Mathematical Optimization Model Research Articles

A comprehensive optimization mathematical model for wind solar energy storage complementary distribution network based on multi-regulatory devices under the background of renewable energy integration

In the context of global energy transformation and sustainable development, integrating and utilizing renewable energy effectively have become the key to the power system advancement. However, the integration of wind and photovoltaic power generation equipment also leads to power fluctuations in the distribution network. The research focuses on the multifaceted challenges of optimizing the operation of distribution networks. It explores the operation and control methods of active distribution networks based on energy storage and reactive power compensation equipment. The stable operation of the distribution network is analyzed under the conditions of wind and photovoltaic integration, with a particular focus on precise regulation to address the limitations of existing methods. Afterwards, the study proposes an improvement plan that combines on load tap changer transformers and reactive power compensation equipment to solve complex power balance problems through second-order cone programming relaxation method. The results of numerical analysis show that the constructed mathematical model maintains a stable voltage of 1 to 1.1 pu at distribution network nodes within 24 h. Especially during peak hours from 15:00 to 24:00, it remains normal without any abnormal fluctuations when the control equipment is not added. These results confirm that precise regulation of multiple devices ensures voltage stability and avoids low or high voltage issues.

Balance of mixed flow assembly line based on industrial engineering mathematics and simulated annealing improved algorithm

The frequent changes in customer orders have led to the need for production line rebalancing and design. The increasing complexity of mixed assembly of multiple products makes it an urgent issue to perfect the balance of mixed flow assembly lines. This study proposes an improved simulated annealing algorithm by combining industrial engineering mathematical methods with intelligent optimization algorithms. The purpose is to achieve balanced optimization of mixed flow assembly lines by minimizing production rhythm, balancing load between workstations, and minimizing loss time within workstations. Firstly, industrial engineering methods are used to analyze the mixed flow assembly line, and then a mathematical optimization model is established by combining simulated annealing algorithm and genetic algorithm. Finally, through example simulation, the effectiveness of the algorithm is verified, and the superiority of its performance is verified through algorithm comparison. The experiment shows that the balance rate of the optimized assembly line for a total of 60 processes in 12 workstations has increased by about 6%. The smoothness index decreases by about 4. The loss coefficient has decreased by approximately 0.06. The overall efficiency has increased by about 12%. The smoothness index decreases by 0.3 in comparison with the solution results of Jackson's law in a case of 11 processes in 5 workstations. This fully demonstrates that the hybrid model has higher optimization efficiency, achieves balanced optimization of the mixed flow assembly line, improves production efficiency, and reduces equipment idle rate.

An optimization model for monthly time-step drilling schedule under planned field production

The field production profile over the yearly horizon is planned for a balance between economy, security, and sustainability of energy. An optimal drilling schedule is required to achieve the planned production profile with minimized drilling frequency and summation. In this study, we treat each possible production process of each well as a dependent time series and the basic unit. Then we ensemble all of them into a tensor. Based on formulated tensor calculation and Lasso regularization, a linear mathematical optimization model for well drilling schedule was developed. The model is aimed at minimizing production profile error while optimizing drilling frequency and summation. Although the model proposed in this work requires more memory consumption to be solved using a computer, it is assured as a linear model and could be numerically globally solved in a stable and efficient way using gradient descent, avoiding complex nonlinear programming problems. Main input data and parameters involved in the model are analyzed in detail to understand the effects of different production parameters on the drilling schedule and production profile. The proposed model in this work can evaluate the manual drilling schedule and automatically generate an optimized drilling schedule for the gas field, significantly reducing development plan formulation time.

GRID-STEP OPTIMIZATION OF THE PARAMETERS OF THERMAL IMPACT ON THE TECHNICAL SYSTEM

The article solves applied problems of optimizing the parameters of technical systems under the influence of concentrated, discrete sources of thermal load. To improve the accuracy and speed of solving applied optimization problems, the authors propose a generalized procedure for finding the optimal thermal load parameters. This procedure consists of well-known computational methods for solving boundary value problems and ensuring the optimization of the objective function and its parameters. To calculate the values of the temperature field, it is necessary to solve a nonlocal boundary value problem of a system of nonlinear differential heat transfer equations. In order to find the conditions for the correctness of boundary value problems, the authors used the theory of pseudo-differential operators in the space of generalized slow power functions. This made it possible to guarantee the correctness of computational and applied optimization mathematical models. The procedure for grid-step optimization of the parameters of thermal action on a multilayer material proposed by the authors is based on a grid approach with discretization of the main parameters of thermal load and grinding of a large uniform grid in the vicinity of the selected node of the large grid. The directed search for local extremes of the mesh model is carried out by the nodes of the crushed mesh. The search for local extrema is performed by selecting the next node of a large grid. This approach will increase the accuracy of solving applied optimization problems by allowing further mesh refinement and refinement of the values of local extremes, and, consequently, refinement of the values of the global extremum of the objective function. The optimization of the thermal impact parameters was carried out according to the criterion of reducing damage to the test material. This makes it possible to increase the accuracy of the technological process of thermal action on a multilayer material.

Pallet Loading Problem: A Case Study in the Automotive Industry Applying a Simplified Mathematical Model

Logistics and the supply chain are areas of great importance within organizations. Due to planning gaps, an increase in extra and unnecessary transport costs is usually observed in several companies due to their commercial commitments and need to comply with the delivery time and the batch quantity of products, leading to a negative economic impact. Thus, the objective of this work was to adjust an optimization model to maximize the shipments usually carried out by the companies. To validate the model, an automotive components manufacturer was selected, allowing us to apply the model to a real case study and evaluate the advantages and drawbacks of this tool. It was found that the company to validate the model exports most of its products, and most pallets sent are not fully optimized, generating excessive expense for the company in terms of urgent transport. To solve this problem, two mathematical optimization models were used for the company’s current reality, optimizing the placement of boxes per pallet and customer. With the use of the new tool, it was possible to determine that five pallets should be sent to the customer weekly, which correspond to their needs, and that have the appropriate configurations so that the pallet is sent completely.

Multi-objective optimization of machining parameters based on an improved Hopfield neural network for STEP-NC manufacturing

Aiming at solving the existing problems of machining parameters optimization for STEP-NC manufacturing, a method for multi-objective optimization of machining parameters based on an improved Hopfield neural network (IHNN) for STEP-NC manufacturing is proposed. In this method, a multi-objective optimization mathematical model of machining parameters compliant with STEP-NC is firstly established taking machining energy, machining time and machining cost as optimization objectives. Next, the IHNN for multi-objective optimization of STEP-NC machining parameters combining with Pareto theory, improved immune algorithm and non-monotone activation function is designed. Based on it, the optimal Pareto solutions of STEP-NC machining parameters are obtained, which intelligently realizes the multi-objective optimization of STEP-NC machining parameters and provides a decision support for the decision-maker. Finally, performance comparisons among the IHNN, classic non-dominated sorting genetic algorithm II (NSGA-II) and multi-objective particle swarm optimization algorithm (MOPSO) are done by classic test functions with three objectives and multiple constraints which correspond to the mathematical model established in this paper, and its effectiveness and feasibility is verified by case study.

Fleet & tail assignment under uncertainty

Airlines solve many different optimization problems and combine the resulting solutions to ensure smooth, minimum-cost operations. Crucial problems are the Fleet Assignment, which assigns aircraft types to flights of a given schedule, and the Tail Assignment, which determines individual flight sequences to be performed by single aircraft. In order to find a cost-optimal solution, many airlines use mathematical optimization models. For these to be effective, the available data and forecasts must reflect the situation as accurately as possible. However, especially in times of a pandemic, the underlying plan is subject to severe uncertainties: Staff and demand uncertainties can even lead to flight cancellations or result in entire aircraft having to be grounded. Therefore, it is advantageous for airlines to protect their mathematical models against uncertainties in the input parameters. In this work, two computational tractable and cost-efficient robust models and solution approaches are developed: First, we set up a novel mixed integer model for the integrated fleet and tail assignment, which ensures that as few subsequent flights as possible have to be canceled in the event of initial flight cancellations. We then solve this model using a procedure that ensures that the costs of the solution remain considerably low. Our second model is an extended fleet assignment model that allows us to compensate for entire aircraft cancellations in the best possible way, taking into account rescheduling options. We demonstrate the effectiveness of both approaches by conducting an extensive computational study based on real flight schedules of a major German airline. It turns out that both models deliver stable, cost-efficient solutions within less than ten minutes, which significantly reduce follow-up costs in the case uncertainties arise.

A bi-objective optimization mathematical model integrated with bulk arrival Markovian queueing system and machine learning in publishing industries

ABSTRACT In the publishing industry, it is vital to comprehend customers’ needs and take their pleasure into account. Thus, publishing houses (PHs) must effectively address the necessity to increase profitability as well as minimize the waiting time of the printing requests in the queue. Although some researchers have studied publishing industries’ management, there is still a lack of research modeling PHs as a practical queueing system that reflects their performance precisely. Moreover, most models have not considered the machine learning technique for predicting the circulation of books integrated with a queueing model and mathematical programming. Furthermore, no study has modeled the PH as a M[X]/M/1 queueing system to practically improve the system. To fill these gaps, this paper develops a novel bi-objective mathematical model with a bulk arrival queueing system and a machine learning technique to minimize the total cost and maximize the resource utilization rate. Also, different machine learning classifier algorithms are implemented to estimate the circulation for each publishing product. Owing to the model’s bi-objective character, an enhanced LP-metrics method is presented. We have also examined a real-world case study to validate our approach and demonstrate its applicability to real-world issues. A 25% increase in profitability served as proof of the model’s effectiveness.

Design and Experiment of a High-Clearance Mid-Tillage Weeder for Dryland Farming

Mechanical weeding is an important technical means for organic and regenerative agricultural systems. Current weed control equipment has a variety of problems, such as difficulty adapting to high-stalk crops and poor operational quality. A high-clearance mid-tillage weeder (HMTW) has been developed to meet the mechanical weed control needs of high-stalk crops. The weeder mainly comprises a suspension device, a frame, parallel four-rod profiling mechanisms, weeding operation components, and depth-limiting soil-cutting devices. Based on the agronomic requirements of dryland flat planting, the overall structure of the HMTW was determined, and the weeding unit and flat shovel hoe were designed. Theoretical analysis was conducted on the depth stability of the HMTW, and an optimization mathematical model of the HMTW was established to further improve its tillage depth stability for agronomic requirements. The optimization objective was to minimize the deflection angle (∆β) of the profiling rod on a vertical plane, and the parameters of the parallel four-rod profiling mechanism were optimized. Based on the optimized structural parameters, a prototype of the HMTW was developed and evaluated. The test results show that the optimized HMTW exhibited a good weeding effect, and the tillage depth stability was within the design operating range. When the driving speed was 1.0 m/s and the tillage depth was 8 cm, the weed removal rate, seedling injury rate, seedling burial rate, and qualified rate of tillage depth were 90.8%, 3.2%, 4.1%, and 94%, respectively. The proposed HMTW successfully meets the weeding agronomic requirements of high-stalk crops for dryland farming, and the performance analysis and optimization models provide technical references for the design and development of such structures.

Modelling assessment of resource competition for renewable basic chemicals and the effect of recycling

AbstractThis work assesses pathways towards a net‐zero greenhouse gas (GHG) emissions chemical industry sector in Germany until 2050, focusing on the ammonia, methanol, ethylene and adipic acid subsectors and the effect of the recycling of C embedded in chemical end products on the GHG abatement cost and primary resource demand. This was done using a bottom‐up mathematical optimization model, including the energy sectors and the chemicals sector, with electricity and biobased options considered. Results show that net‐zero GHG emissions for the considered chemicals in 2050 are attainable at a marginal cost of 640–900 €/tCO2‐eq, even with 26%–36% of demand being satisfied by fossil production routes. This is possible because renewable organic chemicals can act as carbon sinks if, at their end of life, C is permanently stored via landfilling or passed on to the next value chain via recycling. Nonetheless, considering the cost implications, the practical deployment of renewable chemicals is a challenge. The considered renewable chemicals cost 1.3–8 times more than their fossil counterparts, resulting in a marginal CO2 price of 480 €/tCO2‐eq when all primary resources (energy crops, forest residues and renewable electricity) are considered, or 810 €/tCO2‐eq when the availability of arable land is restricted. In the transition to net‐zero emissions for the chemicals under study, a circular economy is important not only for reducing demand for primary resources as is typically the case but also reduces GHG abatement costs by 13%–24% through carbon capture and utilization effects.

IMPROVEMENT OF THE METHODOLOGY FOR OPTIMIZING THE PARAMETERS OF COMPLEX SYSTEMS UNDER THE INFLUENCE OF THERMAL LOAD SOURCES

The article investigates some aspects of solving the problem of constructing mathematical models for optimizing the parameters of local laser action on multilayer microbiological systems. The constraints on the desired laser parameters and on the temperature field in the material subject to laser fission are set. Verification of compliance with the restrictions on not exceeding the maximum value of the temperature field requires multiple calculations of the corresponding temperature field in the microbiological material. Control over the temperature field limits ensures the viability of its parts during the biotechnological process of laser fission. To construct adequate optimization mathematical models, the author substantiates the adequacy of the computational mathematical models describing the state of a microbiological system under the action of laser radiation sources. A multi-point boundary value problem with a system of inhomogeneous differential heat conduction equations for a multilayer microbiological medium is investigated and the correctness of this problem is substantiated for minor perturbations of the right-hand side of the differential equation. The results obtained in the article guarantee the adequacy of applied optimization mathematical models for finding rational values of technical parameters of laser emitters. In order to improve the accuracy of optimization of the technical parameters of laser emitters, the article presents a mathematical modeling of the preparatory stage of embryo defrosting. The presented mathematical models and methods of their implementation are necessary to improve the quality of embryo defrosting. Improvement of the methodology for solving applied biotechnological problems will certainly lead to the complication of mathematical models, but it will increase the accuracy of calculation and optimization of technical parameters of the biotechnological process of laser embryo division.

A linear mathematical optimization model for variable costs calculation in fertilizer production complex

A linear mathematical optimization model for variable costs calculation in fertilizer production complex

Multi-AGV-Driven Pallet-Picking Scheduling Optimization (MADPSO): A Method for Flexible Multi-Level Picking Systems

In the context of increasingly competitive shipbuilding, the flexible multi-level picking system, composed of high-rise shelves, Automated Guided Vehicles (AGVs), and picking stations, has been of gradual interest because of its advantages in operation efficiency, system flexibility, and system robustness. Compared with other simple-level systems, the flexible multi-level picking system has a more complex coupling temporal relationship, which makes the scheduling optimization of shipbuilding automated collaborative order picking (SACOP) extremely difficult. In order to avoid the dilemma of finding a feasible and optimal collaborative scheduling scheme under the constraints of a complex temporal relationship, this paper proposed a multi-AGV-driven pallet-picking scheduling optimization (MADPSO) method, which takes the AGV scheduling scheme as the direct solution and modifies it to a feasible solution under the reasonably designed interaction strategy of stacker, AGV, and the interaction strategy of picking station, AGV. Furthermore, taking the minimum energy consumption and operation time as the optimization objectives, a multi-objective optimization mathematical model was established to describe MADPSO, and an improved NSGA-III algorithm was designed to solve the problem. Finally, several experiments were conducted in various scenarios and verified that using MADPSO can achieve a comprehensive optimization index improvement of 52.02–75.66% compared with traditional picking methods, which has a certain reference significance for shipyards.

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)

Topology optimization of wheel spoke under fatigue tests considering the rotation characteristics of automobile wheels

The topology structure of wheel spoke has a great impact on the safety and lightweight of automobile wheels. However, the rotation process of the wheels is difficult to be reflected in the design and optimization. In this paper, the topology optimization of wheel spoke under fatigue tests considering the rotation characteristics is studied. The bending fatigue test and radial fatigue test are first introduced and the corresponding computation models are presented to calculate the mechanical performances of the wheel hub. The relationship between the internal stress and the number of the wheel spokes is established, and the mechanical performances with different number of wheel spokes are analyzed to guide the selection to the number. Then, the rotation characteristics of the wheel hub are simplified as static loads at different directions or positions according to the configuration of the wheel spokes. A comprehensive evaluation function which includes the test and load levels is defined by the compromise programming method to simulate the stress during the rotation process. Two levels of topology optimization methods are determined. Next, a mathematical model of multi-objective topology optimization for the wheel spoke is established based on the Solid Isotropic Material with Penalization, and a new wheel hub is obtained. Finally, the mechanical performances are compared with the original wheel hub. The obtained results show that the stiffness and strength of the wheel hub are improved under two test conditions, while the weight is reduced by 2.75%.

The use of complex structure splines in roadway design

Objectives. The aim of the work is to develop the theory of spline-approximation of a sequence of points on a plane for using compound splines with a complex structure. In contrast to a simple spline (e.g., polynomial), a compound spline contains repeating bundles of several elements. Such problems typically arise in the design of traces for railroads and highways. The plan (projection on the horizontal plane) of such a trace is a curve consisting of a repeating bundle of elements “line + clothoid + circle + clothoid ...,” which ensures continuity not only of curve and tangent but also of curvature. The number of spline elements, which is unknown, should be determined in the process of solving the design problem. An algorithm for solving the problem with respect to the spline, which consists of arcs conjugated by straight lines, was implemented and published in an earlier work. The approximating spline in the general case is a multivalued function, whose ordinates may be limited. Another significant factor that complicates the problem is the presence of clothoids that are not expressed analytically (in a formula). The algorithm for determining the number of elements of a spline with clothoids and constructing an initial approximation was also published earlier. The present work considers the next stage of solving the spline approximation problem: optimization using a nonlinear programming spline obtained at the first stage by means of the dynamic programming method.Methods. A new mathematical model in the form of a modified Lagrange function is used together with a special nonlinear programming algorithm to optimize spline parameters. In this case, it is possible to calculate the derivatives of the objective function by the spline parameters in the absence of its analytical expression through these parameters.Results. A mathematical model and algorithm for optimization of compound spline parameters comprising arcs of circles conjugated by clothoids and lines have been developed.Conclusions. The previously proposed two-step scheme for designing paths of linear structures is also suitable for the utilization of compound splines with clothoids.

The Mathematical Modeling of the Host-Virus Interaction in Dengue Virus Infection: A Quantitative Study.

Infectious diseases, such as Dengue fever, pose a significant public health threat. Developing a reliable mathematical model plays a crucial role in quantitatively elucidating the kinetic characteristics of antibody-virus interactions. By integrating previous models and incorporating the antibody dynamic theory, we have constructed a novel and robust model that can accurately simulate the dynamics of antibodies and viruses based on a comprehensive understanding of immunology principles. It explicitly formulates the viral clearance effect of antibodies, along with the positive feedback stimulation of virus-antibody complexes on antibody regeneration. In addition to providing quantitative insights into the dynamics of antibodies and viruses, the model exhibits a high degree of accuracy in capturing the kinetics of viruses and antibodies in Dengue fever patients. This model offers a valuable solution to modeling the differences between primary and secondary Dengue infections concerning IgM/IgG antibodies. Furthermore, it demonstrates that a faster removal rate of antibody-virus complexes might lead to a higher peak viral loading and worse clinical symptom. Moreover, it provides a reasonable explanation for the antibody-dependent enhancement of heterogeneous Dengue infections. Ultimately, this model serves as a foundation for constructing an optimal mathematical model to combat various infectious diseases in the future.

A New Car-Body Structure Design for High-Speed EMUs Based on the Topology Optimization Method

In recent years, the research and development of high-speed trains has advanced rapidly. The main development trends of high-speed trains are higher speeds, lower energy consumption, higher safety, and better environmental protection. The realization of a lightweight high-speed car body is one of the key features in the development trend of high-speed trains. Firstly, the basic dimensions of the car body’s geometric model are determined according to the external dimensions of the body of a CRH EMU, and the specific topology optimization design domain is selected to establish the finite element analysis model; secondly, the strength and modal analyses of the topology optimization design domain are carried out to check the accuracy of the design domain and provide a comparative analysis for subsequent design. Then, the variables, constraints, and objective functions of the topology optimization design are determined to establish the mathematical model of topology optimization, and the design domain is calculated for topology optimization under single and multiple conditions, respectively. Finally, based on the topology optimization calculation results, truss-type reconstruction modeling is carried out for the car body’s side walls, roof, underframe, end walls, and other parts. Compared with the conventional EMU body structure, the weight of the reconstructed body structure is reduced by about 18%. The results of the finite element analysis of the reconstructed car-body structure prove the reliability and safety of the structure, indicating that the reconstructed car-body scheme meets the corresponding performance indicators.

Robust optimization modelling of passenger evacuation control in urban rail transit for uncertain and sudden passenger surge

ABSTRACT Effectively addressing the surge in passenger flow caused by emergencies represents a critical challenge in the emergency management of urban rail transit operations. This article introduces a comprehensive control strategy for passenger evacuation, employing robust optimization methods to tackle the uncertainties associated with sudden increases in passenger numbers. Initially, a comprehensive mathematical optimization model for train scheduling and passenger flow coordination is established to ensure efficient passenger transport while maximizing the reduction of operational costs for the operating company’s emergency response. Subsequently, the impact of uncertainty factors on the evacuation model is considered. The fluctuation in passenger flow is represented using a range of intervals, and a robust corresponding model is formulated by introducing an uncertainty budget coefficient. Furthermore, small-scale numerical examples are utilized to discuss passenger evacuation plans, conduct robustness analysis, and assess demand sensitivity. The practical case of the Beijing subway demonstrates that, in contrast to the most optimistic scenario, the robust passenger plan, accounting for a 1% fluctuation in passenger flow, exhibits a reduced cost increase from 10.96% to 9.13%, as compared to the most conservative situation.These findings contribute to enhancing the emergency response capabilities of operational management departments.

Comparison of Total Suspended Solids (TSS) in the estuary of the Bengawan Solo Gresik River using satellite image data

Comparison of Total Suspended Solids (TSS) in Muara Bengawan Solo Gresik River Using Satellite Image Data. The estuary of the Bengawan Solo River, which is in Ujung Pangkah District, has undergone many changes every year. This is influenced by several factors, one of which is the process of settling (sedimentation) from the transport of material carried by river water along the watershed (DAS). Based on this background, efforts are needed to monitor the distribution of Total Suspended Solid (TSS) in the Bengawan Solo Gresik river estuary. The aim of this study is to determine the distribution of Total Suspended Solid (TSS) over 5 years to find the right formula to model the impact of this change, which can be addressed in the future. The method developed below is remote sensing technology with Landsat 8 satellite image data extracting digital number values that are converted into reflectance values to then find the optimal mathematical model algorithm with parameters from Total Suspended Solid (TSS). From the research that has been done, the following results are obtained: the red band reflectance has the best relationship value with TSS In Situ with an R square value of 0.0450. and the appropriate algorithm model for estimating TSS concentrations is the Linear model with the equation Y = 1311.3x + 447.93.