Mathematical Optimization Model Research Articles

Modeling for integrated refinery planning with crude-oil scheduling

This work aims to solve the integrated optimization for a complete refinery, which spans from crude oil operations to the refining processes and blending operations. We define a multi-period refinery planning problem by considering the scheduling for crude oil in which the objective function is to maximize the net profit. The optimization procedure simultaneously determines the variables of crude oil scheduling, refinery planning, and blending recipes in each time period. A hierarchical hybrid continuous-discrete time representation is proposed for the integrated optimization problem. This integrated optimization problem yields a Mixed-Integer Nonlinear Programming model for the refinery-wide multi-period optimization. The main contribution of this work is the novel mathematical optimization model proposed for the entire process optimization of refinery production. Computational results with the solvers DICOPT and BARON illustrate the scope of integrated optimization solutions for a real refinery plant with different horizon lengths, demonstrating the tractability, validity, and capability for obtaining near-optimal solutions of the proposed integrated model.

Achromatic and Athermal Design of Aerial Catadioptric Optical Systems by Efficient Optimization of Materials.

The remote sensing imaging requirements of aerial cameras require their optical system to have wide temperature adaptability. Based on the optical passive athermal technology, the expression of thermal power offset of a single lens in the catadioptric optical system is first derived, and then a mathematical model for efficient optimization of materials is established; finally, the mechanical material combination (mirror and housing material) is optimized according to the comprehensive weight of offset with temperature change and the position change of the equivalent single lens, and achieve optimization of the lens material on an athermal map. In order to verify the effectiveness of the method, an example of a catadioptric aerial optical system with a focal length of 350 mm is designed. The results show that in the temperature range of -40 °C to 60 °C, the diffraction-limited MTF of the designed optical system is 0.59 (at 68 lp/mm), the MTF of each field of view is greater than 0.39, and the thermal defocus is less than 0.004 mm, which is within one time of the focal depth, indicating that the imaging quality of the optical system basically does not change with temperature, meeting the stringent application requirements of the aerial camera.

Research on cold chain logistics optimization model considering low-carbon emissions

AbstractCold chain logistics distribution orders have increased due to the impact of COVID-19. In view of the increasing difficulty of route optimization and the increase of carbon emissions in the process of cold chain logistics distribution, a mathematical model for route optimization of cold chain logistics distribution vehicles with minimum comprehensive cost is established by considering the cost of carbon emission intensity comprehensively in this paper.The main contributions of this paper are as follows: 1) An improved hybrid ant colony algorithm is proposed, which combined simulated annealing algorithm to get rid of the local optimal solution. 2) Chaotic mapping is introduced in pheromone update to accelerate convergence and improve search efficiency. The effectiveness of the proposed method in optimizing cold chain logistics distribution path and reducing costs is verified by simulation experiments and comparison with the existing classical algorithms.

Multi-objective optimization of parameters for magnetically coupled resonant wireless energy transmission systems

To improve the transmission efficiency and output power of a magnetically coupled resonant wireless energy transmission system, this paper proposes a multi-objective optimization method based on the analytical expression and the improved NSGA-II algorithm. First, the analytical expressions of the electrical and performance parameters in the magnetically coupled resonant mechanism are derived. On this basis, the mathematical model of the multi-objective optimization of the magnetically coupled mechanism is established, with the size, many turns, and wire diameter of the transmitting and receiving coils in the magnetically coupled mechanism as design variables; the resonant frequency of the system, the distance between the coils, and the load size as constraints; and the transmission efficiency and transmission power as optimization objectives. Then the mathematical model is solved by the improved NSGA-II algorithm to obtain the Pareto optimal solution. Finally, the physical system is built to verify the correctness of the simulation experiment and the reliability of the experiment. This study is instructive for optimizing the transmission efficiency and output power of a magnetically coupled resonant wireless energy transmission system.

Exergoeconomics evaluation on optimal operation conditions in crude oil gathering and transportation system

ABSTRACT At present, most of the energy analysis of the engineering system is only from the energy point of view. In this paper, the theory of exergoeconomics is combined with the operation optimization of the gathering and transportation system. In terms of exergy flow distribution and the construction of each equipment, the exergy value of total 17 exergy flows and the non-energy cost of 6 main equipment in the process are calculated. An exergoeconomic model in technological process of gathering and transportation system is established. Combined with the exergoeconomic cost valuation strategy, 11 auxiliary equations are used to get the economic cost of each flow unit in the process. Taking the minimum operation exergy cost as the objective function, a mathematical model of operation optimization in exergoeconomics is established, and each decision variable is constrained on the basis of the actual site conditions. The objective function within the range of process requirements is solved by iterative method. The optimal water mixing temperature is 47.1°C, and the optimal water mixing volume is 840.7 m3/d under the actual working condition of the site in light of the calculation results.

Vessel scheduling model with resource restriction considerations for restricted channel in ports

Restricted channels differ from ordinary channels because of their external environmental factors; they have many restrictions on vessel scheduling. In particular, for ports with restricted channels and harbor basins, these restrictions affect the safety and efficiency of vessel scheduling, resulting in traffic congestion and causing long delays and waiting times for vessels. Therefore, in this study, we use a mathematical optimization model to optimize vessel scheduling in ports with restricted channel to reduce vessel waiting time, improve vessel transportation efficiency, and ensure transportation safety. We simultaneously considered constraints such as complex navigation rules of restricted channel and scheduling resources to develop the mathematical optimization model. An elite selection genetic algorithm (e-GA) with the vessel service sequence as the code is proposed to solve the optimization model. Finally, using the optimization model, a customized model of the Port of Huanghua was developed based on the actual layout and rules of the port and case studies were conducted. The research results prove the rationality and reliability of the proposed optimization model as well as the effectiveness of e-GA and provide basic theoretical support for expanding this research direction. The results show that compared with the traditional first come first service (FCFS) strategy, the optimization model and e-GA can yield better auxiliary decision making for vessel scheduling in restricted channel and have practical significance.

The optimal design of 3D-printed lattice bone plate by considering fracture healing mechanism.

The biomechanical stimulus is the most important factor for fracture healing and mainly determined by the structural stiffness of bone plate. Currently, the materials commonly used in bone plates are stainless steel and titanium, which often lead to stress shielding effects because of their higher elastic modulus compared with the bone. This article suggests an optimal design method of lattice bone plate based on fracture healing theory. First, the mechanical regulation model with deviatoric strain is established to simulate the tissue differentiation process during fracture healing process. The ratio of the average elastic modulus of callus at the 120th day to the elastic modulus of mature bone is used to characterize the fracture healing rate. Second, the optimal elastic modulus of the design domain is obtained by the optimization mathematical model with the maximum fracture healing rate. Then, the design domain is filled with microstructures, the porosity of which is adjusted to make it possible that the equivalent elastic modulus is equal to the optimized value. And the finite element analysis of the bone plate with microstructure is executed. Finally, the designed lattice bone plates are manufactured through 3D printing, and the mechanical test is carried out. The simulation results indicate that the fracture healing rate is maximum when the elastic modulus of material in design domain is 38 GPa under the constraints of fixation stability. And both the finite element analysis and experiment results show that the designed lattice bone plate meet the strength requirements of fracture internal fixation implants.

Operations research contribution to totally automated radiotherapy treatment planning: A noncoplanar beam angle and fluence map optimization engine based on optimization models and algorithms

The planning of radiotherapy treatments is based on the use of mathematical optimization models and algorithms. A treatment plan will correspond to an admissible solution to a problem that is defined by the medical prescription. The medical prescription defines the constraints that have to be satisfied, and that are patient dependent. To find a treatment plan complying with all the defined constraints, an objective function is built, having a set of parameters that can be tuned. In the clinical practice, the objective function parameters are tuned through a trial-and-error procedure. One common way of defining this objective function is to consider as parameters weights that are related with the importance of the corresponding structures of interest (volumes to treat and organs to spare), as well as upper and lower bounds that are related with the constraints defined by the medical prescription. Some treatment options, like the set of irradiation directions (beam angles), are usually defined beforehand by the planner, considering previous experiences with similar cases. This trial-and-error process is lengthy, since it can take up to several hours to calculate an admissible treatment plan for a single patient. There have been some research efforts to automate the treatment planning procedure, releasing the planner for other important tasks in the radiotherapy treatment workflow and guaranteeing the consistent calculation of high-quality plans. In this work derivative-free optimization algorithms are integrated with fuzzy inference systems that automatically tune the objective function parameters so that an admissible solution is found. This fully automated approach was tested and assessed considering six head-and-neck cancer cases already treated at the Portuguese Institute of Oncology at Coimbra (IPOC). For the clinical cases tested, comparisons between different treatment plans clearly favor the proposed approach. For a similar tumor coverage, it was possible to improve the sparing of the spinal cord, brainstem and parotids. Automating radiotherapy treatment planning can contribute to improved treatment plans in a consistent way.

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

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.