Mathematical Optimization Model Research Articles

A novel mathematical optimization method to obtain the maximum-power electrical configuration of thermoelectric generators for energy harvesting

Waste thermal energy recovery with thermoelectric generators has been widely studied as a method to make systems that produce hot exhaust gases, such as aircrafts, ground vehicles and factories, more sustainable. In this type of applications, the mismatch in hot and cold side temperatures of thermoelectric modules (TEMs) creates a mismatch in the electrical output. For each situation, there is a certain electrical interconnection between the modules that gives the maximum global power output. Three optimization models to find what is the best way of connecting the TEMs without a trial-and-error process, as usually done in previous literature, based on mathematical programming are proposed: single branch of series-connected TEMs, multiple parallel-connected branches of series-connected TEMs, and multiple groups of independent series-connected TEMs. The main novel contributions of this paper are: (i) a mathematical optimization approach that provides how to connect the thermoelectric modules one by one, (ii) the application of the above-mentioned method in a common case study: an automotive thermoelectric generator, (iii) information about how the optimal connection between modules changes if the heat source changes its operation (iv) a method for selecting a fixed optimal connection even when the heat source operation changes, e.g. different operation modes in a thermal engine, based on introducing weighting parameters in the optimization mathematical model. The optimization approach followed here is novel and has not been applied before to thermoelectric generators.

Collaborative orchard pesticide spraying routing problem with multi-vehicles supported multi-UAVs

The application of UAVs in orchard management presents a substantial opportunity to enhance efficiency and promote environmentally friendly agricultural production. While individual UAVs encounter limitations, such as endurance constraints, these challenges can be mitigated through collaborative efforts involving multiple vehicles and UAVs. This study addresses the issue of multi-UAV cooperative orchard path planning with multiple vehicles by formulating a mathematical optimization model aimed at minimizing the maximum UAV operation time. In the proposed model, the vehicle solely provides batteries and supplies to the UAV. To efficiently solve this model, we propose an improved Simulated Annealing-Lin Kernighan Helsgaun (SA-LKH) algorithm. The proposed algorithm utilizes the K-means and convex hull algorithm to generate the initial solution. Subsequently, the paths of each group of UAVs and vehicles are optimized based on the LKH algorithm. Additionally, we construct a directed perturbation operator that perturbs the maximum and minimum time-consuming paths to achieve fast convergence of the algorithm. The results from four different cases demonstrate that, compared to the general variable neighborhood search algorithm, the improved Ant Colony Algorithm and Improved Genetic Algorithm, the proposed algorithm has demonstrated an average improvement in solution quality of 3.41%, 5.72% and 9.67%, respectively. The proposed method effectively enhances the solution quality, which can provide valuable insights into green cleaning management of orchards.

Optimizing the process of sewage sludge collection for bioenergy generation and biofertilizer production

The conversion of sludge from sewage treatment plants (STPs) into bioenergy is a promising approach to sustainable energy generation and effective waste management. This process occurs through anaerobic digestion in the biodigesters, resulting in biogas production. However, given that the sludge comes from various STPs in different cities, identifying the ideal locations requires careful selection due to the complexity of sludge management, associated costs, and transportation logistics. In this context, this work aims to formulate a mathematical optimization model to determine the best locations for the installation of sludge processing centers, considering the minimization of the economic, environmental, and social costs. The model is implemented in MATLAB software, and geospatial analysis of the regions of interest is performed using QGIS software. For model validation, three distinct instances are considered. The results obtained demonstrate significant potential in terms of biogas and electricity production, with the highest values for the third instance being 61,997,501 Nm³/year and 149,275 MWh/year, respectively. The proposed methodology represents a crucial step toward sustainability, as it promotes the generation and use of bioenergy from STP sludge and contributes to improved waste management and the prevention of air, soil, and water pollution.

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.

Optimal design of water immersion sensor layout for helicopter emergency flotation system based on the nsgaII algorithm

Aiming at the problem of sensor layout in an emergency flotation system, a sensor layout scheme design method based on the NSGAII method is proposed. The ALE method is used to simulate the water landing process of the helicopter on different pitch angles. The logic relationship of the 4/5 voting system is used to improve the sensor module reliability. Further, a mathematical model of layout scheme is established to maximize the detection coverage and minimize the force acting on the water immersion sensors when helicopter emergent water landing as the objective functions. Based on the mathematical model of water immersion sensor layout optimization constructed in this paper, NSGAII is used to solve this problem. The results show that the proposed method can realize the optimization of the layout of the water immersion sensor, the detection coverage of optimized schemes is increased by 3.26% on average compared with the value under the original scheme, and the force acting on the water immersion sensors is reduced by 61.86%.

Differential Diagnosis of Inflammatory Bowel Disease and Functional Bowel Disorder in Children Based on Ultrasonography

Objective: To study the diagnostic efficiency (DE) of sonographic signs in differentiation of inflammatory bowel disease (IBD) and functional bowel disorder (FBD) in children and to develop an optimal mathematical model for differential diagnosis of IBD and FBD using comprehensive assessment of sonographic signs.Material and methods: We examined 79 children with and without clinical signs of large-bowel disease. All the children underwent bowel ultrasonography with strain elastography. We also determined the level of fecal calprotectin (FC). The FC level > 120 μg/g was a cutoff value to differentiate IBD from FBD.Results: We determined the DE of sonographic signs in verification of IBD and FBD: large-bowel wall thickening (DE, 87%; P < .0001), large-bowel wall stratification (DE, 93.1%; P < .0001), enlarged mesenteric lymph nodes (DE, 53.4%; P=.591), interloop ascites (DE, 98.3%; P < .0001), Color Doppler findings in the large-bowel wall (DE, 98.3%; P < .0001), strain elastography findings in the large-bowel wall (DE, 96.5%; P < .0001). We developed an optimal model for differentiation of FBD and IBD using the analysis of sonographic signs (DE, 98.7%).Conclusions: The sonographic signs (large-bowel wall thickening, large-bowel wall stratification, interloop ascites, color Doppler findings in the large-bowel wall, stiffness found on strain elastography) can be effectively used for differential diagnosis of FBD and IBD in children. The developed mathematical model enables to reliably differentiate children with FBD and IBD.

A ReLU-based linearization approach for maximizing oil production in subsea platforms: An application to flow splitting

Oil and gas extraction from subsea reservoirs is a complex process that is highly reliant on accurate mathematical modeling for optimization. A key challenge is identifying control settings to maximize oil production while accounting for the nonlinear behavior and constraints of the underlying physical systems. This paper introduces a new method using Rectified Linear Units (ReLU) neural networks to model these complexities. We focus on a subsea system connecting multiple oil wells to a manifold with multiple headers, explicitly modeling flow splitting to optimize oil yield. Our approach employs mixed-integer reformulations of ReLU neural networks to approximate pressure-drop functions in risers, allowing efficient optimization of production platforms considering routing possibility and flow-splitting operations. Computational analysis employing a branch-and-cut approach and p-split partitioning (for the ReLU model) shows that our ReLU-based methodology converges faster than standard piecewise-linear (PWL) approaches while delivering comparably effective results. Notably, ReLU found solutions in scenarios where PWL failed to find an incumbent solution within the time limit. These results underscore a significant advancement in the optimization of offshore production platforms by using ReLU-based models.

Analysis of Dissolved Oxygen on Tuban Coast Using Remote Sensing Algorithms from Landsat 8 Satellite Image Data and Interpolated Polynomials

Dissolved oxygen is one of the parameters to detect whether a water body is experiencing interference or pollution due to the influence of pollutants and the presence of dirt from outside such as garbage discharges from local communities. Dissolved oxygen plays an important role in the life of biota in the aquatic environment, especially in coastal areas because with sufficient oxygen levels in water bodies, living things will be able to grow and multiply properly. This study wants to try to analyze dissolved oxygen levels in the coastal area of Tuban, where this coast is good for study because the morphology of the beach is relatively gentle and close to the recreation area of Boom Tuban beach. The method used in analyzing the distribution of dissolved oxygen is by remote sensing technology to obtain reflectance values from satellite images used to compile algorithms where later the most optimal mathematical model of dissolved oxygen can be obtained on the coast of Boom. Furthermore, it will also be modeled with a polynomial interpolation approach to obtain the best results from the reflectance relationship of the image with dissolved oxygen levels. The results obtained show that the polynomial approach of degrees 2 and 3 does not provide a significant increase in the correlation value besides that dissolved oxygen levels are still within normal limits, and have not experienced significant pollution so that it does not require expensive coastal handling, only needs monitoring every year to get a healthy water situation to support coastal areas intended for regional tourism.

Study on Reactive Power Optimization Including DSSC for New Energy Access to the Power Grid

The vigorous development of new energy has effectively reduced carbon emissions, but it has also brought fluctuating impacts on the carrying capacity of the power grid. In order to improve the voltage stability after integrating new energy sources and promote the scientific consumption of more new energy, this paper proposes the use of Distributed Static Synchronous Compensator (DSSC) devices for flexible and controllable voltage regulation in new energy integration. An improved particle swarm optimization algorithm is then developed to optimize the reactive power considering the regulation of DSSC. The paper conducts power flow calculations based on the DSSC power injection model and establishes a reactive power optimization mathematical model with objectives of minimizing active power loss, minimizing node voltage deviation, and maximizing voltage stability margin in the grid with new energy integration. The improved particle swarm optimization algorithm is utilized to achieve the reactive power optimization. Experimental simulations are conducted using the IEEE 33-node system to analyze the voltage improvement before and after adopting the improved particle swarm optimization algorithm considering the DSSC device in the grid with new energy integration. It is found that the proposed method effectively reduces active power loss and stabilizes voltage fluctuations, demonstrating its practical value.

A New Method for Optimizing Water-Flooding Strategies in Multi-Layer Sandstone Reservoirs

As one of the most important and economically enhanced oil-recovery technologies, water flooding has been applied in various oilfields worldwide for nearly a century. Stratified water injection is the key to improving water-flooding performance. In water flooding, the water-injection rate is normally optimized based on the reservoir permeability and thickness. However, this strategy is not applicable after oilfields enter the ultra-high-water-cut period. In this study, an original method for optimizing water-flooding parameters for developing multi-layer sandstone reservoirs in the entire flooding process and in a given period is proposed based on reservoir engineering theory and optimization technology. Meanwhile, optimization mathematical models that yield maximum oil recovery or net present value (NPV) are developed. The new method is verified by water-flooding experiments using Berea cores. The results show that using the method developed in this study can increase the total oil recovery by approximately 3 percent compared with the traditional method using the same water-injection amounts. The experimental results are consistent with the results from theoretical analysis. Moreover, this study shows that the geological reserves of each layer and the relative permeability curves have the greatest influence on the optimized water-injection rate, rather than the reservoir properties, which are the primary consideration in a traditional optimization method. The method developed in this study could not only be implemented in a newly developed oilfield but also could be used in a mature oilfield that has been developed for years. However, this study also shows that using the optimized water injection at an earlier stage will provide better EOR performance.

Identification of critical links based on the optimal reliable path in stochastic traffic networks.

In urban stochastic transportation networks, there are specific links that hold great importance. Disruptions or failures in these critical links can lead to reduced connectivity within the road network. Under this circumstance, this manuscript proposed a novel identification of critical links mathematical optimization model based on the optimal reliable path with consideration of link correlations under demand uncertainty. The method presented in this paper offers a solution to bypass the necessity of conducting a full scan of the entire road network. Due to the non-additive and non-linear properties of the proposed model, a modified heuristic algorithm based on K-shortest algorithm and inequality technical is presented. The numerical experiments are conducted to show that improve a certain road link may not necessarily improve the overall traffic conditions. Moreover, the results indicate that if the travel time reliability is not considered, it will bring errors to the identification of key links.

A novel morphing nose cone for underwater gliders: Performance analysis, parameter optimization, and driving mechanism design

As an autonomous underwater vehicle with low energy consumption, underwater glider has been widely applied to long-term ocean exploration missions. To better deal with complex working environments and various mission requirements, morphing underwater gliders are receiving increasing attention. This paper attempts to introduce the morphing nose cone that can achieve length and bending angle adjustments into the glider to improve its comprehensive performance. The performance indicators of the glider include energy utilization rate, static stability, and voyage velocity. Based on dynamic analysis and CFD simulation, performance evaluation models of a glider are established, and the effect of morphing nose cone configurations on the glider's hydrodynamic characteristics is discussed. Then, mathematical optimization models for morphing parameters of the nose cone are established, and they are solved by a multi-objective optimization algorithm and surrogate model technology. Especially, the diving and ascending motion processes of the glider are separately considered in the above optimization. Finally, the multi-objective optimization results are used for guiding the driving mechanism design of the morphing nose cone, and the principle prototype of a novel design scheme is manufactured to verify the feasibility. The research methods and results will provide new development direction for the morphing underwater glider technology.

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.

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.

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.