Multi-criteria Optimization Problem Research Articles

Multi-Criterion Client Selection for Efficient Federated Learning

Federated Learning (FL) has received tremendous attention as a decentralized machine learning (ML) framework that allows distributed data owners to collaboratively train a global model without sharing raw data. Since FL trains the model directly on edge devices, the heterogeneity of participating clients in terms of data distribution, hardware capabilities and network connectivity can significantly impact the overall performance of FL systems. Optimizing for model accuracy could extend the training time due to the diverse and resource-constrained nature of edge devices while minimizing training time could compromise the model's accuracy. Effective client selection thus becomes crucial to ensure that the training process is not only efficient but also capitalizes on the diverse data and computational capabilities of different devices. To this end, we propose FedPROM, a novel framework that tackles client selection in FL as a multi-criteria optimization problem. By leveraging the PROMETHEE method, FedPROM ranks clients based on their suitability for a given FL task, considering multiple criteria such as system resources, network conditions, and data quality. This approach allows FedPROM to dynamically select the most appropriate set of clients for each learning round, optimizing both model accuracy and training efficiency. Our evaluations on diverse datasets demonstrate that FedPROM outperforms several state-of-the-art FL client selection protocols in terms of convergence speed, and accuracy, highlighting the framework's effectiveness and the importance of multi-criteria client selection in FL.

Methodology for Selecting Optimal Routes for the Transportation of Dangerous Goods in Conditions of Risk Uncertainty

Abstract * A risk situation is a type of uncertainty situation where events are likely to occur. In other words, risk is an estimated probability, and uncertainty is something that cannot be quantified. The greater the uncertainty when making a decision, the greater the degree of risk. The investigation is devoted to the development of a unified methodology for selecting optimal (from the proposed alternatives) routes for transporting dangerous goods (any of the 9 standard classes) by road. A model for determining two groups of risk components for transporting dangerous goods on separate routes is proposed, namely: parameters of risks of probability of occurrence of emergency situations and parameters that affect the risks of complexity of eliminating their possible consequences. This opened up opportunities for correct selection of criteria when forming a multi-criteria optimization problem of transportation. Mathematical algorithms for a comprehensive solution of the multi-criteria optimization problem of routing dangerous goods transportation are developed using the classical criteria of Laplace, Wald, Savage, and Hurwitz. To confirm the legal capacity of the proposed approach and mathematical apparatus, the optimal route for transportation of cylinders with technical gases through the transport network of Lutsk was calculated. Possible alternative transportation routes have been identified and safety criteria have been formalized for two groups of risk components

Optimal Temperature Calculation for Multicriteria Optimization of the Hydrogenation of Polycyclic Aromatic Hydrocarbons by NSGA-II Method

Introduction. Multicriteria optimization, taking into account contradicting criteria, is used to improve production efficiency, reduce costs, improve product quality and environmental safety of processes. The literature describes the application of multicriteria optimization for production purposes, including the selection of reaction conditions and improvement of technological processes. In the presented paper, the object of research is the process of hydrogenation of polycyclic aromatic hydrocarbons (PAH) in the production of high-density fuels. To determine the optimal conditions of the process, the problem of multicriteria optimization based on the kinetic model is solved. The criteria include maximizing the yield of targeted naphthenes and conversion of feedstock. The research objective is to create a program implementing the multicriteria optimization non-dominated sorting genetic algorithm-II (NSGA-II). Due to this, it is possible to calculate the optimal temperature for the PAH hydrogenation process on the basis of the kinetic model.Materials and Methods. The NSGA-II genetic algorithm was used to solve the multicriteria optimization problem. Modified parental and survival selection within the Pareto front was also used. If it was necessary to divide the front, solutions based on the Manhattan distance between them were selected. The program was implemented in Python.Results. In the system of ordinary nonlinear differential equations of chemical kinetics, the concentration was designated yi, the conditional contact time of the reaction mixture with the catalyst — τ. The system was solved for the hydrogenation reaction of polycyclic aromatic hydrocarbons. The calculations showed that at τ = 0 y1(0) = 0.025; y2(0) = 0.9; y6(0) = 0.067; y9(0) = 0.008; yi(0) = 0, i = 3–5, 7, 8, 10–20; Q(0) = 1. The process temperature was considered as a control parameter according to two optimality criteria: maximizing the yield of target naphthenes (f1) at the end of the reaction, and maximizing the conversion of feedstock (f2). Values f1 were in the range of 0.43–0.79; conversion — 0.01–0.03; temperature — 200–300 K. The growth of temperature was accompanied by an increase in the yield of target naphthenes and a decrease in the conversion of feedstock. Each solution obtained was not an unimprovable one. When modeling the process of hydrogenation of PAH, an algorithm was launched with a population size of 100 and a number of generations of 100. A program implementing the NSGA-II algorithm was developed. The optimal set of values of the PAH hydrogenation reaction temperature was calculated, which made it possible to obtain unimprovable values of the optimality criteria — maximizing the yield of target naphthenes and conversion of feedstock.Discussion and Conclusion. The NSGA-II algorithm is effective for solving the problem of non-dominance, and deriving the optimal solution for all criteria. Future research should be devoted to the selection of optimal algorithm parameters to increase the speed of the solution. Based on the obtained theoretical optimal conditions of the PAH hydrogenation reaction, it is possible to implement the process in industry

Search for Optimal Parameters in the Control Structure of a Surgical System for Soft Tissue Operations Based on In Vitro Experiments on Cardiovascular Tissue

The surgical robots currently used in cardiac surgery are equipped with a remote center of motion (RCM) mechanism that enables the required spherical workspace. The dynamics model of the surgical robot’s RCM mechanism presented in this work includes a direct current (DC) motor, an optimal proportional–integral–derivative (PID) controller, and a LuGre friction model that takes into account the Stribeck effect and surface deformation. A finite element method (FEM) analysis of transients was carried out using the energy hypothesis of von Mises with an optimal input signal from the mechatronic system with a PID controller obtained using the Runge–Kutta differentiation method in the Dormand–Prince ordinary differential equations variant (ODE45). Five criteria were adopted for the objective function: the safety factor related to the stress function in the time-varying strength problem, the first natural frequency related to stiffness and the resonance phenomenon, the buckling coefficient in the statics problem related to stability, the static factor of safety, and the displacement of the operating tip. The force inputs to the dynamics model were derived from in vitro force measurements on cardiovascular tissue using a force sensor. The normality of the statistical distribution of the experimental data was confirmed using the Kolmogorov–Smirnov statistical test. The problem of multi-criteria optimization was solved using the non-sorter genetic algorithm (NSGA-II), the finite element method, and the von Mises distortion energy hypothesis. Velocity input signals for the transient dynamics model were obtained from a second in vitro experiment on cardiovascular tissue using the minimally robotic invasive surgery (MIRS) technique. An experienced cardiac surgeon conducted the experiment in a modern method using the Robin Heart Vision surgical robot, and a system of four complementary metal–oxide–semiconductor (CMOS) optical sensors and ariel performance analysis system (APAS-XP 2002) software were used to obtain the endoscopic tool trajectory signal. The trajectory signal was accurate to ±2 [mm] in relation to the adopted standard, and it was smoothed using the Savitzky–Golay (SG) polynomial smoothing, whose parameters were optimally selected using the Durbin–Watson (DW) statistical test.

Combining discrete and continuous information for multi-criteria optimization problems

AbstractIn multi-criteria optimization problems that originate from real-world decision making tasks, we often find the following structure: There is an underlying continuous, possibly even convex model for the multiple outcome measures depending on the design variables, but these outcomes are additionally assigned to discrete categories according to their desirability for the decision maker. Multi-criteria deliberations may then take place at the level of these discrete labels, while the calculation of a specific design remains a continuous problem. In this work, we analyze this type of problem and provide theoretical results about its solution set. We prove that the discrete decision problem can be tackled by solving scalarizations of the underlying continuous model. Based on our analysis we propose multiple algorithmic approaches that are specifically suited to handle these problems. We compare the algorithms based on a set of test problems. Furthermore, we apply our methods to a real-world radiotherapy planning example.

Development of optimization mathematical models for making compromise decisions on the efficiency of an agricultural moving power units in fleet

In order to build a calculation routine for making compromise decisions on the efficiency of a fleet of agricultural moving power units, this work analyzed mathematical models characterizing the efficiency of the agricultural moving power units fleet in the context of digitalization of agriculture. In order to select initial data for solving a multicriteria optimization problem for making compromise decisions, the main quality criteria for the efficiency of an agricultural moving power units fleet and their functional limitations were selected. A formulation of the problem of multi-criteria optimization of the efficiency of the agricultural moving power units in fleet and a list of variable parameters, in the amount of 14, as well as the range of their variation have been generated for further adjustment of the problem statement for making compromise decisions when assessing the efficiency of the agricultural moving power units in fleet. In the future, when forming a mathematical and software complex, according to multi-criteria assessment, they will be significant for the decision maker (DM)

A column generation approach for the lexicographic optimization of intra-hospital transports

AbstractOver the last few years, the efficient design of processes in hospitals and medical facilities has received more and more attention, particularly when the improvement of the processes is aimed at relieving the workload of medical staff. To this end, we have developed a method to determine optimal allocations of intra-hospital transports to hospital transport employees. When optimizing transport plans in hospitals, there are various optimization goals to strive for. Therefore, we used a lexicographic approach to solve this multi-criteria optimization problem. To calculate optimal transport plans in a sufficiently short computation time, we have decomposed the problem at hand with the Dantzig–Wolfe reformulation and solved the resulting pricing subproblem with an enumerative column generation approach. To improve the efficiency of the column generation process, we have investigated and implemented different pruning methods, dominance rules and a column reuse mechanism for the online setting of the application at hand. In an extensive computational study, we first evaluated the efficiency of the different pruning methods before we compared our solution approach with the standard branch-and-bound column search approach, classical column generation methods and the solution of an integrated MIP model solved by a commercial solver. Finally, we present performance indicators of the transport optimization tool, which was developed from our method and is now productively used in a German hospital.

Model predictive control for demand flexibility of a residential building with multiple distributed energy resources

One of the major challenges with increasing penetration of renewable energy sources (e.g., solar and wind) is to maintain grid stability. Grid-interactive efficient buildings are regarded as a promising approach to advance the role buildings can play in energy system operations and planning. This paper evaluates the demand flexibility in a residential building located in Karlsruhe, Germany, incorporating multiple distributed energy resources, including a photovoltaic and battery system, an electric vehicle, an electric water heater and a heat pump. A multi-criteria optimization problem is formulated with model predictive control (MPC) for five cases of demand flexibility. The simulation results of five winter days show that the peak power during the peak periods can be reduced by 92%, 69%, 100%, and 100% for real-time pricing, demand limiting, load shedding, and load shifting, respectively. For the power tracking scenario, the MPC tracked the reference power profile successfully for 70% of the simulation time. Achieving demand flexibility does not necessarily cause an increase in energy costs.

Machine learning and similar image-based techniques based on Nash game theory

The use of computer vision techniques to address the task of image retrieval is known as a Content-Based Image Retrieval (CBIR) system. It is a system designed to locate and retrieve the appropriate digital image from a large database by utilizing a query image. Over the last few years, machine learning algorithms have achieved impressive results in image retrieval tasks due to their ability to learn from large amounts of diverse data and improve their accuracy in image recognition and retrieval. Our team has developed a CBIR system that is reinforced by two machine learning algorithms and employs multiple clustering and low-level image feature extraction, such as color, shape, and texture, to formulate a Nash game. Consequently, we are faced with a multicriteria optimization problem. To solve this problem, we have formulated a three-player static Nash game, where each player utilizes a different strategy (color descriptor, Zernike descriptor, and SFTA descriptor) based on their objective function. The Nash equilibrium is defined as the membership classes of the query image.

Information System Concept for a Sports and Game Mobile Application with Elements of Artificial Motivation to Lead a More Active Lifestyle

The article presents the idea of a sports and gaming mobile application. The proposed concept has a number of indisputable advantages over the analogue products. The main one is the presence of a mechanism of artificial motivation to lead a more active lifestyle. This approach is especially relevant for modern children and teenagers, most of whom prefer virtual entertainment. The analysis of approaches and methods for encouraging and retaining the user of the mobile application was carried out based on the studied literature. The problem of reducing the physical activity of the population is highlighted. Based on the model of additive convolution for the problem of multi-criteria optimization, the feasibility of implementing the system and its superiority over similar software products presented on the market are substantiated. The expected implementation effects of the system are formulated. Mathematical model for substantiation of educational and physical culture and health effects are proposed. Decomposition of the system into subsystems was carried out using Gain-Sarson DFD-notation. The skeleton architecture of the application has been developed and substantiated. The UML activity diagram of the main process of system functioning has been developed. One of the possible options for implementing the system is proposed: the model of the project life cycle is chosen and substantiated, the stages of its implementation are determined, and the list of minimum necessary human resources is assigned. Implementation of the proposed application will have positive sports, health and educational effects. In addition to improving physical fitness, users will increase their awareness of the achievements of world-famous athletes and the sports they represent. The proposed mechanics for a gradual transition from regular walks to runs will minimize the chance of injury. The implementation of the proposed application is the first step for quantitative and qualitative analysis of physical activity of users. On the basis of statistical data, which is going to be collected in the following versions of the system, it is possible to determine to what extent the use of modern technologies and gamification mechanisms can motivate people to a more active lifestyle. The basis for this stage is the model presented in this paper.

STUDY OF PHASE VOLTAGE AND LOAD SYMMETRATION IN ACTIVE-ADAPTIVE DISTRIBUTION ELECTRIC NETWORKS

Networks of 0.4 kV are characterized by a large unbalance of loads in phases. Current unbalance leads to voltage unbalance and additional losses of electrical energy. As a result, the voltage at the consumer may not meet the quality standards of electrical energy. In addition, due to unbalance, the service life of electrical equipment is reduced. Since the effect of stress balancing significantly depends on the place of balancing loads on the line, the paper proposes to determine the places of balancing loads by solving a multicriteria optimization problem. The paper proposes an objective function that minimizes active power losses and contains the total index of active power losses and indices of voltage unbalance coefficients in the negative and zero sequence.
 
 The purpose of the study is to obtain an effective objective function for determining the places of balancing loads and voltages in the network, which ensures a minimum of active power losses and the values of the voltage unbalance factors within the required limits; conduct a study of balancing loads and voltages depending on the places of balancing.
 
 Materials and methods. In the work, methods for calculating electrical networks were used, taking into account voltage losses and active power. To study the places of balancing loads and voltages, the method of multicriteria optimization with restrictions was used. The study of the objective function was carried out on a mathematical model of a low voltage overhead line. All calculations were carried out in MATLAB.
 
 Research results. A review and analysis of modern tools and methods for balancing loads and voltages in low voltage networks has been carried out. As a result of the analysis, it was concluded that there is no algorithm for determining the places of load balancing in low-voltage networks that provide minimal active power losses and the values of the voltage unbalance factors within the required limits. The task of finding places for balancing loads and voltages is a multiobjective optimization problem with constraints. Therefore, an objective function was proposed that minimizes active power losses in the network and contains the total index of active power losses and indices of voltage unbalance coefficients for the reverse and zero sequence. To study the proposed objective function, a model overhead line of a 0.4 kV network with specified phase loads and voltages was used. For the model line, the calculation of active power losses and the values of the voltage unbalance coefficients in the initial mode before balancing was carried out. All calculations were carried out for each phase separately. At the first stage, the calculation of the sensitivity coefficients of active power losses and the sensitivity coefficients for the voltage unbalance coefficients was carried out. To study the balancing of loads, nodes were selected that have the maximum values of the sensitivity coefficients. It follows from the calculation results that the best effect from balancing is observed when balancing loads simultaneously in two nodes: in the node with the highest value of the total sensitivity factor of active power losses, and in the node with the maximum value of the phase sensitivity factor of active power losses. When balancing loads in only one of the nodes, the most optimal of the selected ones will be the node most remote from the TS. We also obtained weight coefficients that provide a minimum of the objective function.
 
 Conclusions. The proposed objective function is effective for determining the places of load and voltage balancing in low voltage networks. In this case, the best effect is observed when balancing loads in nodes that have the highest values of the sensitivity coefficients of total active power losses and by phases. The node most remote from the TP will be more optimal. When balancing loads in places determined using the proposed objective function, it is possible to reduce power losses and ensure the values of the unbalance coefficients in the nodes on the line less than the maximum allowable value.

Distributed Data Proceeding Systems Architectures Resource Efficiency Improvement on the Basis of Apriory Data about the Jobs Late Completion Times

Purpose of research. The purpose of this study is to develop a method for improving the efficiency of distributed architectures of data processing systems operating in the fog and edge layers of the network. In conditions of high dynamics of both the network infrastructure and the load, the task of forming the architecture of data processing systems is solved regularly (migration of virtual machines, horizontal scalingб etc.) At the same time, the issue of the consumption of the residual resource of computing nodes is practically not considered, while the often used devices have relatively low capacity, and their high workload leads to a reduction in the service life. Therefore, the creation of methods for forming an architecture of a computing device system that is effective in terms of saving a computing resource is an urgent task.Methods. The main scientific methods used in this study are domain analysis, operations research methods, optimization methods and computer modeling, confirming the feasibility of the main aspects of the developed method. To improve the efficiency of placing computational tasks on the nodes of a network fragment, this paper formulated a multicriteria optimization problem, where each element of the vector objective function corresponds to an individual value of the probability of failure-free operation of a computing device. To obtain estimated values of the cost function, a priori estimates of the late completion of the solution of computational problems by nodes are used, since the resource allocated for solving depends on the allocated time, and the time for solving the problem, respectively, on the allocated computing resource. The value of the cost function is calculated on the basis of approximate a priori estimates, which leads to a positive effect in terms of the consumption of computing resources of devices.Results. The result of the study is a developed method for improving the efficiency of distributed architectures of data processing systems operating in the fog and edge layers of the network.Conclusion. The method proposed in this work allows to choose such a load distribution in order to reduce the workload of devices and thus reduce the consumption of computing resources of the devices.

Model of Multi-Parameter Optimization of the Characteristics of a Cable Car in a Solid Waste Transportation System

Introduction. Modern scientific and applied literature examines the problems of cable cars functioning quite thoroughly. First of all, it concerns ensuring the reliability and safety of traffic, both during operation and during project development. In addition, the paper considers the relationship of cable cars with the environment and the level of environmental load from this type of transport. A good solution could be the use of mathematical models that can take into account a set of parameters and criteria that characterize the cable car as a system. The same approach would be useful for optimizingtechnical characteristics of the object. However, there is no description of such a solution in the literature. This gap is partially filled by the presented work. The study aims to create a model of multivariable optimization of cable car technical characteristics for the transportation of municipal solid waste (MSW). Material and Methods. To clarify the theoretical basis, the literature describing the problems of cable cars and their solutions in general has been studied. Mathematical calculations were justified by a volume of equations that proved their adequacy in determining the useful transport work, load, adjustment of time and speed of cargo movement and other significant parameters of the system under study. When forming the model, we proceeded from the principles of L. S. Pontryagin (needle variation) and Hamilton — Ostrogradsky (kinematics of a certain road segment). Text data about the features of the system elements and their interaction were summarized in tables. The main calculations results were visualized in the form of graphs. Results. The solution to the problem of optimal control of the cable car on which solid waste was moved was presented. The motion control vector was shown as a vector of optimized technical parameters of the system: speed of movement, rope tension, number and weight of containers. The well-known solution to the optimization problem was reproduced in a general form, which involved determination of a control vector function and its corresponding trajectory with the achievement of a minimum of the target functional. The weak point of the system of differential equations for the realization of the goals of this scientific work was noted. In this regard, it was proposed to consider the investigated section of the cable car as a dynamic system with distributed parameters. The formulation of the multi-criteria optimization problem was described in detail. The advantages of reducing the number of criteria taken into account were listed and the use of the reduction method, which was based on the hierarchical structuring of the system of partial optimality criteria, was justified. Four main elements of the municipal solid waste (MSW) transportation system were considered in interrelation. This was a cable car, a transport and logistics point, a transport and logistics terminal and an environment that generated solid waste. Within the framework of this work, we considered an urbanized environment. The sub-elements of the named elements were listed and 12 directions of their interactions were shown. In detail, within the framework of a three-level hierarchy, four main complex indicators of the complexity of the system under study were described: environment, road, point and terminal. The solution of a multi-criteria optimization problem was shown, calculations were performed for the optimized parameters — the characteristic of the complexity of the road and the characteristic of the terrain. The results of calculations were presented in the form of graphs. Thus, the dependences of the optimized parameters on the weight of the loaded container, the length and speed of the cable car were illustrated. Conclusions. The main result of the study is an idea of the possibility of a mathematical solution of a multivariable and multi-criteria problem of optimizing two characteristics of a cable car (complexity and terrain feature). The proposed approach allows you to change the hierarchy in the complex of indicators. The results of this scientific work can be used, if necessary, to integrate the road project with neural network models, to work with fuzzy linguistic indicators, to solve applied problems.

Мathematical model of the problem of optimizing logistics networks under conditions of interval determination of input data

Problem. In the conditions of rapid changes in demand and supply in transportation markets, there is a need for corresponding changes in logistics technologies and networks, which are carried out through their reengineering. Existing mathematical models for the optimization of logistics networks are designed for conditions with point-wise, clearly defined input data, which does not allow obtaining solutions resistant to changes in the external environment. This determined the relevance of the scientific and applied task of developing mathematical models of multi-criteria optimization problems of logistics networks for the conditions of interval submission of input data. Goal. The goal is to increase the efficiency of the logistics network optimization technology at the stage of re-engineering by developing a mathematical model of the multi-criteria optimization problem for the conditions of interval submission of input data. Methodology. According to the results of the decomposition of the problem of system optimization of logistics networks as the most complex defined task of their structural and topological optimization. When developing the model, the methodology of system design of territorially distributed objects, methods of multi-criteria optimization, theories of utility and decision-making were used. The apparatus of interval mathematics was used to compare solution options with vaguely specified input data. The results. The result are the formulated and completed formalization of the task of optimizing logistics networks as territorially distributed objects. The relationship for the objective function and constraints of the optimization task of topological structures of centralized three-level logistics networks is proposed. Originality. A mathematical model of the task of reengineering topological structures of centralized three-level logistics networks according to cost and efficiency indicators for interval defined input data and values of local criteria using comparison indices based on the Hukuhara difference has been developed. Practical value. The obtained results make it possible to increase the reliability of optimization results in the processes of design, development planning and reengineering of logistics networks, to obtain variants of the construction of their topological structures that are resistant to changes in external conditions.

A linearized approach for solving differentiable vector optimization problems with vanishing constraints

In this paper, two mathematical methods are used for solving a complex multicriteria optimization problem as the considered convex differentiable vector optimization problem with vanishing constraints. First of them is the linearized approach in which, for the original vector optimization problem with vanishing constraints, its associated multiobjective programming problem is constructed at the given feasible solution. Since the aforesaid multiobjective programming problem constructed in the linearized method is linear, one of the existing methods for solving linear vector optimization problems is applied for solving it. Thus, the procedure for solving the considered differentiable vector optimization problems with vanishing constraints is presented in the paper.

Multicriteria Optimization of Software Development Platform Selection

The problem of multicriteria optimization of tech stack selection in a non-linear software development environment is formalized. Approaches to solving the problem based on the formation of a compromise area of local quality criteria, additive convolution of vector criteria and their scalarization are considered. An aggregate quality criterion of the software development platform is proposed. It allows taking into account the nonlinearities of the external environment in the framework of solving the problem of extremal control. The coordinates of the vector criteria are piecewise continuous functions A comparative analysis of various approaches to changing the software development tech stack in the face of significant disturbances in the development tools market has been carried out. The possibilities of boxed solutions, custom development and Open Source software development in ensuring information security of the software development environment are shown. The information stability of a software development project using Less Code tools is established and the advantages of technological solutions are shown. The analysis of the adequacy of the obtained solutions was carried out using the Open Source Less Code of the Jmix platform. The data of a comparative analysis of the budgets of the Less Code platform and custom software from vendors are given, which showed the benefits of using Open Source software development tools for long-term operation of the development platform.

Optimisasi Program Linear Pada Permasalahan Multikriteria Menggunakan Metode ε-constraint

The purpose of this study is to solve multi-criteria problems using the ε-constraint method with the help of an excel solver. The multi-criteria optimization problem is an optimization problem that has more than one objective function. A multi-criteria optimization problem can be said to be a multiple criteria decision making (MCDM) if there is more than one thing that must be considered in the model as a goal or criterion. In general, the weighting method and the ε-constraint method are the most widely used. The weighting method converts a set of options into options by multiplying each option by the inventory weight. On the other hand, the ε-constraint method only saves one of the existing goals and limits the goals with a certain number of values to get an efficient limit.

МЕТОД АВТОМАТИЗОВАНОЇ КЛАСИФІКАЦІЇ НАДЗВИЧАЙНИХ СИТУАЦІЙ ІЗ СУДНОМ В АКВАТОРІЇ МОРСЬКОГО ПОРТУ

The aim of the study is to develop a method that allows to improve the accuracy of classification of emergencies with a ship in the seaport area. To achieve the research objective, an improved method for automated classification of ship emergencies in the seaport area under conditions of deterministic uncertainty is proposed. The method consists of methods for formalising and processing knowledge on determining the classes of ship emergencies. The method of knowledge formalisation is based on the formation of a set of factors influencing the classification of ship emergencies in the seaport water area based on fuzzy binary relations of non-strict preference. The method of knowledge processing is based on the formation of productive rules for classifying emergencies with a ship in the seaport area according to the predicted or current values of the desired factors in a fuzzy formulation. The determination of the membership functions of several fuzzy variables to linguistic variables is based on the processing of expert data represented by a matrix of binary relations of the values of the membership function of the elements of the domain of determining linguistic variables. A comparative assessment of the classes of recognisable emergencies with a vessel in the seaport water area involves solving a multi-criteria optimisation problem using the hierarchy analysis method. As a mathematical model for determining the classes of emergency situations with a vessel in the seaport waters, the article substantiates a logical-linguistic productive hierarchical model. The process of determining the classes of emergency is described with the help of an algebraic model, which is closest to the linguistic description. In case of inexpediency of synthesis of products, it is proposed to use the method of fuzzy identification to reduce the number of product rules. The proposed method allows to improve the accuracy of classification of emergencies with a ship in the seaport area under conditions of deterministic uncertainty. Keywords: classification, maritime port, hierarchy analysis, fuzzy identification, logicallinguistic production hierarchical model, vessel, class of emergency situations, fuzzy variable, linguistic variable

Multi-Criteria Optimization Problems with Vector Heterogeneous Convolutions of Criteria

Multi-Criteria Optimization Problems with Vector Heterogeneous Convolutions of Criteria

The debt component as a factor in assessing the financial security of the economy: The cross-country aspect

Subject. The article addresses trends in basic financial indicators formed under global political and economic challenges of our time, with an emphasis on debt policy to substantiate the significance of their impact on the financial security of the economy of various States. Objectives. The purpose is to develop economic and mathematical justification for assessing the financial security of the State based on mathematical modeling and rating of macroeconomic indicators, from the perspective of debt approach assessment. Methods. We employ the method of weighted sums as the main approach to solve multi-criteria optimization problems and the method of attributing points. A weighting factor is calculated for each criterion, on the basis of which the individual rating of each factor is calculated. The basis for the application of the weighted sum method is a factor analysis, implemented on the basis of statistical and dynamic approaches. Results. The paper assesses the financial security of the economy of various States on the basis of predominance of the debt policy importance. The rating enables to assess the effectiveness of the State's financial policy, depending on priorities of its implementation for a certain representative period. The selected indicators characterize a multidirectional impact on the financial security of the economy, however, the optimization approach allows for objective assessment and assumes the possibility of their expansion and variation to determine financial security based on assessment of the predominant impact of certain groups of stimulator and destimulator indicators. Conclusions. The study serves as a basis to systematize a set of diverse indicators of financial flows redistribution in the economy to characterize financial security, depending on the parameters characterizing the main directions and instruments of financing priority areas of economic development.