Mathematical Optimization Model Research Articles

A mesh refinement method for low‐thrust orbit transfer problems

AbstractThis paper researches the fuel‐optimal geocentric orbit transfer problem using a low‐thrust, electric propulsion. First, the transfer trajectory is divided into N burn‐coast arcs via introducing (N−1) intermediate orbits between the initial and the target orbits. By restricting the time duration of each burn, the changes in orbital states caused by one time of ignition can be represented by a discrete velocity impulse; therefore, a considerable large N, a great many optimization variables, and a months and revolutions long trajectory will be calculated to solve the optimization problem. By proposing a new transfer coordinate system, the performance index is analytically calculated, and strict constraints derived from the continuous condition between adjacent orbits are removed from the mathematical optimization model. Meanwhile, an improved particle swarm optimization (PSO) method and a mesh refinement method are proposed to address the optimization problem. The mesh refinement algorithm begins with a simple bi‐impulse transfer problem, automatically increases/decreases N, and finally converges to the optimal solution. Numerical simulation shows the efficiency of the method with some classical and representative scenarios.

Modeling a Multi-Parameter Interaction of Geophysical Controls for Production Optimization in Gas Shale Systems.

Well bottomhole pressure optimization issue has been a significant concern for efficiently developing unconventional systems due to strong stress sensitivity. Therefore, it is of practical interest to clarify influence mechanisms involved in stress sensitivity for gas shale, which is further included in the production model to determine main controlling factors for bottomhole pressure strategy optimization for long term hydrocarbon extraction. Currently, many production models were limited in exploring stress sensitivity mechanisms but adopted common empirical equations regarding net pore stress instead. In addition, geophysical control analysis for unconventional systems optimization was mostly conducted using local sensitivity qualitative analysis, which should be validated to be reliable and applicable to fields using multi-parameter interaction influence. As a result, in this paper, an efficient workflow to rationally optimize gas well production system was provided by combining the production model, orthogonal design approach, and response surface method. To be specific, the compound flow model for shale gas reservoirs, incorporating multiple stress sensitivity mechanisms, was proposed to function as a theoretical basis for production optimization simulation. Last but not least, local sensitivity analysis was conducted to qualitatively analyze the impact of influencing factors on 20 year-production of gas wells under different bottomhole production methods. The simulation results showed that the managed pressure drawdown scheme can be adopted for reservoirs with high reservoir pressure and tight matrix properties, while the high-pressure drawdown scheme is suitable for reservoir with better fracturing effect and high external water content. Finally, based on the proposed gas flow model and orthogonal design experiments, response surface design and single factor analysis as well, an optimization mathematical model for shale gas multi-parameter interaction was established, which intuitively quantified the effects of multi-geophysical controls on EUR increase in different production durations, including matrix properties, fracture properties, and production system indicator parameters. These findings provide a more reliable reference for production system optimization based on a series of mathematical approaches to improve overall long-term recovery from shale gas reservoirs.

Collaborative Determination Method of Metro Train Plan Adjustment and Passenger Flow Control under the Impact of COVID-19

Aiming at the problem of metro operation and passenger transport organization under the impact of the novel coronavirus (COVID-19), a collaborative determination method of train planning and passenger flow control is proposed to reduce the train load rate in each section and decrease the risk of spreading COVID-19. The Fisher optimal division method is used to determine reasonable passenger flow control periods, and based on this, different flow control rates are adopted for each control period to reduce the difficulty of implementing flow control at stations. According to the actual operation and passenger flow changes, a mathematical optimization model is established. Epidemic prevention risk values (EPRVs) are defined based on the standing density criteria for trains to measure travel safety. The optimization objectives of the model are to minimize the EPRV of trains in each interval, the passenger waiting time and the operating cost of the corporation. The decision variables are the number of running trains during the study period and the flow control rate at each station. The original model is transformed into a single-objective model by the linear weighting of the target, and the model is solved by designing a particle swarm optimization and genetic algorithm (PSO-GA). The validity of the method and the model is verified by actual metro line data. The results of the case study show that when a line is in the moderate-risk area of COVID-19, two more trains should be added to the full-length and short-turn routes after optimization. Combined with the flow control measures for large passenger flow stations, the maximum train load rate is reduced by 35.18%, and the load rate of each section of trains is less than 70%, which meets the requirements of COVID-19 prevention and control. The method can provide a theoretical basis for related research on ensuring the safety of metro operation during COVID-19.

Mathematical optimisation of extruded mixed plant protein-based meat analogues based on amino acid compositions

Developing meat analogues of superior amino acid (AA) profiles in the food industry is a challenge as plant proteins contain less of some essential AA than animal proteins. Mathematical optimisation models such as linear/non-linear programming models were used to overcome this challenge and create high-moisture meat analogues (HMMA) with AA profiles as close as possible to chicken breast meat. The effect on the physiochemical properties and specific mechanical energy (SME) of the HMMA was investigated. The AA content of HMMA was generally lower than chicken. Strong intermolecular bonds present in the globulin fraction could hinder protein acid hydrolysis of HMMA. Plant proteins also affect the HMMA colour as certain AA forms Maillard reaction products with higher browning intensity. Lastly, different characteristics of plant proteins resulted in different SME values under the same extrusion conditions. While mathematical programming can optimise plant protein combinations, fortification is required to match the AA profile of HMMA to an animal source.

Mathematical modeling and optimization of wastewater stabilization ponds using nonlinear programming

This research work proposes a mathematical optimization model for constructing two ponds (1. Facultative pond and 2. Maturation pond) provided in series. The model uses concrete volume as its objective minimization function. There were two decision variables; the first was the detention time (DT) and the second in the list was the number of provided baffle walls (NBW) in both ponds. The constraint parameters include fecal coliforms and biochemical oxygen demand (BOD5). The model was applied with the help of an Add-Ins of MS Office: Excel solver. The generalized reduced gradient algorithm was utilized in the solver (GRG). Before applying the mathematical optimization model, ponds were designed with the conventional method and then using optimized values of the variables. A comparison of the findings reveals that a 13.79 percent reduction in the DT, an 11.55 percent reduction in the area, and a 7.19 percent reduction in the volume of concrete occurred. The reduction values mentioned above are significant since these systems' fundamental drawback is the area's requirement. In addition, sensitivity analyses of the objective function and the removal of pollutants are also provided. The model described above is sensitive to variations in the parameters. Both analyses demonstrated that the effluent characteristics comply with the class-B irrigation standards in Turkey. It is advised to do more optimization studies for WSPs with the help of other algorithms and tools available in the literature for distinct wastewater treatment plants.

Multi-Clustered Mathematical Model for Student Cognitive Skills Prediction Optimization

The outbreak of COVID-19 boosted the rapid increase in E-Learning platforms. It also paves the way for Massive Online Open Courses (MOOCs) to break the record for students’ enrollment in online courses. In such circumstances, it is significant to timely identify at-risk students’ Cognitive Skills (CS) through an optimized E-Health service. CS is profoundly influenced (negatively and positively) by many human factors, including anxiety and biological age group. Literature has massive findings that correlated CS with anxiety and ageing. However, the earlier studies contributed to CS prediction algorithms are still limited and not up to the mark to efficiently estimate CS under the umbrellas of anxiety and age clusters. The CS prediction system requires an optimization algorithm to mathematical model the influence of age and anxiety clusters. This work predicts students’ CS under the influence of anxiety and age clusters, referred to as the Anxiety and Ageing (AA) mathematical model. It solves threefold challenges. First, the study quantizes students’ CS, age, and the adverse effects of anxiety. Second, it iteratively computes CS with respect to the anxiety cluster and further revises it under the influence of the age cluster. Third, the study provides a novel data collection method for future researchers by demonstrating assumption-based datasets. The prediction results manifest that the current model achieved excellent precision, recall, and F1 score performance.

Development of a mathematical model for the analysis of different load modes of operation of induction motors

This paper explores the conditions for creating and using mathematical models for the analysis of various modes of operation of the load of induction motors. Widely used in industrial plants, these motors play an important role in the world’s energy consumption. Improving their energy efficiency is essential to reduce energy consumption, waste and improve sustainability. The paper also provides information on the introduction of modern mathematical models for accurate analysis and optimization of energy saving modes in asynchronous motors.

The method of navigation performance optimization analysis for high speed monohull ships

This paper is based on the drag resistance test data of the high-speed monohull model, a mathematical model for comprehensive optimization of the navigation performance of a high-speed monohull taking into account the rapidity, maneuverability, seakeeping and static performance of the ship is constructed. The optimization calculation software based on particle swarm, standard genetic algorithm and growth mechanism genetic algorithm is designed and written. Taking a high-speed monolithic sea-going ship with a displacement of 1500 tons and a large inclination-measuring single propeller as the object of discussion, the comparison of optimization methods, the comprehensive navigation performance of different ship types and the sensitivity analysis of design variables are carried out respectively. It provides a practical approach and an effective and practical scientific method for analysis and evaluation of how to maintain the comprehensive optimal navigation performance of high-speed monohull ships. At the same time, it provides a way to quickly evaluate the comprehensive performance of similar high-speed monolithic ships in the preliminary design stage, and can also obtain the model diagram with the best comprehensive performance through this software or method, which is useful for shortening the preliminary design cycle of the ship and improving the design quality of the ship. It has important reference value.

Layout Scheme Comparison of the Switching Station of Guoduo Hydroelectric Project Based on AHP-TOPSIS

The combination of AHP and TOPSIS can make the evaluation method easy to operate, and improve the objectivity and accuracy of the results. The mathematical model for the switching station scheme optimization was set up to choose an appropriate layout for the Guoduo hydropower station. Through the field survey and literature review, the expert questionnaire was finished. The weights of the index were calculated using the AHP method. Then the improved TOPSIS was employed for the index standardization and the sequencing calculation. The final option of layout 2 was obtained.

A robust solution for optimizing facility location and network design with diverse link capacities

In this paper, the authors proffer a novel mathematical model for the simultaneous optimization of facility location and network design in the presence of uncertainty, with the aim of minimizing operational and transportation costs. The proposed model constitutes a departure from conventional methods in its consideration of probable events in the real world and the incorporation of uncertainty assumptions into the mathematical framework. An algorithm based on simulated annealing is then advanced for the solution of the problem, and the performance of the algorithm is evaluated through comparison with exact methods for problems of modest size, as well as with a basic simulated annealing algorithm for larger problems. The results of these comparisons demonstrate the superiority of the proposed meta-heuristic algorithm. Finally, the robust approach is compared with four other approaches in the presence of uncertainty, with a thorough analysis of the results obtained from each of the methods conducted in a suite of sample problems.

A Stress Index-based Tendon Optimization Method for Prestressed Concrete Continuous Girder Bridges

PDF HTML XML Export Cite reminder A Stress Index-based Tendon Optimization Method for Prestressed Concrete Continuous Girder Bridges DOI: 10.59238/j.pt.2023.01.001 Author: Affiliation: (1. Department of Bridge Engineering, Tongji University, Shanghai 200092, China; 2. Anhui Transport consulting & Design Institute Co., Ltd. Anhui 230088, China) Clc Number: Fund Project: Article | Figures | Metrics | Reference | Related | Cited by | Materials | Comments Abstract:Traditional tendon design methods for prestressed concrete (PC) continuous girder bridges are tedious since they obtain feasible solutions based on trial calculation, and the existing optimization methods that can obtain the optimal solution have deficiencies regarding structural stress. In this study, based on research on the refined bridge design conducted in the Department of Bridge Engineering at Tongji University in recent years, a stress index-based tendon optimization method for PC continuous girder bridges is pro-posed. First, various tendon layouts are summarized, and a reasonable tendon layout is selected. Then, a mathematical tendon optimization model is established. After meeting the specifications and construction feasibility requirements, a genetic algorithm is used to find the optimal solution. This method not only realizes tendon forward design but also obtains a satisfactory solution. Finally, this method is used to successfully optimize the tendons of a three-span PC continuous girder bridge, which verifies the ration-ality of the method. Reference Related Cited by

A Mathematical Optimization Model for the Pharmaceutical Waste Location‐Routing Problem Using Genetic Algorithm and Particle Swarm Optimization

Pharmaceutical waste management is a significant concern that poses risks to human and environmental health. The ineffective management of expired and unused medications can harm individuals and communities. This study proposes a novel approach to address the issue of pharmaceutical waste management by developing a location‐routing problem (LRP) model using mixed‐integer linear programing (MILP) to optimize the collection and disposal of pharmaceutical waste. The proposed model aims to minimize transportation costs, construction of collection centers, disposal costs, and carbon dioxide emissions, making it a cost‐effective and environmentally sustainable approach to managing pharmaceutical waste. Initially, the feasibility, validity, and efficiency of the proposed model are examined by solving the problem in the GAMS software using CPLEX solver for small‐scale problems. Sensitivity analyses are conducted to ensure the accuracy, reliability, robustness, and usefulness of the mathematical model for decision‐making. In view of the inherent computational complexity of the proposed model, which is classified as nondeterministic polynomial time‐hard and poses considerable difficulties when exact solutions are sought for large‐scale problems, the present study resorts to two metaheuristic algorithms, specifically particle swarm optimization (PSO) and genetic algorithm (GA), as a means minimizing the computational burden. The results indicate that GA outperforms PSO in terms of objective function and solution time, with an average improvement of approximately 1% and 20%, respectively. The proposed model and algorithms provide a comprehensive approach to addressing the critical issue of pharmaceutical waste management, benefiting the healthcare industry, and society as a whole.

Job-scheduling Model For an Autonomous Additive Manufacturing: a Case of 3D Food Printing

Three-dimensional food printing (3DFP) is an emerging application of additive manufacturing (AM) as it offers customized designs, personalized nutrition, simplified and efficient supply chain, and reduced waste. Grouping parts into jobs (batches) and sequencing these jobs (known as job-scheduling) is considered a key operational factor in additive manufacturing (AM). The task of job-scheduling is complex because the number of possible solutions grows exponentially with the number of parts and various constraints has to be considered (e.g., machine's capacity). In the case of 3DFP, scheduling presents a unique challenge since different 3D printed foods have different time constraints depending on material's shelf-life. In this paper, we propose a mathematical optimization model for job-scheduling in 3DFP that minimizes the makespan (total accumulative manufacturing time) and the deadline violation simultaneously. We reformulate the proposed optimization model to the form of mixed-integer linear programming (MILP) and solve in using MILP solver in MATLAB 2022. We demonstrate the effectiveness of the proposed model with a numerical case study. The obtained results show that our algorithm obtains scheduling that significantly reduces the deadline violation while achieving the same production time as the state-of-the-art baseline.

Energy Management and Capacity Optimization of Photovoltaic, Energy Storage System, Flexible Building Power System Considering Combined Benefit

Building structures themselves are one of the key areas of urban energy consumption, therefore, are a major source of greenhouse gas emissions. With this understood, the carbon trading market is gradually expanding to the building sector to control greenhouse gas emissions. Hence, to balance the interests of the environment and the building users, this paper proposes an optimal operation scheme for the photovoltaic, energy storage system, and flexible building power system (PEFB), considering the combined benefit of building. Based on the model of conventional photovoltaic (PV) and energy storage system (ESS), the mathematical optimization model of the system is proposed by taking the combined benefit of the building to the economy, society, and environment as the optimization objective, taking the near-zero energy consumption and carbon emission limitation of the building as the main constraints. The optimized operation strategy in this paper can give optimal results by making a trade-off between the users’ costs and the combined benefits of the building. The efficiency and effectiveness of the proposed methods are verified by simulated experiments.

Dynamic selection of clarification channels in rumor propagation containment.

Rumors refer to spontaneously formed false stories. As rumors have shown severe threats to human society, it is significant to curb rumor propagation. Rumor clarification is an effective countermeasure on controlling rumor propagation. In this process, anti-rumor messages can be published through multiple media channels, including but not limited to online social platforms, TV programs and offline face-to-face campaigns. As the efficiency and cost of releasing anti-rumor information can vary from media channel to media channel, provided that the total budget is limited and fixed, it is valuable to investigate how to periodically select a combination of media channels to publish anti-rumor information so as to maximize the efficiency (i.e., make as many individuals as possible know the anti-rumor information) with the lowest cost. We refer to this issue as the dynamic channel selection (DCS) problem and any solution as a DCS strategy. To address the DCS problem, our contributions are as follows. First, we propose a rumor propagation model to characterize the influences of DCS strategies on curbing rumors. On this basis, we establish a trade-off model to evaluate DCS strategies and reduce the DCS problem to a mathematical optimization model called the DCS model. Second, based on the genetic algorithm framework, we develop a numerical method called the DCS algorithm to solve the DCS model. Third, we perform a series of numerical experiments to verify the performance of the DCS algorithm. Results show that the DCS algorithm can efficiently yield a satisfactory DCS strategy.

Research on Flexible Job Shop Scheduling Optimization Based on Segmented AGV

As a typical transportation tool in the intelligent manufacturing system, Automatic Guided Vehicle (AGV) plays an indispensable role in the automatic production process of the workshop. Therefore, integrating AGV resources into production scheduling has become a research hotspot. For the scheduling problem of the flexible job shop adopting segmented AGV, a dual-resource scheduling optimization mathematical model of machine tools and AGVs is established by minimizing the maximum completion time as the objective function, and an improved genetic algorithm is designed to solve the problem in this study. The algorithm designs a two-layer coding method based on process coding and machine tool coding and embeds the task allocation of AGV into the decoding process to realize the real dual resource integrated scheduling. When initializing the population, three strategies are designed to ensure the diversity of the population. In order to improve the local search ability and the quality of the solution of the genetic algorithm, three neighborhood structures are designed for variable neighborhood search. The superiority of the improved genetic algorithm and the influence of the location and number of transfer stations on scheduling results are verified in two cases.

Research on Multi-Objective Scheduling Algorithm of Job Shop Considering Limited Storage and Transportation Capacity

As with the continuous improvement of the workshop automation rate and the importance in energy consumption, more and more enterprises not only need to make scheduling decision on production equipment, but also need to consider whether the scheduling of transportation equipment supports scheduling decisions on workshop production. At the same time, because both workshop production scheduling decision and transportation scheduling decision are NP-hard problems, it is necessary to design an efficient algorithm to improve productivity of the workshop. In order to solve this problem, firstly, based on the analysis of the problem structure, production environment and optimization objectives, a “manufacturing-transportation” multi-objective joint scheduling optimization mathematical model is established. By converting the energy consumption into the total transportation time objective of the transportation equipment, both total transportation time and makespan are taken as the optimization objectives. Secondly, based on the design idea of memetic algorithm (MA), non-dominated sorting genetic algorithm-Ⅱ(NSGA-II) is employed as the basis framework of our new developed algorithm. An effective discrete encoding scheme of MO-MA, a new initialization method for initial population and a neighborhood search mechanism based on critical path are incorporated into our new proposed algorithm. Then the parameter design of the algorithm is completed through variance analysis. Finally, the proposed algorithm is compared and analyzed with other algorithms in the dimension of hypervolume and Set Coverage (SC), and advantages of the algorithm in solving this problem are verified.

Methods of data analysis in the problem of optimizing the rental schedule

In this paper, the main problems of scheduling screenings for a cinema were considered. The activity of one cinema “X” is described and the restrictions that must be observed and taken into account when planning the schedule of sessions are analyzed. The solution to this problem is due to the complexity and time-consuming planning of the cinema schedule. To achieve this goal, the article analyzes the statistical data obtained in the cinema “X”. An analysis was carried out using the methods of statistical data analysis and predictive factors of movie attendance were identified, regression models of attendance were developed. Based on the developed regression models, statistical estimates of attendance predictive factors were obtained. Taking into account the results obtained, an optimization mathematical model for the formation of a rental schedule has been developed, which makes it possible to increase the box office of a cinema.

Optimization of Physical Parameters and Analysis of Rock Movement and Deformation Patterns in Deep Strip Mining

China’s shallow coal resources are gradually diminishing, and deep coal resources have slowly become the main energy source. However, the destruction mechanism and evolution of deep rock formation structure are not clear, which seriously restricts the exploitation and utilization of deep energy. Here, the optimization of the physical parameters and the deformation law of the overlying rock in a deep mine in Shandong Province were studied with an integrated approach including similar simulation, mechanical analysis, numerical simulation, and measurement verification, etc. First, the paper simplified the rock formation and developed a numerical model using the field exploration data; second, we analyzed the mechanical properties of each rock formation, obtaining the key rock formation that affects the surface deformation of the mining area. Furthermore, we tested the physical parameters of rock formation by using the orthogonal test, optimizing the physical parameters of rock formation with the extreme difference, and variance analysis of the orthogonal test results. Then, using FLAC3D, we conducted numerical calculations for strip mining of deep wells with numerous working faces, analyzing the maximum surface subsidence value, the maximum horizontal movement value of ground surface at different mining depths, and the change in the subsidence coefficient. By analyzing the linkage relationship between the surface phenomenon and deep mining, we obtained the optimal mathematical model of the three and the coal seam mining depth, which revealed the linkage law of “deep formation–earth surface”. Finally, the model relationships of the influence boundary value, maximum subsidence value, maximum horizontal movement value, and mining depth for each rock layer were separately established.

Стохастичний і динамічний підходи при моделюванні процесів поширення шкідливого програмного забезпечення автоматизованих енергетичних об'єктів та їх систем

The rapid development of information technologies in today's conditions makes it possible to control and automate processes and enterprises, institutions to ensure the correct and efficient operation of various energy systems. The mathematical apparatus used in the software for such objects and systems makes it possible to manage their states in various regular conditions. Sometimes unpredictable factors arise in the operation of energy facilities, which can lead to global catastrophes not only for a particular region, but also for all of humanity is the deliberate damage to the logic of the software that controls all the processes of the power system is one of these factors, for the purpose of terror or other malicious purposes. Such factors require the construction of models with which it is possible to predict the scale of risk and extent of damage, as well as to obtain a general estimate of the costs of protecting power system software against such malicious actions. An optimization mathematical model and a corresponding description of the implementation of a complex software tool for modeling the spread of malicious software (malware) in modern energy facilities and systems is the result of the work. The developed optimization mathematical model is based on the use of methods of optimization of functions and functionals with restrictions in the form of systems of ordinary differential equations with given corresponding initial conditions. To develop process simulation software modules based on the PSIDR mathematical model, stochastic population methods, models and algorithms were used to determine the control parameter at each time step. The use of such optimization methods and algorithms makes it possible to solve more complex tasks. It requires a procedure for predicting the spread of processes of various origins in general. The developed mathematical model consists in the minimization of costs for the purchase of antiviruses for the protection of relevant systems in energy facilities and systems. Keywords: malware, prediction, optimization, stochastic model, deterministic model, cellular automaton, energy objects