Nonlinear Programming Method Research Articles

Superlinear convergence of a stabilized SQP-type method for nonlinear semidefinite programming

Superlinear convergence of a stabilized SQP-type method for nonlinear semidefinite programming

Optimization of Fuzzy Economic Order Quantity using Machine Learning and Weka

Inventory management is a crucial need for businesses because it requires a significant financial and human resource investment. Machine Learning models are used by e-commerce huge companies to manage their inventory to the demand for specific products. Businesses can benefit from inventory management as a service to increase sales and forecast product demand. Inventory Management might be revolutionised by AI and ML technologies, which would allow businesses to automate repetitive processes, make data-driven choices, and instantly optimise inventory levels. By analysing vast amounts of both historical and current data, these technologies can spot inclination, forecast, and recommend, all of which increase inventory accuracy and lower the chance of stockouts or overstocking. The most efficient solution is determined using the Kuhn-Tucker Method for Nonlinear Programming, which has an impact on the monthly cost. The proposed model employs the Signed distance approach for defuzzification and the Pentagonal fuzzy number to find the lowest cost and met the demand. To evaluate the inventory concept, purchased a dataset and calculated the profit and non profit using apriori algorithm and use the Weka software to analyse the average order quantity and total cost.

Home energy management system for residential fuel cell-based combined heat and power system

The goal of this paper is to propose an optimization scheme for enhancing power dispatch and load scheduling for residential fuel cell-based combined heat and power systems (FC-CHPS) using mixed integer linear programming (MILP), considering the lifetime degradation of both the fuel cell system (FCS) and battery energy storage systems (BESS). The scheme is applied in the home energy management system that oversees the electric and thermal power of residential FC-CHPS. First, the nonlinearity in the relationship between the natural gas consumption and output electric power, and between the residual thermal power and output electric power of the fuel cell system (FCS) in the FC-CHPS is approximated using piecewise linearization. Then, the piecewise linearization is integrated with MILP to derive optimal power dispatch and load scheduling solutions, while accounting for the nonlinearity of the FCS. Next, cost functions representing the lifetime degradation of FCS and BESS are formulated. These cost functions result in nonlinear optimization constraints. Therefore, innovative methods are proposed to linearize these constraints, allowing the continued use of MILP as the optimization method and factoring in the lifetime degradation of FCS and BESS. Compared to the mixed-integer non-linear programming (MINLP) method that does not linearize the non-linearity in the FCS or the lifetime degradation of the FCS and BESS, the proposed MILP scheme achieves the identical objective function value. Furthermore, the computation time for the proposed MILP scheme is 99.94 % lower than that required by the MINLP method. The proposed scheme provides accurate results in short computation times.

PROBLEMS OF FREIGHT CAR FLOWS DISTRIBUTION ON RAILWAY NETWORKS

Purpose. The purpose of the article is a critical analysis of the existing methods of freight car flows distribution on the railway network and the determination of the directions of these methods adaptation to the operating conditions of the Ukrainian railway transport. Methodology. The research was carried out on the basis of the processing of literary sources in the scientometric databases Scopus and Google Scholar. Results. The distribution of car flows on the railway network is one of the stages of developing a plan for the trains formation. The methods of solving this problem, which are currently used in the practical work of railway transport, were developed during the time of the planned state economy. They are based on the solution of a single-criterion optimization problem aimed at finding such a distribution of car flows on the network that minimizes the cost of transportation for the railway. Reforming the railway transport market with the aim of introducing competition requires the complication of methods of solving the problem of distribution of car flows to take into account the conflicting goals of independent participants in the transport process. The conducted studies showed that the main method of modeling the structure of the railway transport network and the volumes of car flows in it is the theory of graphs; determination of the carrying capacity of elements of the railway network is carried out by the methods of the theory of railway operation, simulation modeling and correlation analysis; determination of the optimal distribution of bandwidth is carried out by comparing competing options, as well as by linear and non-linear programming methods, adaptive control methods using neural networks; the behavior of participants in the transportation process during the allocation of bandwidth is investigated by game theory methods. It has been established that in modern conditions, the task of determining the criterion of equal access to congested sections on the branched railway network and the task of distributing car flows on the network in conditions of fluctuating car flows during transportation by regular trains and trains to order require additional research. Originality. The scientific novelty of the work consists in the critical analysis and generalization of modern methods used to solve the problem of distribution freight car flows distribution on railway networks. Practical value. The practical significance of the results lies in determining the inconsistency of the methods that are practically used on the railways of Ukraine for the distribution of car flows, with the modern conditions of operation of railway transport. Scientific methods have been established that allow to improve approaches to solving the problem of rational distribution of car flows, taking into account the interests of various participants in the transportation process.

Impact of resource reconfiguration on the dairy supply chain resilience

Investment in food supply chain resilience, as a critical infrastructure, has become necessary for all governments. Disruption of food supply chains can lead to significant economic challenges. Building a resilient supply chain requires resources; however, it is difficult for firms to allocate resources to various resilience strategies. This study allocates the budget to resilient capacity, that is, absorptive, adaptive, and restorative capacity, to minimize supply chain costs and maximize service levels. We developed a novel multi-objective mixed-integer nonlinear programming method for problem formulation. The developed model was converted into an equivalent linear model. We used the Monte Carlo approach to generate the scenarios and the average sample approximation to determine the required scenarios. Finally, the Lexicographic max-min approach solves the model using actual data from a dairy supply chain. The analysis revealed that allocating 50% of the budget to restorative capacity and the remaining to adaptive and absorptive capacity optimizes supply chain performance. This study provides insights for managers to make better decisions with a knowledge-based background, allocate resources to various resilient strategies, and build a more resilient and efficient supply chain.

Development of the scientific and pedagogical school of the department “Ground Transport and Technological Complexes”

The scientific article reflects the main stages of the historical development of the scientific and pedagogical school of the cycle “Technology of structural metals. Materials Science”, which is one of the areas of the department “Ground transport and technological complexes”. Employees of the department made a significant contribution to solving practical problems in assessing the effectiveness of existing technological processes for restoring the tread surface profile of wheel pairs of wheels, the proposed processes of face milling and turning when restoring the wheel rim profile, including the use of preliminary induction annealing to improve machinability, optimization of cutting conditions wheels based on linear and nonlinear programming methods. A large amount of research and implementation work has been carried out to improve the repair technology and increase the reliability of the wheel-motor unit of rail crews of railway rolling stock. Issues related to surfacing operations during repairs and increasing the wear resistance of deposited surfaces were considered.At the same time, the teachers of the department conduct training sessions on disciplines at a high methodological level, without which it is impossible to imagine a modern engineer.Over the years of work of the cycle “Technology of Structural Metals. Materials Science” a large number of textbooks, teaching aids, guidelines and manuals on laboratory work and course design, as well as collections of scientific papers, articles and monographs on the main areas of research work were published.The historical digression presented in this article gives an idea of the scientific potential of the department accumulated over many years, which can serve as a reliable basis for further development of new scientific directions.

Optimization of Batch Cooling Crystallization of Sodium Phosphite Through Genetic Algorithm

AbstractIn this paper, the seeded batch cooling crystallization of sodium phosphite (SP) is simulated and optimized through a coupled method of the genetic algorithm and nonlinear programming. At first, the modeling and simulation test methods of the crystallization process are applied for the crystallization of SP, which expands the relevant study of SP from the experiment to the simulation. A comprehensive model is established in MATLAB/Simulink, and based on this model, the results of the common cooling strategy (linear cooling) on the process are investigated. Meanwhile, the process sensitivity to the change of seeding conditions is analyzed. Then, the coupled optimization method based on the genetic algorithm and nonlinear programming is applied to optimize the crystallization process for the first time, and the obtained optimized cooling strategy is compared to the result of the traditional nonlinear programming method (NLPM). The traditional NLPM has more significant effects on large seeding mass and small mean size, while the coupled method has better adaptability. When the coefficient of variation is almost fixed, the cooling strategy obtained by the coupled method could produce more crystals with large mean size. In addition, the end of the process can be reached earlier. The results show that the coupled method is more suitable for the optimization of the batch cooling crystallization of SP.

Innovative Technology for Managing Biofuel Production from Timber Industry Waste

The relevance of this study is determined by the growing worldwide interest in renewable energy sources against the backdrop of depleting fossil fuel reserves. This study aims to develop an innovative technology for managing biofuel production from wood waste, including a set of interrelated economic and mathematical models focused on maximizing the fuel and energy efficiency of biofuels depending on the location of waste generation, feedstock moisture content, and distance to the biofuel production site. This technology should also combine the main directions of international research in the field of environmental responsibility of countries in terms of carbon dioxide (CO2) emissions and the Paris Climate Agreement. The methodological basis of the research comprises the authors’ innovative technology based on a set of interconnected economic and mathematical models and managerial decision-making systems, methods for nonlinear programming, system analysis, an information approach to the analysis of systems, accepted technological processes, norms, and standards established in the international practice of the timber industry. This innovative technology was implemented in practice using the capabilities of the MathCad and MS Excel software products. The article determines the optimal operating parameters of timber industry enterprises at which the specific thermal energy of the produced biofuel exceeds by at least 15% the thermal energy spent on processing this biofuel as an energy carrier. Wood waste biofuel production is profitable if the distance for feedstock transportation to the production site does not exceed 80 km and the relative humidity of the raw materials does not exceed 60%. Doi: 10.28991/ESJ-2024-08-03-03 Full Text: PDF

효율성 향상을 위한 방안으로 최적조합을 찾는 휴리스틱 방법에 관한 연구

This paper explores the optimal combination as a way to improve efficiency. Nonlinear optimization, random search, and greedy algorithm methods were used to find an optimal project combination of projects for government research institutes. According to our numerical experiments, the nonlinear programming method is not computationally efficient (i.e., requiring long computational time) to find an optimal combination. However, the greedy algorithm can produce multiple optimal project combinations in a short time window. Random search can also generates multiple optimal combinations, but it has disadvantage that computational time increases in the number of random generations. By using the proposed greedy method, multiple optimal combination can be quickly found in a situation where the number of R&D projects increases. Therefore, a research institute has a greater flexibility in selecting one among multiple optimal combinations.

The establishment of a performance evaluation model using education informatization to evaluate teacher morality construction in colleges and universities

Abstract To improve the effectiveness of the construction of teacher morality in colleges and universities, this article employs the performance evaluation model of education informatization to construct an evaluation system for the construction of teacher morality in colleges and universities. The evaluation of the construction effect of teacher morality is carried out through intelligent data analysis, and the significant error is used as the parameter of the teacher’s morality to make estimations. Moreover, a binary variable is introduced to judge whether the data have a significant error. Mixed integer linear and nonlinear programming methods are employed to detect significant errors. In addition, the idea of synchronizing teachers’ moral data is added. The effectiveness of the proposed method is verified by a simulation study using MATLAB 2017. The results show that it is necessary to establish and improve the talent flow mechanism that conforms to the requirements to promote the rational flow of teachers.

Regulation of Fat Content in Triticale Based on Optimization of Technological Processing Modes

Introduction The aim of the study was to regulate the fat content based on the optimization of technological processing modes. A promising method of preparing grain for animal feeding is its preliminary germination. Sprouted grain is a dietary food product, as it increases the content of proteins, essential amino acids, and macro- and microelements in comparison with non-sprouted grain. Methods The purpose of this study was to regulate the fat content based on the optimization of technological processing modes. Regression equations describing the dependences of the quality indicators of the triticale grain germination modes on the factors tw, τ, w and tg affecting them were investigated and obtained. During the study of triticale grains, it was found that the most significant parameter affecting the germination process is the fat content. The optimization of the germination modes of triticale Leather grain was carried out by the method of nonlinear programming. Results During the study, it was found that the maximum fat content during germination of triticale grain was observed with the following technological parameters of germination: grain temperature = 30°C; germination time = 24 h; grain moisture = 13%; and grain temperature = 26°C. When controlling the fat content in triticale based on the optimization of technological modes, the target function was 2.83%. Conclusion The presented results and conclusion will allow to regulate the fat content in triticale grain during germination.

Optimal resource allocation in hierarchical organizations under uncertainty: An interval-valued n-person cooperative game approach

In many real production scenarios, departmental organizations often exhibit a hierarchical structure, where departments cooperate with subordinate departments to optimize resource allocation and maximize their respective benefits. However, due to a lack of information or data, many model parameters in the allocation process cannot be precisely defined. In response to this challenge, an interval n-person hierarchical resource allocation model is proposed to achieve maximum economic benefit in uncertain environments. Based on the concepts of satisfactory degrees of comparing intervals and interval-valued cores of interval-valued n-person cooperative games, an auxiliary nonlinear programming model and method are developed to solve the interval-valued cores of such cooperative games. The approach explicitly considers the inclusion and/or overlap relations between intervals, whereas the traditional interval ranking method may not guarantee the existence of interval-valued cores. The proposed method offers cooperative opportunities under uncertain conditions. Finally, the feasibility and applicability of the models and methods are demonstrated through a numerical example and comparison with other methods.

Reentry trajectory planning for hypersonic vehicles via an improved sequential convex programming method

The reentry trajectory planning problem of hypersonic vehicles is generally a continuous and nonconvex optimization problem. The solution efficiency and convergence properties of the planning algorithm become an essential point when considering the practical application scenarios. In this paper, an augmented-Lagrange-based improved sequential convex programming algorithm is proposed to solve it and achieve superior solutions with higher accuracy and efficiency. Firstly, the mapped Chebyshev pseudo-spectral method is utilized to convert the continuous optimal control problem into a highly approximately discretized one. In this framework, the discretization technique is employed to discretize the states and control variables at the time interval, which leads to the improvement of ill-conditioned differential matrix and better approximation properties of the variables. Moreover, by introducing slack variables, automatically updated penalty parameters and Lagrange multipliers during the convexification processing, the original nonconvex problem is transformed into an augmented-Lagrange-function-formed relaxed convex one. Then, the arrived convex subproblem can be solved iteratively by the matured interior-point method until the predetermined precision is satisfied. Based on this transformation, it can effectively alleviate the numerical difficulty and improve the convergence property of the proposed improved sequential convex programming algorithm. Finally, Rigorous theoretical analysis is conducted to prove that the solution sequence generated by the proposed algorithm could converge to an approximate global solution of the original problem. Numerical simulations are also presented, and it is demonstrated that the solution time of the proposed algorithm is more than 95% less than that of the traditional nonlinear programming methods without losing the merits of high precision.

Разработка методики определения параметров преобразования систем координат на основе метода нелинейного программирования первого порядка при сопровождении строительства зданий и сооружений

Objective: to analyze the advantages and disadvantages of existing nonlinear programming methods for solving problems of coordinate system transformation (SC). To consider the need to convert the coordinates of points from local SC to urban. To determine the possibility of using the generalized reduced gradient method to transform the coordinates of points located both at a distance between points of about 150 m and at a distance of about 1.5 km. Methods: the theoretical foundations of this method are revealed. Information is provided on the procedure for performing transformations of coordinate systems. The algorithm of the generalized reduced gradient (OPG) method is given. A study has been conducted on the transformation of coordinate systems of starting points from SK1 to SK2 using the OPG method. The requirement for the value of the mean square error (SQR) of determining the position of the starting points when converting them from one coordinate system to another is justified. Results: a check was performed on the possibility of applying the obtained transformation parameters to recalculate the coordinates of points from the local SC to the city SC. Based on the verification of the obtained transformation parameters, the possibility of using them to recalculate the coordinates of points located at a distance of about 1,5 km was revealed. The need for additional research on the application of the generalized reduced gradient method to solve coordinate system transformation problems has been identified. Practical significance: the necessity of transformation of coordinate systems in the field of construction of buildings and structures is shown. The possibility of applying the generalized reduced gradient method to transform coordinate systems is presented. Using this method will allow you to convert the coordinates of the starting points from the local coordinate system to the coordinate system of the city with geodetic support for the construction of buildings and structures of various categories.

Математическое обеспечение информационно-управляющей системы для хранения продукции с ограниченным сроком хранения

The work presents a solution to the problem of developing mathematical support for an information and control system for storing products with a limited shelf life using the example of storing sugar beets in field conditions and in heaps at sugar factories based on experimental experiments published in the open press data. An end-to-end ranking of methods for storing root crops was carried out, starting with a root lying separately on the field (rank 0.1 points), from simple windrows and heaps (rank 0.2 points) to specialized root storage and ventilated piles covered with special bactericidal coatings with reflective and protective properties (rank 4 points). An end-to-end ranking of mechanical damage to sugar beet roots has been implemented, starting from 1 point (the root crop is practically undamaged) to 0.1 point (fragments and tails). The studied hybrids were ranked according to sugar content. Based on the rankings, taking into ac-count storage time and temperature, mathematical models (mm) of the dependence of technological indica-tors of beet raw materials, including losses of beet mass and sucrose, on storage parameters were built for each study. Extensive computational experiments were per-formed using an interactive identification and optimization system (isio), which is based on a genetic algorithm and the Hooke Jeeves nonlinear programming method. The errors of the developed models do not exceed the errors of the experimental data used to construct them.

Поиск глобального минимума целевой функции для определения псевдообратной матрицы поисковым методом при уравнивании свободных геодезических сетей

When evaluating the accuracy of equalized free geodetic networks based on the search method of nonlinear programming, a degenerate matrix of unknowns’ normal equations coefficients is formed. It must be pseudoinverse in order to calculate the inverse weight one of the equalized parameters. Performing a mathematical procedure for calculating a pseudoinverse matrix based on the mentioned technology of nonlinear programming at equalizing free geodetic constructions, a situation may arise when the minimization step is incorrectly selected or the approximate values in the desired array of numbers are set roughly. It can lead to finding a local, not a global minimum, as well as to cycling the algorithm. The authors provide the conclusion of the formula and substantiate the conditions on which the elements of the required matrix change, so that the value of the objective function either comes as close as possible to the global minimum, or indicates that it is impossible to achieve it. The correctness of the proposed conditions and the derived formula are confirmed by a test example

Optimisasi Portofolio Saham Syariah dengan Pendekatan Fuzzy Goal Programming

This study discusses about solving the problem of stock portfolio optimization. The portfolio optimization problem can be modeled as a multiobjective model with two objective functions, they are maximizing return and minimizing risk. This study uses the mean-variance Markowitz model to model the portfolio. The fuzzy goal programming approach is used to solve stock portfolio problems by converting a multi-objective model into a fuzzy mathematical programming model which is solved using a nonlinear programming method. The results of implementing the model on stocks listed on the Jakarta Islamic Index show that the best investment proportion forms an optimal portfolio according to the level of aspirations. Several different optimal portfolios can be formed using the fuzzy goal programming approach. The difference in the results of these portfolios depends on the level of aspiration of investors.

Investigation of non-axisymmetric endwall contouring in a high loaded turbine stator cascade

The intensity and structure of the secondary flows have significant influences on the turbine cascade losses. Combining with the extension method of Non-linear Programming by Quadratic Lagrangian (NLPQLP), two endwall parametric methods respectively based on the B-spline surface and Fourier series are used to optimize the aerodynamic losses of a turbine cascade. The optimization processes are based on Computational Fluid Dynamics (CFD) analysis and two final designs are obtained by different methods. The endwall profile generated by the B-spline surface method (EW-B1) appears to relatively reduce the total pressure loss by 16.58% and the secondary kinetic energy coefficient ( C SKE) by 27.08%, while the endwall profile generated by the Fourier series method (EW-F1) relatively reduces the loss by 16.18% but increases C SKE by 8.99%. The radial movement of upper Passage Vortex (PV) and the weakening of the pressure branch of the Horseshoe Vortex (HVps) are confirmed to be the reasons of loss reduction in EW-B1, while the movement of PV is the main reason for EW-F1 to decrease the total pressure loss. In EW-B1, the weakening of HVps has a much more significant effect on the decrease in loss, which is affected by the non-axisymmetric shapes upstream of the vortex trajectory and the drop in C SKE generation near the throat.

Optimizing the LQ45 Stock portfolio using Piecewise Linear Function: A Case Study from an Investor's Point of View

In optimization problem solving, both linear and nonlinear approaches can be used, with nonlinear programming considering constraints or not. One effective method of nonlinear programming is the Piecewise Linear approach, which breaks down complex nonlinear functions into straight-line segments to make their solution easier. This method can be applied in the financial sphere, such as in stock investment. This study discusses the application of piecewise linear function in optimizing investment portfolios in Bank Jago Tbk. (ARTO), Barito Pacific Tbk. (BRPT), and Go To Gojek Tokopedia Tbk. (GOTO) stocks. The purpose of this study is to provide insight that Piecewise Linear can provide optimal solutions in managing investment portfolios by calculating the risks and returns of selected stocks. The results showed a risk with a level as big as 0.01, the expected profit from the investment of the three stocks in the calculation period reached Rp 1,803,109. On the other hand, for investors who are more cautious and have a Level as big as 1, the anticipated profit in the same investment is around Rp 1,275,052.

Sustainable supply chain of distributed multi-product gas fields based on skid-mounted equipment to dynamically respond to upstream and market fluctuations

Efficient operation of the gas field supply chain is an important guarantee for oil and gas energy security, and it needs to dynamically adapt to upstream and market fluctuations. This paper proposes an innovative design and operation optimization mixed integer nonlinear programming (MILP) method for distributed supply chain based on skid equipment. Unlike the traditional methods, the proposed MILP method can simultaneously obtain upstream production planning, midstream modular equipment and processing capacity allocation, and downstream transportation allocation schemes for various natural gas products such as liquefied natural gas (LNG), compressed natural gas (CNG) and pipeline natural gas (PNG) of each time periods by making the maximum net present value (NPV) of the full development cycle as the target. In order to prove the superiority and usability of the proposed method, four operation scheduling modes are compared through two comprehensive case analysis. Additionally, the effects of gas well productivity, market demand and product price are investigated through sensitivity analysis. The results show that comparing with the traditional method, the proposed method can effectively improve the loading rate of the processing equipment, increase the overall revenue of gas field development, integrate the operation in the upstream, midstream and downstream of the supply chain, dynamically adapt to the gas production and marketing fluctuations. This study provides a creative way to obtain better profit, reduce energy utilization and promote cleaner production for sustainable supplies management in gas industry.