scheme of GA operation has been developed, methods of GA modification have been presented and tested.

В обучении искусственной нейронной сети одной из центральных проблем является начальная инициализация и настройка весовых коэффициентов, связанная с псевдослучайной инициализацией весовых коэффициентов. В статье описан базовый генетический алгоритм, а также метод определения весовых коэффициентов с использованием данного алгоритма. Также представлен комбинированный метод определения весовых коэффициентов, предусматривающий на первом этапе начальную инициализацию с помощью генетического алгоритма и использование стохастического градиентного спуска на втором этапе обучения Предлагаемые методы проверены на ряде искусственных нейронных сетей прямого распространения для различных задач по бинарной классификации реальных и синтетических данных, а также для однозначной многоклассовой классификации рукописных цифр на изображениях из базы данных MNIST. Искусственные нейронные сети сконструированы на основании теоремы Колмогорова-Арнольда. В данной статье проведен сравнительный анализ двух методов определения весовых коэффициентов – с использованием генетического алгоритма и градиентного спуска. По результатам сравнительного анализа сделан вывод о возможности применения генетического алгоритма для определения весовых коэффициентов как в качестве алгоритма начальной инициализации искусственной нейронной сети, так и в качестве алгоритма настройки весовых коэффициентов

Modeling of batteries is necessary to control their operating mode and diagnose their condition. It is important to model the life cycle, i. e. degradation of basic parameters over a long service life. This is due to the fact that the cost of buffering electricity by batteries is associated with their cycling resource, which can be increased by optimizing the mode of operation of the drive in the energy system. The existing models of battery degradation are characterized by specificity, limited work on standardized charge-discharge cycles, and mathematical cumbersomeness. The article proposes a universal approach devoid of the above disadvantages. The concept of continuous battery wear during the service life is used. A simple empirical model is presented that does not consider in detail the characteristics of the state of batteries during a separate charge-discharge cycle, and does not include voltaic variables. The model considers the intensity of the current wear of the battery as a function of the state of its charge, temperature, the current of the external circuit and the current of self-discharge, the full charge that has flowed through the battery since the beginning of its operation. In this case, the amount of wear (degradation) is determined by the integral of the function of the intensity of current wear over the battery life. To optimize the parameters of the model, a random search method is used in combination with a genetic selection algorithm. The corresponding model of degradation of parameters for the Delta GEL-12-55 lead-acid battery has been constructed, in which the data on degradation of capacity given in the technical description from the manufacturer are used. The efficiency of the parameter optimization algorithm and the adequacy of the resulting model are shown. The model developed by the authors can be used for technical and economic calculations of generator – storage –consumer systems, hybrid power storage systems, and compact representation of large volumes of experimental data on the degradation of specific batteries.

This work addresses the development of a hybrid approach to solving threeperson polymatrix games (hexamatrix games). On the one hand, this approach is based on the reduction of the game to a nonconvex optimization problem and the Global Search Theory proposed by A.S. Strekalovsky for solving nonconvex optimization problems with (d.c.) functions representable as a difference of two convex functions. On the other hand, to increase the efficiency of one of the key stages of the global search — constructing an approximation of the level surface of a convex function that generates the basic nonconvexity in the problem under study — operators of genetic algorithms are used. The results of the first computational experiment are presented.

Highly efficient reflectors are in demand in the rapidly developing optoelectronics. At the moment, distributed Bragg reflectors made of semiconductor materials are mainly used in this capacity. A lot of time and financial resources are spent on their production. Reducing the thickness of the reflector while maintaining its reflectivity would make these devices more affordable and extend their lifetime by reducing thermal noise. With the help of genetic optimization algorithms, the structures of multilayer semiconductor and combined metal-semiconductor reflectors were obtained, having a smaller thickness and equal optical characteristics than those of classical analogues. In particular, a 29% reduction in the thickness of the silicon/silica Bragg reflector was achieved without compromising performance.

The article presents an adaptive genetic algorithm developed by the authors, which makes it possible to optimize the topology of a power network with distributed generation. The optimization was based on bioinspired methods. The objects of the study were a 15-node circuit of a power net-work with photovoltaic stations and a 14-node IEEE augmented circuit with distributed generation sources (three wind farms and two photovoltaic plants). The simulation of the modes of electric power systems was performed using the Pandapower library for the Python programming language, which is in the public domain. Three types of electric load of consumers were considered, reflecting the natures of electricity consumption in the nodes of real electric power systems, the results of numerical studies were presented. The proposed genetic algorithm used two different functions of interbreeding, the function of mutation, selection of the best individuals and mass mutation (complete population renewal). At the end of each iteration of the algorithm operation, statistical dependencies were de-rived that characterized its work: the best (minimal losses) and average adaptability in the population, a list of the best individuals throughout all iterations, etc. The verification was carried out in comparison with the results obtained by a complete search of possible radial configurations of the system, and it showed that the developed genetic algorithm had fast convergence, high accuracy and was able to work correctly with different configurations of electrical circuits, generation and load structures. The algorithm can be used in conjunction with renewable energy sources generation forecasting systems for the day ahead when planning the operating modes of power units in order to minimize the costs of covering electricity losses and improve the quality of electricity supplied.

The features of the organization of distance learning of students in a higher educational institution, as well as the information and educational technologies necessary for this, are considered. A system of automatic assessment of students’ knowledge is proposed. It is based on a model in the form of an artificial neural network. The features of such a model are given. The two implemented methods for constructing artificial neural networks have been used in the software module for testing students’ knowledge. The choice of the type of network, its structure, and parameters has been substantiated. The first method is related to the construction of an artificial neural network in the manual mode. An algorithm is presented that reflects the iterative process of its training. In the second case, the network is built automatically by applying a genetic algorithm. At the beginning of the work, a set of randomly generated initial data arrives at the input of the algorithm. In the course of its work, the genetic algorithm determines the architecture and parameters of the neural network, which ensure the successful solution of the assigned applied problem. Trained networks are used to classify data. Both networks showed acceptable classification accuracy of the results obtained in the course of the students’ knowledge testing.

The activation of innovation processes always requires the presence of an appropriate enabling environment - an effective national innovation system (NIS), which determines the country’s ability to generate and implement various kinds of innovations. However, the formation of a full-fledged country’s innovation system is quite difficult, at least for two reasons: the presence of purely national features of the functioning of the main agents of change, as well as the specifics of the modern world, when many important processes for innovation go beyond individual countries, forming a globalized environment, the presence and the specifics of which determine the potential and strategic directions for the further development of each NIS. The scientific and methodological approach proposed in the paper is generally based on the hypothesis of the expediency of regulating a particular national innovation system development, taking into account its belonging to a certain basic type, which determines the specific features of development. For its implementation, the methods of genetic algorithms, cluster analysis, and neural network training were used. Within the framework of the study, four basic types of NIS were identified and qualitatively interpreted, which have characteristic features in the context of the quadruple helix concept of development. To identify the national innovation system, a neural network, which simplifies the modeling of its development, was built. As a demonstration of the additional possibilities of the toolkit, four supranational associations of countries have been identified and analyzed. The practical significance of the results lies in the possibility of conducting variable analytical and predictive studies in the course of substantiating the optimal directions for the further development of the national innovation system in terms of global and cluster trends.

Objectives. Recent research in machine learning and artificial intelligence aimed at improving prediction accuracy and reducing computational complexity resulted in a novel neural network architecture referred to as an extreme learning machine (ELM). An ELM comprises a single-hidden-layer feedforward neural network in which the weights of connections among input-layer neurons and hidden-layer neurons are initialized randomly, while the weights of connections among hidden-layer neurons and output-layer neurons are computed using a generalized Moore– Penrose pseudoinverse operation. The replacement of the iterative learning process currently used in many neural network architectures with the random initialization of input weights and the explicit computation of output weights significantly increases the performance of this novel machine learning algorithm while preserving good generalization performance. However, since the random initialization of input weights does not necessarily guarantee optimal prediction accuracy, the purpose of the present work was to develop and study approaches to intelligent adjustment of input weights in ELMs using bioinspired algorithms in order to improve the prediction accuracy of this data analysis tool in regression problems.Methods. Methods of optimization theory, theory of evolutionary computation and swarm intelligence, probability theory, mathematical statistics and systems analysis were used.Results. Approaches to the intelligent adjustment of input weights in ELMs were developed and studied. These approaches are based on the genetic algorithm, the particle swarm algorithm, the fish school search algorithm, as well as the chaotic fish school search algorithm with exponential step decay proposed by the authors. By adjusting input weights with bioinspired optimization algorithms, it was shown that the prediction accuracy of ELMs in regression problems can be improved to reduce the number of hidden-layer neurons to reach a high prediction accuracy on learning and test datasets. In the considered problems, the best ELM configurations can be obtained using the chaotic fish school search algorithm with exponential step decay.Conclusions. The obtained results showed that the prediction accuracy of ELMs can be improved by using bioinspired algorithms for the intelligent adjustment of input weights. Additional calculations are required to adjust the weights; therefore, the use of ELMs in combination with bioinspired algorithms may be advisable where it is necessary to obtain the most accurate and most compact ELM configuration.

A modification of the local search algorithm is considered using tournament selection for the task of operational planning in the production of plastic products. A comparative analysis of the results of the algorithm showed a direct dependence of the results on the presence of tournament selection and population size. The program is designed for operational planning in the production of plastic products, where it is necessary to take into account the volume and period of production of each type of product with the minimum number of changes in equipment settings. The objective of optimization is to minimize the number of product shifts in the production plan. It is proposed to modify the genetic algorithm using tournament selection for the task of planning types of products at production facilities. This algorithm is a local search method that allows you to gradually improve a certain result in some vicinity of the known solution. Purpose. The goal is to minimize the number of product shifts in the production plan. Methodology of work: the article used methods of system analysis, operations research, optimization theories, economic and mathematical methods and statistical methods of analysis. Results: on average, the solution is most quickly found with an initial population size of 100 individuals, and this time is less than the largest average values by 2 times. Tournament selection, reducing time costs, reduces the likelihood of finding an optimal solution. Practical implications. Results are useful on production lines to distribute capacity loads.

The article presents the results of combining 4 different types of neural network learning: evolutionary, reinforcing, deep and extrapolating. The last two are used as the primary method for reducing the dimension of the input signal of the system and simplifying the process of its training in terms of computational complexity.In the presented work, the neural network structure of the control device of the modeled system is formed in the course of the evolutionary process, taking into account the currently known structural and developmental features of self-learning systems that take place in living nature. This method of constructing it makes it possible to bypass the specific limitations of models created on the basis of recombination of already known topologies of neural networks.

O b j e c t i v e s. To develop a control system for the movement of a mobile robot along a color-contrast line, as well as to find the values of the coefficients of a proportional-integral-differentiating (PID) controller that allows the robot to move along the line at a given speed.M e t ho d s. To adjust the values of the coefficients of the PID controller, methods of enumeration, automatic tuning and a genetic algorithm are used.Re s u l t s. A software package for tuning the PID controller of the educational mobile robot RoboCake, designed to move along a closed color-contrast line at a given speed, has been developed. The software package consists of a simulation model of the specified robot in the Simulink environment, several virtual traces-polygons and a specialized solver based on the developed genetic algorithm. With the help of the proposed fitness function, a mobile robot control system that satisfies the stated conditions is implemented. Based on the conducted model experiments, the desired values of the parameters of the PID controller are obtained.Co n c l u s i o n. A comparison of the effectiveness of various methods of tuning the PID controller is carried out. The developed software package is designed to solve the practical problem of moving a mobile robot along a color-contrast line at a speed of 1 m/s. The results obtained can be used to study methods of evolutionary tuning of stabilization systems for transport robots, ensuring their movement without overshoot.

The article focuses on the use of genetic algorithms for the design of linear induction motors. Comparison of genetic algorithm with classical methods in the context of electrical machines designing has been carried out. The results of solving an optimization problem for two designs are presented, viz. a laboratory linear induction electric motor based on a three-phase SL-5-100 inductor and a traction single-sided linear induction electric motor of an urban transport system. The optimality criterion included maximizing the power factor and efficiency, as well as the rigidity of the mechanical characteristic while ensuring a starting traction force of at least a set value. The results of optimization of such parameters of the secondary element as the width and thickness of the conductive strip as well as the thickness of the magnetic circuit are described. The relevance of the problem of optimizing the parameters of the secondary element with unchanged parameters of the inductor is due to the fact that the same inductor can be used to build various structures, while the secondary element is created for each specific application and integrated directly into the working body of the mechanism or is a driven product. To calculate the traction and energy characteristics of linear induction electric motors, an electromagnetic model based on detailed equivalent circuits was used, taking into account longitudinal and transverse edge effects and providing a calculation time for one set of parameters of about 1 s. In accordance with this model, the electric motor is reduced to a set of three detailed equivalent circuits: a magnetic circuit, primary and secondary electrical circuits. The result of the optimization of these electric motors was an increase in the efficiency by 1.6 and 1.4 %, respectively, an increase in the power factor by 0.9 and 0.2 %, and an increase in the rigidity of traction characteristics and starting traction force.

Creating of courses timetable is an extremely difficult, time-consuming task and usually takes a long time. In many educational institutions, the courses schedule is developed manually. Schedule theory includes problems that are actually less complex than problems in practice, but theoretical analysis provides a fundamental understanding of the complexity of the schedule. The logical result is that the schedule is very difficult to build in practice due to many constraints [1]. Scheduling courses is a planning problem. In 1996, the problem of scheduling was described as the allocation of some resources with restrictions on a limited number of time intervals and at the same time to satisfy the set of stated objectives [2]. This is a general statement and is a common description of the courses timetabling creation problem. Schedule of courses is an important administrative activity in most educational institutions. The timetable problem is the distribution of classes by available audiences and time intervals, taking into account the constraints. We usually distinguish between two types of constraints: hard and soft. Hard constraints are compulsorily fulfilled by the educational institution. Decisions that do not violate hard constraints are called possible solutions. With the development of the general theory of the schedule, the approaches to the formalization and solution of the courses timetabling creation problem in educational institutions also changed. Currently, the problem of automation of the courses timetabling creation remains relevant. The urgency of the problem is determined by the growing requirements for the quality of education, student work planning, rational use of the audiences, as well as taking into account additional optimization parameters. The task of finding the optimal schedule of courses in most cases belongs to the class of complex problems. If we take into account the real conditions, the problem is even more complicated, because the desired solutions must meet numerous constraints of production, organizational and psychophysiological nature, which contradict each other. The genetic algorithm helps to efficiently search for optimal solutions in spaces with a very large dimension.

Permanent magnet synchronous motors (PMSM) are widely used in various fields of application of electric drives of industrial enterprises. For each application of the electric drive, it is necessary to accept technical requirements, such as the maximum torque of the electric motor and the fulfillment of the required conditions for the strength characteristics of the rotor and stator.PMSM has a number of advantages over other types of engines. Asynchronous motors have developed resource rational energy efficiency, while synchronous motors are more energy efficient without modifications. PMSM have smaller weight and size parameters, which allows them to be used in a wider field of application, for example, in household appliances, robots and many other drives.TARGET. The aim is to develop a methodology for topological complex optimization of the engine design, based on a genetic algorithm.METHODS. The genetic algorithm is more accurate than traditional analytical methods, the method used in the analysis of AC machines, takes less time than the usual trial and error design procedure based on the finite element method. The main optimization criterion is an increase in torque while maintaining the mass of the most expensive material (permanent magnets). This feature is important for the manufacture of a designed engine in production.RESULTS. A program has been written in Python, which made it possible to carry out a comprehensive topological optimization for the engine under consideration.CONCLUSION. Topological optimization based on the method of modifying the rotor design using a genetic algorithm with the additions necessary for correct operation with synchronous motors is presented.

This article is devoted to solving the quadratic assignment problem using a hybrid algorithm contains both genetic and evolutionary algorithms. The quadratic assignment problem is one of the fundamental problems of combinatorial optimization in the field of mathematical optimization, belonging to the category of object placement problem. The article provides a simple statement of this problem and its more detailed mathematical model. Since the quadratic assignment problem is NP-hard and even small input data can take large computational costs for an accurate algorithm, it is reasonable to use a hybrid heuristic approach to solve this problem. The article describes in detail the construction of a hybrid algorithm, the sequence of its steps, and the flowchart. Further, the article provides a graphical interface with the ability to adjust various parameters of the algorithm, allowing it to be optimally configured. The last part of the article covers a comparative analysis of the effectiveness of the resulting algorithm: comparing the accuracy of the developed hybrid algorithm with a new method of invasive weed optimization algorithm, comparing it with the best-known solutions for modern benchmarks. It was found that the hybrid algorithm shows a strong advantage in accuracy over the invasive weed optimization algorithm. Also, the hybrid algorithm was able to find a solution equal to the best known for the tai12a problem. For the tai15a problem, the algorithm showed a deviation of 0.2% from the best-known solution. For the rest of the considered benchmarks, the algorithm showed a deviation from the best solutions of no more than 4.2%, which proves the high efficiency of the created algorithm in comparison with the world's best solutions. In addition, this algorithm has a high economic value due to the wide application of the solution to the problem in practice, for example, in placement of factories or enterprises in places or in placement of associated electronic components on printed circuit boards or integrated circuits, etc.

This article covers the population-based hybrid algorithm for solving the traveling salesman problem. The algorithm is built on two algorithms: the genetic algorithm and the particle swarm algorithm. Hybridization was performed using high level hybridization. This article presents a detailed problem statement of the traveling salesman problem. The traveling salesman problem belongs to the class of NP-complete combinatorial optimization problems. There are arguments in favor of heuristic algorithms for this problem – the traveling salesman problem is considered to be NP-hard, and existence of an algorithm that could solve it in polynomial time is not proven, even more it is not known whether there is a heuristic algorithm that will guarantee accuracy of its solution (this question is still open). In addition, the traveling salesman problem is classified as a transcomputational problem – if the number of cities is more than 66, it is necessary to process more than 1093 bits of information in order to find the exact solution using the exhaustive search. Therefore, effective approximate methods of solving this problem are very important. Further in the article, population-based hybrid algorithm is formulated in a form of a step-by-step structure with detailing the steps of the algorithm. Then a block diagram of the formulated algorithm is presented. In addition, the article presents the results of the program, the developed user interface with the ability to adjust various parameters of the algorithm, which allows us to change the performance of the algorithm. The last part of the article devoted to: comparative efficiency analysis of the formulated algorithm, comparison of the developed population-based hybrid algorithm with the nearest neighbor algorithm and the ant colony algorithm.

Environmental threats of coal usage in the electricity production combined with the consumption of renewable and non-renewable resources had led to worldwide energy challenges. The cost of coal mining and economical and environmentally sustainable usage of mined coal could be optimized by efficient management of coal supply chain. This paper provides a mathematical model for improving coal supply chain sustainability including the cost of exergy destruction (entropy). In the proposed method, exergy analysis is used to formulate the model considering not only economic costs but also destructed exergy cost, while genetic algorithm is applied to efficiently solve the proposed model. In order to validate the proposed methodology, some numerical examples of coal supply chains are presented and discussed to show the usability of the proposed exergetic coal supply chain model and claim its benefits over the existing models. According to the results, the proposed method provides 17.6% saving in the consumed exergy by accepting 2.7% more economic costs. The presented model can be used to improve the sustainability of coal supply chain for either designing new projects or upgrading existing processes.

The article is devoted to the development and improvement of the systems of formation of rational routes of mobile robots that use a genetic algorithm. For the functioning of the mobile robot it is necessary to solve the problem of route formation. This task is global, contains many solutions and does not require absolute precision. To solve this problem, a genetic algorithm is suitable, it is a heuristic algorithm of global search. This algorithm operates with different genetic operators, such as crossover, mutation, selection, generation of populations and generations. These operators can be adapted to the need for route search. Thus, the genotype as a value that can operate on the algorithm can be represented as a route consisting of distant from each other waypoints. Then, with the help of genetic operators, routes are created and changed until a route is found, it should avoid various navigational hazards and satisfies the specified parameters. However, the search engine itself depends on the coefficients that determine the mode of operation of genetic operators. The effectiveness of this method of solving the navigation problem directly depends on the selected factors that make solving the problem fast and reliable or completely ineffective the algorithm. Thus, before the direct application of the algorithm, it is necessary to identify the basic patterns between the coefficients used, as well as to determine their optimal values, which will be most effective for the algorithm. Ref. 5, pic. 8.

With the development of economy, the distribution problem of logistics becomes more and more complex. Based on the traffic network data, this study analyzed the vehicle routing problem (VRP), designed a dynamic vehicle routing problem with time window (DVRPTW) model, and solved it with genetic algorithm (GA). In order to improve the performance of the algorithm, the genetic operation was improved, and the output solution was further optimized by hill climbing algorithm. The analysis of example showed that the improved GA algorithm had better performance in path optimization planning, the total cost of planning results was 31.44 % less than that of GA algorithm, and the total cost of planning results increased by 11.48 % considering the traffic network data. The experimental results show that the improved GA algorithm has good performance and can significantly reduce the cost of distribution and that research on VRP based on the traffic network data is more in line with the actual situation of logistics distribution, which is conducive to the further application of the improved GA algorithm in VRP.

Abstract. Objective. This article studies the problem of increasing the efficiency of fuzzy controller synthesis in a control system using a genetic algorithm. The best parameters of the fuzzy controller are selected using the crossing-over and mutation operators in the genetic algorithm. The operation of the mutation operator can lead to the formation of an incorrect set of parameters, which complicates the procedure for synthesizing a fuzzy controller.Methods. Arrays of parameter sets of membership functions, conclusions, and rule weights that are included in the fuzzy controller are compiled using mathematical simulation. The mechanism of operation of single-point and two-point variation operators in the genetic algorithm is described by the simulation modeling.Results. Mathematical models of single-point and two-point variation operators for the genetic algorithm are proposed. The mechanism for changing the values of elements in the array of a set of parameters of a fuzzy controller with one input and output variable is presented.Conclusion. Replacing the mutation operator with the variation operator eliminates the formation of incorrect sets of parameters of the fuzzy controller in the control system.

The partitioning a set of professional programmers into a set of teams when a programming project specifies requirements to the competency in various programming technologies and tools is a hard combinatorial problem. The paper proposes a genetic algorithm, which is capable of finding competitive and high-quality partitioning solutions in acceptable runtime. The algorithm introduces chromosomes in such a way as to assign each programmer to a team, define the team staff and easily reconstruct the teams during optimization process. A fitness function characterizes each chromosome with respect to the quality of the programmers partitioning. It accounts for the average qualification of teams and the qualification of team best representatives on each of the technologies. The function recognizes the teams that meet all constraints on the project and are workable from this point of view. It is also capable of recognizing the teams that do not meet the constraints and are unworkable. The algorithm defines the genetic operations of selection, crossing and mutation in such a way as to move programmers from unworkable to workable teams, to increase the number of workable teams, to ex-change programmers among workable teams, to increase the competency of every workable team, and thus to maximize the teams overall qualification. Experimental results obtained on a set of programmers graduated from Belarus universities show the capability of the genetic algorithm to find good partitioning solutions, maximize the teams’ competency and minimize the number of unemployed programmers.

Efficiency and quality of operation of local automatic control systems as part of an autonomous object is mainly determined by the regulator in their composition and the used control law, for the synthesis of which is necessary to use modern computer-aided design systems. The article presents the results of the application of genetic algorithm as a method of parametric synthesis of the PID-controller implemented in the SimInTech visual dynamic modeling environment, which currently is used by enterprises in the rocket and space sectors of Russian Federation. Object of research is the dynamic negative feedback system on the example of the automatic angular position of artificial satellite control system. The functional scheme and the simplified mathematical model of the system in the form of the transfer functions of its links are presented. The computer model of the system as well as a process of synthesis of the controller are implemented as a package of projects, based on standard blocks and submodels SimInTech. Projects interact using a common signal base, which provides information exchange between projects, making the system model flexible and versatile. An interactive computing environment for programming language Python, Jupyter Notebook, is used as a third-party software. The organization of interaction between SimInTech and Jupyter Notebook is described, scripts of programs for its implementation are presented.

Purpose. In recent years, the problem of allocation of distributed generation and capacitors banks has received special attention from many utilities and researchers. The present paper deals with single and simultaneous placement of dispersed generation and capacitors banks in radial distribution network with different load levels: light, medium and peak using genetic-salp swarm algorithm. The developed genetic-salp swarm algorithm (GA-SSA) hybrid optimization takes the system input variables of radial distribution network to find the optimal solutions to maximize the benefits of their installation with minimum cost to minimize the active and reactive power losses and improve the voltage profile. The validation of the proposed hybrid genetic-salp swarm algorithm was carried out on IEEE 34-bus test systems and real Algerian distributed network of Djanet (far south of Algeria) with 112-bus. The numerical results endorse the ability of the proposed algorithm to achieve a better results with higher accuracy compared to the result obtained by salp swarm algorithm, genetic algorithm, particle swarm optimization and the hybrid particle swarm optimization algorithms.

The concept of adaptive learning emerged a few decades ago, but most theoretical findings have never been put into practice, and software solutions had no significant reach for a long time due to insufficient e-learning technology development and coverage. The recent advancements of information technology allow the elaboration of complex big data analytics and artificial intelligence solutions, in adaptive learning in particular. This article investigates exploitation of adaptive learning technology and techniques.The solutions proposed allow mapping optimal individualized learning paths for students in online courses, using the ratio of the level of knowledge at course completion to time spent on the course as an optimality criterion. A genetic algorithm is used to solve this optimization problem. A model based on the speed of forgetting was applied to extrapolate the level of retained knowledge. Practical implementation of the technology proposed involves a set of tools to expand the adaptive learning opportunities of distance learning systems and a module to operate the genetic algorithm. We developed a few options of software architecture using different technologies and programming languages and either one or two servers. The solution was tested during the design of adaptive learning courses for National University of Science and Technology MISIS (NUST MISIS) and Tomsk State University of Control Systems and Radioelectronics (TUSUR).

The use of sanctions as means of coercion and motivation is not always effective. Ruling elites have an ability to shift the burden on less protected population of the country despite the risk of social unrest. The paper aims to perform an empirical analysis of the impact of economic sanctions on the population of the target countries in general and its individual groups in particular. We test three hypotheses: about the negative impact of economic and financial sanctions on the welfare of the poorest people, about the nonlinear relationship between economic growth and income inequality, and about the impact of country characteristics and the duration of sanctions on income distribution. Having applied econometric modelling to panel data, we found that economic and financial sanctions are detrimental to the low-income population and inappropriate for policies aimed at reducing income inequality. Indicators of economic growth can be linked with both an increase and a decrease in economic inequality due to the nonlinear form of their dependence. Regional characteristics of the countries of Africa, North America and South America determine their propensity to a higher level of inequality, as well as the long duration of sanctions. Finally, sanctions are not harming the richest people, as they are able to shift the burden of sanctions on the rest of the population. The research is relevant in practice, as its results can be taken into consideration when developing a sanctions policy to minimize harmful consequences for the civilian population.

The purpose of the article is to present the results of a study on the development of a genetic algorithm to solve the problems of career guidance for graduates of secondary educational institutions and to verify the possibility of its implementation in a computer system. The issue of career guidance for graduates is still relevant, problematic and not fully resolved. According to the authors, the introduction of artificial intelligence technologies in career guidance systems is a promising area that should be paid attention to. Genetic algorithms are widely used to solve search and optimization problems in various subject areas. The authors propose to automate the process of identifying the tendency of secondary school graduates to a particular type of activity by building a vocational guidance system based on a genetic algorithm.Materials and methods. To identify an individual’s predisposition to a specific type of activity, it is necessary to have a list of requirements and contraindications to the profession. Among the ways of describing the norms and requirements for the applicant-specialist are professiograms, lists of necessary competencies and others. To determine the characteristics of the individual that affect the choice of profession, it is possible to use special tests, activating questionnaires, grades in school subjects. The authors carry out the comparison of personality characteristics and requirements through a genetic algorithm. Genetic algorithms belong to the group of evolutionary methods and are based on the evolutionary theory. Among their advantages are conceptual simplicity and wide applicability, resistance to dynamic environmental changes and the ability to self-organize.Results. The genetic algorithm has been developed, in which as a source of information for creating a new population individual certificate evaluations are accepted. Based on these estimates, an initial population of professions is formed. As a result of crossing a pair of individuals from the parent population, a descendant is obtained whose chromosome consists of the genes of both parents. The selection of surviving specimens is based on the percentage of success in the development of each of the professions in the list and the fitness function. The developed algorithm was implemented in a software system. As experiments showed, the genetic algorithm successfully copes with the task of finding the optimal list of professions according to a given criterion.Conclusion. The results of the study show that the use of genetic algorithms provides convenient mechanisms for introducing artificial intelligence methods into the field of career guidance, which improves the quality of recommendations for choosing a profession.

The paper presents an algorithm for the worst case response time (WCRT) estimation for multiprocessor systems with fixed-priority preemptive schedulers and the interval uncertainty of tasks execution times. Each task has a unique priority within its processor, a period, an execution time interval [BCET, WCET] and can have data dependency on other tasks. If a decrease in the execution time of the task A can lead to an increase in the response time of the another task B, then task A is called an anomalous task for task B. According to the chosen approach, in order to estimate a task’s WCRT, two steps should be performed. The first one is to construct a set of anomalous tasks using the proposed algorithm for the given task. The paper provides the algorithm and the proof of its correctness. The second one is to find the WCRT estimation using a genetic algorithm. The proposed approach has been implemented software as a program in Python3. A set of experiments have been carried out in order to compare the proposed method in terms of precision and speed with two well-known WCRT estimating methods: the method that does not take into account interval uncertainty (assuming that the execution time of a given task is equal to WCET) and the brute force method. The results of the experiments have shown that, in contrast to the brute force method, the proposed method is applicable to the analysis of the real scale computing systems and also allows to achieve greater precision than the method that does not take into account interval uncertainty.

Introduction. Modern radar and communications systems contain phased array antennas. One of the synthesis problems of such systems is the formulation of requirements for components, modules and units which are comprised in it. To solve this problem, one needs to build a coverage area and to analyze an impact of characteristics of its parts. The quality of analysis and synthesis of such complex systems can be enhanced by use of interactive data visualization, which requires a fairly quick calculation of characteristics.Aim. Development of an interactive application for increasing the synthesis capabilities of communication systems containing antenna arrays and for improving the characteristics of systems of interest.Materials and methods. To accelerate the calculation of radiation patterns, the antenna array pattern in a form suitable for the fast Fourier transform algorithm was used. To find the required amplitude-phase distributions, Kotelnikov series expansion and genetic algorithm were used.Results. In the developed application, amplitude-phase distribution, directivity pattern of a linear equidistant array and coverage area were displayed. An interactive change of the amplitude-phase distribution at radiation elements and synthesized radiation patterns in given directions were possible. With introduction of changes to the radiation pattern, the amplitude-phase distribution and the array radiation pattern itself changed in directions other than the specified one. The coverage area was rebuilt when any of the characteristics changes. If necessary, the coverage area display could be turned off. The paper provides an example of using the application in the synthesis of a communication system with an aircraft.Conclusion. The use of the developed application allows one to extend the capabilities and significantly reduce the analysis and synthesis time of the communication secondary radar systems with antenna arrays too. Besides, the application is used for training specialists for industry enterprises.

The paper aims to identify the main innovation activity factors in the Russian regions using econometric analysis. Assessment of the current state of the innovation environment in the Russian Federation reveals that there is a number of problems impeding innovation growth, which affects the country’s position in international rankings. The methodological basis of the research includes the theoretical principles of innovation economics, innovation management and regional development. There is a plethora of approaches to modeling the factors of innovative development of countries and regions, as well as to measuring innovation. In the article, we analyze patent activity in Russia’s regions and stimulating factors. The information base includes Rosstat panel data for 1999–2015 in 77 subjects of the Russian Federation. To optimize the set of variables of the econometric model, the authors apply a genetic algorithm. We find that factors reflecting human capital, financial performance of enterprises, market competition, ownership and general macroeconomic indicators of regions affect the indicators of patent activity. The research results can be used to formulate recommendations for improving regional innovation policy. In particular, it is reasonable to encourage the management and research staff of organizations to design and introduce innovations, develop venture business, promote active interaction of business with universities and research institutes, as well as strengthen international cooperation.

Introduction. With the snowballing requirement of renewable resources of energy, solar energy has been an area of key concern to the increasing demand for electricity. Solar photovoltaic has gotten a considerable amount of consideration from researchers in recent years. Purpose. For generating nearly realistic curves for the solar cell model it is needed to estimate unknown parameters with utmost precision. The five unknown parameters include diode-ideality factor, shunt-resistance, photon-current, diode dark saturation current, and series-resistance. Novelty. The proposed research method hybridizes flower pollination algorithm with least square method to better estimate the unknown parameters, and produce more realistic curves. Methodology. The proposed method shows many promising results that are more realistic in nature, as compared to other methods. Shunt-resistance and series-resistance are considered and diode constant is not neglected in this approach that previously has been in practice. The values of series-resistance and diode-ideality factor are found using flower pollination algorithm while shunt-resistance, diode dark saturation current and photon-current are found through least square method. Results. The combination of these techniques has achieved better results compared to other techniques. The simulation studies are carried on MATLAB/Simulink.

The genetic algorithm of clustering of analysis objects in different data domains has been offered within the hybrid concept of intelligent information technologies development aimed to support decision-making. The algorithm makes it possible to account for different preferences of the analyst in clustering reflected in a calculation formula of fitness function. The place of this algorithm among those used for cluster analysis has been shown. The algorithm is simple in its program implementation, which increases its usage reliability. The used technology of evolutionary modeling is rather expanded in the mentioned algorithm. Firstly, the decimal chromosomes coding is used instead of the traditional binary coding. This has resulted from the fact that the chromosome genes condition is multiple and not binary. Moreover, this is due to the absence of the genetic operator of inversion in this algorithm. Secondly, a new genetic operator used for filtering has been implemented. This operator eliminates chromosomes that do not meet the required clusters quantity condition in a task. Such chromosomes can appear in the stochastic process of their evolution. The presented algorithm has been studied in a series of simulation experiments. As a result, it has been found that stabilization of splitting into clusters is reached when the number of completed generations of evolution is 200 and more, and the population size is rather small: from 150 chromosomes (in this case no considerable amount of random-access store is required). The calculations carried out on real data showed for this algorithm the high quality of clustering and the acceptable computing speed of the same order with the computing speed of SOM and “k-means” algorithms.

All companies are challenged to match supply and demand, and the way the company tackles this challenge has a tremendous impact on its profitability. Due to the fact that markets are rap-idly evolving and becoming more complex, flexible, and information-intensive, notorious binging-and-purging approach is inappropriate. Scuh an approach, in which product is, firstly, overpurchased or over-produced in order to prepare for expected demand spikes and then discarded by sharp decline in price. Thus, in order to tailor inventory control to urgent industrial needs, the discrete-event simulation model is proposed. The model is stochastic and operates with multiple products under constrained total inven-tory capacity. Besides that, the model under consideration is distinguished by uncertain replenishment lags and lost-sales. The paper contains both mathematical description and algorithmic implementation. Besides that, an optimization framework based on genetic algorithm is proposed for deriving an optimal control policy. The proposed approach contributes to the field of industrial engineering by providing a simple and flexible way to compute nearly-optimal inventory control parameters.

The object of the research is the process of design calculation of linear dimensional chains. The purpose of this article is development of a method to choose the most rational combination of admissions and deviations on the basis of modeling of accidental combinations of these parameters by means of a genetic algorithm and selection. Imitating modeling of calculations with the choice of the best option by the criterion used in the article provides the solution of a design problem of calculation of dimensional chains with high probability at rather broad range of a combination of the sizes and technical requirements to them. This criterion evaluates an error of a deviation of a design value of the closing link from a preset value. It gives the chance to the designer, even at the worst combination of parameters of the sizes, to solve a problem with the maximum error and to evaluate the directions of change of a design for the purpose of its reduction.

Introduction. Practical tasks (location of service points, creation of microcircuits, scheduling, etc.) often require an exact or approximate to exact solution at a large dimension. In this case, achieving an acceptable result requires solving a set cover problem, fundamental for combinatorics and the set theory. An exact solution can be obtained using exhaustive methods; but in this case, when the dimension of the problem is increased, the time taken by an exact algorithm rises exponentially. For this reason, the precision of approximate methods should be increased: they give a solution that is only approximate to the exact one, but they take much less time to search for an answer at a large dimension.Materials and Methods. One of the ways to solve the covering problem is described, it is a genetic algorithm. The authors use a modification of the Goldberg model and try to increase its efficiency through various types of mutation and crossover operators. We are talking about gene mutations, two-point mutations, addition and deletion mutations, insertion and deletion mutations, saltation, mutations based on inversion. The following types of crossover operator are noted: single-point, two-point, three-point and their versions with restrictions, uniform, triad. The effect of the stopping condition and the probability values of genetic operators on the accuracy of the solutions is investigated. It is shown how an increase in the number of individuals in a generation affects the efficiency of a solution. Research Results. The experiment results allow us to draw three conclusions. 1) It is recommended to use a combination of gene mutation and single-point crossing. 2) With an increase in the number of individuals, the accuracy of the result and the time to obtain it increases. The average deviation from the exact result at a task size of 25 × 25 was 0%, at 50 × 50 – 0%, at 75 × 75 – 0.013%, at 100 × 100 – 0%, at 110 × 110 – 0% (the number of individuals was 500).3) It is advisable to use the probabilities of the mutation and crossover operator 100% and 100%, respectively. Discussion and Conclusions. Recommendations are given to improve the efficiency of covering problem solution. To this end, a preferred combination of the genetic algorithm parameters, of types of crossover and mutation operators is indicated.

The article describes the process of collaborative management at airports A-CDM in dynamically changing conditions of the productive process, defined as the occurrence of emergency situations capable of altering the planned actions. In real operation, in this case, a large number of possible solutions for each emergency situation appears, the lower the level of recording for these options, the more their number. This paper focuses on external factors that significantly affect the activities of airlines and airports and to the relevant management retaliation formalized in the form of five points. The relevance of the choice is dictated by the presence of conflicting interests of stakeholders. Objective explanation in favor of a decision based on the minimization of the total losses from the outbreak of emergencies would significantly strengthen the position of each participant in the process. The authors have introduced a number of mathematical notations and assumptions, a list of which can be supplemented. Dynamic priorities for each participant in the process are formulated. The tool for optimization of joint decision-making is the genetic algorithm, which allows for a smaller number of iterations in the real time to get suboptimal decision that meets the requirements of the participants in the process. As an example, the article describes a situation that may occur in a real-world production. Based on the multiplicative form a dynamic priority for delayed flights is assigned, taking into account the conflicting interests of the participants in the process, private ranking criteria for flights during each step of the rescheduling are formed, a genetic algorithm is applied. As a result, a specific decision of the emergency situation, arising spontaneously from the impact of external factors is obtained. This mathematical apparatus has prospects of introduction into the productive process as any emergency can be built into the solving algorithm and taken into account.

The article clarifies the definition of «activity» in the context of the proposed and/or developed further on paradigms of «resources - activity - result» and «effectiveness - scale - performance» as a genetically modified form, taking into account the structure (composition) of this activity, involving herein the concept of «morphology of system» (with consideration of enterprise as a system at the micro-level). It is substantiated that in the researches concerning the activities of industrial enterprises as production systems, in addition to common scientific and well-known specific methods, approaches and instrumentarium of scientific developments, it is possible to take advantage of the possibility of supplementing the prevailing in modern economic theory method of structural analysis with a genetic approach. The basic signs have been defined and some classifications of the activities of industrial enterprises have been allocated. It is emphasized that the unity of the form and content of activity implies their relative self-sufficiency and active role of the form of activity in relation to its content. It is pointed out that in the process of activity the cause-effect relations should be taken into account. Making use of the modified Euler – Venn diagram, the logic-methodological link between the trueness of the paradigms of «resources – activity – result» and «effectiveness – scale – performance» of an industrial enterprise as a production system are illustrated, taking into account the essence of the category of efficiency, which combines the qualitative (effectiveness) and quantitative (scale) components. The first of the above paradigms is visualized in the context of «system input – output» (using the «black box») for exploration of further directions of the enterprise’s activities, taking into account existence of the internal and external environment. It is emphasized that the optimal managerial decision on performance can be sought in simple both scientific and specific methods. It is determined that the use of the theory of genetic algorithms as methods that allow finding the optimal solution to problems of any complexity, due to the fact that they operate not by the ways of obtaining results, but the results of solving problems, – serves as an effective means of finding the best solution for enterprises’ performance due to the principle of evolution embedded in such algorithms. The main stages and a variant of the genetic algorithm are provided.

Optimal management of fuel supply system boils down to choosing an energy development strategy which provides consumers with the most efficient and reliable fuel and energy supply. As a part of the program on switching the heat supply distributed management system of the Udmurt Republic to renewable energy sources, an "Information-analytical system of regional alternative fuel supply management" was developed. The paper presents the mathematical model of optimal management of fuel supply logistic system consisting of three interconnected levels: raw material accumulation points, fuel preparation points and fuel consumption points, which are heat sources. In order to increase effective the performance of regional fuel supply system a modification of information-analytical system and extension of its set of functions using the methods of quick responding when emergency occurs are required. Emergencies which occur on any one of these levels demand the management of the whole system to reconfigure. The paper demonstrates models and algorithms of optimal management in case of emergency involving break down of such production links of logistic system as raw material accumulation points and fuel preparation points. In mathematical models, the target criterion is minimization of costs associated with the functioning of logistic system in case of emergency. The implementation of the developed algorithms is based on the usage of genetic optimization algorithms, which made it possible to obtain a more accurate solution in less time. The developed models and algorithms are integrated into the information-analytical system that enables to provide effective management of alternative fuel supply of the Udmurt Republic in case of emergency.

Practical implementation methods for parallel computations in the genetic algorithm for discrete optimization, using the example of calculating dimensional chains are considered. An approach for determining the boundary dimensions of population on the basis of probability calculating for independent random events is proposed.

The work is devoted to the identification of images in pictures, which is performed as a result of the classification and localization procedures. Analysis of models, methods and algorithms has shown that for solving the set task it is preferable to use machine learning, an artificial neural network and a genetic algorithm. The architecture of a convolutional artificial neural network is proposed. It can solve both the problem of classification and the problem of localizing images. First the network is trained, then a class is determined for the image fed to its input. Objects are localized in the image at the final stage of operations of the convolutional neural network. For this, the output values of the penultimate layer of the model are analyzed, after which the layers are traversed in the reverse order. Its goal is to find the regions with the highest response on the source image. The combined model showed acceptable results both in classification and in localization of objects. All parameters for the network are determined automatically using a genetic algorithm. Further improvement of the proposed model results will be performed by implementing distributed computing on it.