Multi-criteria Optimization Problem Research Articles

Optimal control of coupled buildings under seismic excitation

The article explores the concept of managing coupled buildings under seismic excitation. Connecting two closely spaced structures enables the redistribution of energy and reduction of structural responses. To minimize the resulting damage, the use of smart control is proposed. Smart control operates using feedback, allowing the system to adapt in real-time. To solve the problem of finding an optimal control, the paper suggests considering it within the framework of multicriteria optimization problems, with the criteria being the maximum deformation of each building described using the generalized H 2 -norm. The article presents a method for solving multicriteria problems using linear matrix inequalities (LMIs) and Hermeyer convolution. Detailed examples are provided for a system of two coupled buildings. The results of computing the optimal smart control for systems of varying dimensions, as well as the outcomes of modeling using real earthquake data, are presented MATLAB software, utilizing the SDPT3 and YALMIP libraries, is employed for performing the calculations and visualizing the results.

Developing an optimal energy system model for a sustainable urban transportation framework planning in the long term through different climatic zones

The modern lifestyle highlights the demand for an improved urban transportation infrastructure and a shift to renewable, efficient technologies. This evolution is essential for both developed and developing countries. The transportation system in a developing country such as Iran faces significant challenges, including low energy efficiency and high emissions. This situation makes the development of a sustainable transportation plan increasingly critical. Furthermore, there is considerable potential for renewable energy across various climatic zones in the country that should be utilized. This study presents a sustainable development model for the transportation system that incorporates zero-emission vehicles and renewable energy supply technologies in competition with traditional ones. The model is designed for long-term application and includes five case studies from various climatic zones in Iran, each featuring different renewable potentials and system scales. Determining the optimal structure of the system in each case study requires solving a linear, dynamic, and multi-criteria optimization problem. The objective function focuses on minimizing total costs, which include technological, energy, and social. All case studies indicate that developing a sustainable transportation system is optimal. However, larger case studies tend to produce more favorable optimization outcomes. According to the results, the scale of the case study is the most important factor in this research.

ІНКРЕМЕНТНИЙ ПІДХІД ДО ПЛАНУВАННЯ РОБОТИ СТУДЕНТІВ НАД СПІЛЬНИМ ПРОГРАМНИМ ПРОЄКТОМ

As of today, well-known product and outsourcing IT companies use Agile models for the software development life cycle (SDLC), the advantages of which include rapid adaptation to changes, continuous feedback, improved product quality, increased team engagement, focus on customer value, transparency and control, as well as the reduction of internal and external risks. All Agile models are iterative, meaning the development process is divided into separate, similar iterations, which have different names in different models. Familiarization with and practical application of modern Agile models by students at the first (bachelor’s) level of higher education in the field of information technology is an important task for future IT specialists. To achieve this task, the most popular Agile model, Scrum, was chosen, which is also incremental, meaning that each iteration delivers additional functionality that is ready for use. The main roles of participants and their responsibilities, artifacts, and ceremonies of the Scrum process are reviewed. The article proposes applying the Scrum model for iterative and incremental software development that will solve a multi-criteria optimization problem using a game-theoretic approach. The formulation and general algorithm for solving the multi-criteria optimization problem using a game-theoretic approach are presented, as well as an example of formulating the Product Backlog, which contains twelve functional requirements to be implemented by the student Scrum team over twelve iterations (sprints). The recommended process for dividing students into Scrum teams and assigning roles to participants is described. An example of incremental implementation based on the Scrum model of the SDLC for solving the multi-criteria optimization problem using a game-theoretic approach is also provided.

Encoding consumer interests into product snippets with a multi-criteria genetic optimization approach

As an essential product cue in consumer information foraging, textual snippets can convey valuable scents that attract consumers to further access products, paving the way for online sellers to seize a competitive advantage. Premised on shopping goals theory, this study proposes a novel approach to designing high-quality product snippets that are particularly enhanced with consumer interests. First, snippet encoding is formulated as a multi-criteria optimization problem in which information sources are incorporated to distill consumer-appealing keywords considering both driving search and attracting selection, as well as to integrate the perspectives of sellers and consumers. Subsequently, a constrained genetic solution algorithm is developed, which copes well with the evolutionary nature of the problem to optimize snippets in an effective and efficient manner. Extensive experiments are conducted to verify the validity and superiority of the proposed approach.

DEVELOPMENT OF METHODOLOGY AND STUDY OF THE INFLUENCE OF TECHNICAL, ORGANIZATIONAL AND TECHNOLOGICAL FACTORS ON THE DURATION OF THE PROCESS OF LIQUIDATION AND LOCALIZATION OF THE DEVELOPMENT OF DESTRUCTIONS

Analysis of the influence of technical, organizational and technological factors on the duration of the process of liquidation and localization of the development of destruction is an important stage of research into the process of liquidation of the consequences of accidental destruction. In order to compare options for liquidation and localization of the development of destruction of an emergency building, three options for reinforcement systems were analyzed: metal typical, wooden individual and combined. The work uses the method of analysis of hierarchies - a mathematical tool of a systematic approach to complex decision-making problems. The method does not impose the "correct" option, but allows you to interactively find an alternative (rational reinforcement option) that best matches the requirements for solving optimization tasks. To reduce the subjectivity of making a justified optimization decision in the conditions of complex multi-criteria optimization problems, a solution to the local problem of finding the optimal alternative according to the duration criterion, or a group of alternatives, taking into account the ratio of advantages based on the vector criterion, is proposed. To indicate the influence of advantages in quantitative expression, a pairwise comparison scale was used, which consists in a qualitative and quantitative assessment of relative advantage: equal in importance - 1; weak advantage – 2; average degree of preference ‒ 3; preference above the average degree ‒ 4; moderately stronger advantage ‒ 5; strong advantage ‒ 6; much stronger advantage ‒ 7; the most significant advantage is 8; absolute advantage ‒ 9. Initial data for choosing a temporary reinforcement option were obtained by comparing the estimated duration of dismantling and restoration works and optimizing the sequence of their execution for three options using wooden individual, metal typical and combined temporary reinforcement systems. It was established that it is impossible to ensure complete unification of reinforcement elements using only typical elements, therefore it is effective to use combined reinforcement systems using typical metal and individual wooden elements.

Methods of Multi-Criteria Optimization of Technological Processes in a Fuzzy Environment Based on the Simplex Method and the Theory of Fuzzy Sets

Many modern technological objects in practice are characterized by the uncertainty of the initial information necessary for their management. Recently, one of the pressing scientific and practical problems is the development of new optimization methods for controlling the operating modes of such objects in a fuzzy environment. In this regard, the objective of this study is to develop methods of multi-criteria optimization in a fuzzy environment by modifying the simplex method and various optimality principles based on fuzzy mathematics methods. The methodology of the proposed study is based on a hybrid approach, which consists of the integrated use and modification of simplex methods and optimization methods with various optimality principles for working in a fuzzy environment. The main results are as follows: a simplex method of multi-criteria optimization of immeasurable criteria (here, we are talking about the impossibility of physical measurements of criteria, the values of which are estimated by decision maker); a theorem on the convergence of the solution sequence obtained using the proposed method to the minimum value of the criteria; a heuristic method based on a modification for fuzziness and a combination of the maximin and Pareto optimality principles, which allows effectively solving multi-criteria optimization problems in a fuzzy environment. The heuristic method proposed will be used to solve a real production problem—optimization of the technological process of benzene production.

Design and multiobjective optimization of a two‐point contact ladder‐climbing robot using a genetic algorithm

AbstractThis paper presents the design and optimization of a climbing robot. The design of a ladder‐climbing robot is done with fundamental mathematical considerations. The designed robot is robust enough to manage all environmental calamities, and at the same time, it is optimized for lightweight to reduce the actuator's cost and ease of transportation. An analytical evaluation is carried out for both static and dynamic conditions to determine strength and motion characteristics. The multiobjective optimization of the design parameters of a ladder‐climbing robot is done to obtain optimized values of design parameters. The formulation of an optimization problem that considers the minimization of weight and natural frequency is performed. Using an evolutionary genetic algorithm (GA) for the multicriteria optimization problem is solved, and a Pareto front solution is obtained. The optimal values of the parameters are decided based on the knee selection technique. As both objective functions are contradictory, the optimum results significantly improve the robot's performance. Controlling the proportional–integral–derivative (PID) parameters is crucial as the robot climbs with a two‐point contact gait pattern. The controlling parameters impart stability to the robot. PID parameters like proportional, integral and derivative gain are tunned using the GA. Finally, the developed prototype is tested on the ladders of the tower, and satisfactory climbing motion is achieved.

Optimization of the Parameters of a Model Predictive Control System for an Industrial Fractionator

The problem of parametric synthesis of a model predictive control (MPC) system by the chemical process of production of the kerosene fraction of an industrial fractionator under conditions of constraints and uncertainty is considered. The optimal parameters of the MPC algorithm are obtained as a result of solving the problem of multi-criteria optimization, taking into account the intervally specified parameters of the plant model.

TECHNOLOGICAL DESIGN OF CAR SERVICE STATIONS USING GENETIC ALGORITHMS

The study describes the use of evolutionary methods or genetic algorithms for the technological design of newly constructed or modernized car service stations. Genetic algorithms are one of the types of machine learning models and are actively used to solve multifactor optimization problems. A task of this type is to search for the technical parameters of a car service enterprise under which the economic indicators of its activities will correspond to the profit or capital cost restrictions set by the user. The paper presents the parameters of the developed model, fitness functions, and also provides an assessment of the effectiveness of using the method of genetic algorithms relative to the method of simply enumerating different options for combinations of initial factors. Purpose. Increasing the efficiency of management of road transport enterprises by using the method of genetic algorithms for strategic planning tasks. Methodology. The research uses the method of genetic algorithms to solve a multi-criteria reverse optimization problem in the technological design of a car service station Results. The use of the method of genetic algorithms for the design of service stations and enterprises for the maintenance and repair of vehicles is justified, taking into account the restrictions or targets established at the beginning of the design. Practical implications. The results of the research can be used by the management of enterprises for the maintenance and repair of vehicles in their technological design, strategic planning of activities and modernization.

Three-objective optimization of a concentrated photovoltaic thermoelectric system via student psychology-based optimization algorithm and an external archive strategy

Thermoelectric generators (TEGs) present a promising avenue for capturing waste heat from photovoltaic (PV) panels in a hybrid concentrated photovoltaic thermoelectric (CPV-TE) setup. However, advancements in CPV-TE technology, especially in optimizing design parameters, remain crucial. A comprehensive thermodynamic analysis reveals non-monotonic, coupling influences of design factors on system performances. In light of this, we tackle a multi-criteria optimization problem using the Student Psychology-Based Optimization (SPBO) algorithm with an external archive strategy. This approach successfully identifies a range of alternative (Pareto frontier) solutions in a three-objective optimization scenario. Results indicate that setting grid density and repertoire number to 10 and 100, respectively, ensures both excellent convergence and computational efficiency. Further, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method aids in selecting an energy-efficient solution from the Pareto frontier. In an efficiency-oriented strategy, total output power, overall efficiency, and TEG power generation stand at 491.32 W, 10.85 %, and 15.91 W, respectively. Conversely, prioritizing total power output yields figures of 540.9 W, 9.61 %, and 26.35 W, respectively.

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

Development of decision-making technology for the provision of services in project implementation

The object of research is decision-making processes regarding the provision of services within the framework of cross-border projects. To achieve the aim of the research, an analysis of the service provision market was first conducted, its features have been revealed and problems arising in the processes of its functioning have been identified. The main problem is to find the optimal distribution of services between performers in the service management system. A mathematical model of the problem of single- and multi-criteria optimization has been developed, where the problem is decomposed into independent sub-problems. The problem is presented in the form of a linear programming problem. Various efficiency criteria of the found distributions are proposed. Depending on the number of criteria, the problem will be a single-criteria Boolean programming problem or a multi-criteria optimization problem. An iterative method for finding the optimal distribution of services has been created, and individual methods are laid out in the form of production rules, which is understandable and allows to gain new knowledge. Based on the obtained data, a decision-making technology has been developed regarding the distribution of service consumers between performers. At the same time, decision-making methods were used, which allow optimizing the processes of service provision. A systematic approach was used when designing information technology. This made it possible to create an effective and problem-relevant technology that helps in making informed decisions about the distribution of services between participants of cross-border projects. A structural and functional diagram of the decision support system has been developed. Its structural elements are detailed. The obtained results reflect a thorough analysis of the current state of the services market and the development of effective decision-making technology, which contributes to the optimization of work in the field of cross-border projects. This approach can be useful for various subjects involved in the implementation and coordination of international projects.

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

In 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.