Multi-objective Optimization Mathematical Model Research Articles

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.

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.

Lightweighting Study of Rotary Kiln Cylinder Structure Based on Response Surface

To achieve the lightweight design of the rotary kiln cylinder, reduce its manufacturing costs, and improve its mechanical properties, the maximum stress and deformation were determined through a static and thermal structural analysis of the rotary kiln equipment. Employing the Box-Behnken response surface method, an optimization of the rotary kiln cylinder structure was performed, with the aim of minimizing the cylinder mass and deformation, while considering constraints such as cylinder thickness and yield strength. A multi-objective optimization mathematical model was established, and three sets of Pareto solutions were obtained using a multi-objective genetic algorithm. The optimized design of thickness structure was determined for the stall section, transition section, and cylinder section of the rotary kiln. The finite element method was utilized to simulate the optimized solutions and verify their validity and accuracy. The results showed that the rotary kiln cylinder mass was reduced by 13.8%, and the maximum deformation under static structural conditions was reduced by 4.6%, while maintaining the strength requirement of the structural stiffness. The relevant geometric parameters of the optimal solution were verified by finite element numerical tests, and the optimized cylinder mass, maximum stress and deformation under static structural conditions, and maximum deformation and stress under thermal structural coupling were in good agreement with the numerical test results, with a deviation of less than 2%. Additionally, this study realized the lightweight design of the rotary kiln cylinder and provided useful references for the thickness design of the rotary kiln cylinder.

Research on project schedule optimization model construction and engineering efficiency improvement method

Abstract Project schedule management is an important guarantee for the smooth implementation of the project, which is closely related to the interests of all parties involved in the project, and how to improve the efficiency and quality of the project is a problem that still needs to be solved. In this paper, with reference to the actual situation in the project engineering, the objective function of schedule, cost, quality, and safety is proposed, and the multi-objective optimization mathematical model of the project engineering is obtained through multi-attribute utility theory modeling. Based on the objective function and constraints, the fitness function is established, the constructed model is solved using a genetic algorithm, and safeguard measures are designed to improve the efficiency of project engineering. The empirical results show that the duration and labor demand in the project schedule optimization scheme proposed by the model in this paper are much lower than those in the planning scheme of traditional project schedule optimization methods. Compared to the traditional method, the total cost of the project works decreased by 8.70%, while the quality of the work improved by 0.71%. It shows that the model can improve the quality of project efficiency and enhance the economic benefits of the entire project. The model proposed in this paper makes project schedule optimization more scientific, reasonable, and practical and has certain theoretical and practical significance. In addition, the establishment of a perfect schedule risk management mechanism can be considered in future research in this field to further improve the project schedule optimization model.

Multi-Objective Optimization of a Long-Stroke Moving-Iron Proportional Solenoid Actuator.

In this study, the performance of a long-stroke moving-iron proportional solenoid actuator (MPSA) was improved by combining numerical simulations and experiments. A finite element model of the MPSA was developed; its maximum and mean relative absolute errors of electromagnetic force were 4.3% and 2.3%, respectively, under typical work conditions. Seven design parameters including the cone angle, cone length, depth of the inner hole of the coil skeleton, cone width of the armature, inner cone diameter, and initial position of the moving-iron core were selected for developing the model, and the coefficient of the variation in electromagnetic force, nominal acceleration, 95% of the maximum stable output electromagnetic force, and corresponding response time were used as the performance indicators. The constraint relation between each performance indicator and the influence of each design parameter on the performance indicators were revealed using the uniform Latin hypercube experiment design, correlation analysis, and the main effect analysis method. A multi-objective optimization mathematical model of the MPSA was developed by combining traditional surrogate and machine learning models. The Pareto solution set was obtained using the nondominated sorting genetic algorithm II (NSGA-II), and three decision schemes with different attitudes were determined using the Hurwicz multi-criteria decision-making method. The results showed that a strong contradiction exists among the 95% of the maximum stable output electromagnetic force and its corresponding response time and the coefficient of the variation in electromagnetic force. The cone angle considerably influenced the performance indicators. Compared with the initial design, the coefficient of the variation in electromagnetic force was reduced by 54.08% for the positive decision, the corresponding response time was shortened by 15.65% for the critical decision, and the corresponding acceleration was enhanced by 10.32% for the passive decision. Thus, the overall performance of the long-stroke MPSA effectively improved.

Research on Multi-Objective Optimization Model of Foundation Pit Dewatering Based on NSGA-II Algorithm

This study focuses on optimizing the foundation pit dewatering scheme using the foundation pit dewatering theory and the principles of multi-objective optimization. It explores the development of a multi-objective optimization model and efficient solution technology for foundation pit dewatering. This research focuses on the foundation pit dewatering project at the inverted siphon section of Xixiayuan canal head, specifically from pile number XZ0+326 to XZ0+500. It establishes an optimized mathematical model for foundation pit dewatering that incorporates three objectives. Additionally, a dewatering optimization program is developed by utilizing the MATLAB optimization toolbox and the multi-objective optimization algorithm program based on the NSGA-II algorithm (Gamultiobj). The multi-objective optimization mathematical model is solved, and a Pareto-optimal solution set with uniform distribution is obtained. The multi-objective optimization evaluation system based on AHP is constructed from the three aspects of dewatering cost, the impact of settlement on the environment, and the safety and stability of the foundation pit. The optimization scheme of the Pareto-optimal solution set is selected as the decision result to provide multiple feasible schemes for the dewatering construction of foundation pits. The optimization scheme is verified by using the GMS software. The simulation results demonstrate that the optimization scheme fulfills the requirements for water level and settlement control. Moreover, the developed optimization program efficiently solves the multi-objective optimization problem associated with foundation pit dewatering. Lastly, an evaluation system incorporating the NSGA-II algorithm and AHP is developed and utilized in the context of dewatering engineering in order to offer multiple viable optimal dewatering schemes.

Energy Management Strategy Optimization for a Novel Electric‐hydraulic Power Coupling Vehicle Considering the Influence of Multiple Driving Cycles

Hydraulic hybrid technology can further improve the economy of electric vehicles (EV). In this article, a novel electric‐hydraulic power coupling vehicle (EHPCV), which is endowed with multiple drive modes and energy regenerative braking modes, is investigated. The electric‐hydraulic power coupler (EHPC) is an innovative device for realizing power coupling and conversion. The design and optimization of the energy management strategy (EMS) are key to ensuring the efficient and stable operation of the hybrid electric vehicle. Based on the analysis of energy flow, a rule‐based EMS (RB‐EMS) is built. To achieve more reasonable energy management of the EHPCV in random driving environments, the article proposes an optimization framework for the EMS based on multiple driving cycles. More precisely, a multiobjective optimization mathematical model is established with the goal of maximizing the battery state of charge and minimizing velocity error. Moreover, the optimal Latin hypercube design is used to select the design variables that have a significant impact on the optimization objective. Definitively, the nondominated sorting genetic algorithm II algorithm combines with RB‐EMS to optimize the control parameters. The verification results show that the optimized EMS enables the EHPCV to have superior economic advantages.

Reactive Power compensation Optimization of Distribution Network with Distributed Power Supply

In recent years, distributed generation has been fully developed, and its permeability is rising, which also brings great challenges to the reactive power regulation of the power distribution network. By analyzing the output characteristics of active power and reactive power of distributed power supply, in this article, a multi-objective optimization mathematical model of reactive power compensation is established, which takes the economy and security of the power distribution network into consideration. The results indicate that the reactive power compensation optimization model and the solution algorithm in this paper have good effectiveness and superiority. This thesis will provide the theoretical foundation and technology support for the design and realization of the DG reactive power compensation scheme.

Optimal Control of Rural Water Supply Network Based on Intelligent Algorithm

Optimizing Rural Water Supply Network (RWSN) is the basis for improving rural people’s lives and improving people’s health. Currently, the RWSN in China is relatively backward and can no longer meet the needs of the unified management of rural water resources. To optimize the RWSN, this study innovatively established a Multi-Objective Optimization Mathematical Model (MOMM) of RWSN, combining economic factors and reliability. This experiment first analyzes the characteristics of the RWSN system and then establishes a MOMM of a water supply network. NSGA-II algorithm and LM algorithm are introduced to handle the multi-objective model. The research results show that compared to Web decision tools, the RWSN based on the LM-NSGA-II algorithm can save 5.4% of the total annual cost of water supply pipelines. Therefore, the MOMM of the rural water supply pipeline based on the LM-NSGA-II algorithm has better economy and reliability. The experiment aims to provide certain reference values for the optimal control of RWSN through this study.

Optimization design and analysis of internal gear transmission with double contact points

Internal gear transmission with double contact points is consist of the pinion having circular-arc tooth profile and the internal gear having parabola tooth profile. To further improve load capacity and reduce total volume of internal gear drive with double contact points, a multi-objective and multi-parameter optimization mathematical model is established based on genetic algorithm. Through the comparison analysis, contact stress of tooth surfaces after optimization design is reduced by 21.9% and the volume of gear after optimization design is reduced by 3.93%. Furthermore, contact characteristics of tooth surfaces are discussed considering the parameters optimization of contact angles and pressure angles. Based on Hertz contact theory, theoretical calculations of contact stresses under different contact angles and pressure angles are provided. And finite element method is used to analyze the contact conditions of tooth surfaces to verify theoretical calculation results. Research results show that contact angle of the internal gear pair with double contact points should less than 12.5° and pressure angle of the internal gear pair with double contact points should be 20°–30°.

Optimal calculation of the operation strategy of a distributed heating system combining wind, solar and electrical energy

In this paper, a distributed combined heating system is proposed, composed of an electrically driven air source heat pump (two-stage compression type), solar collector, wind turbine heater, and thermal storage device. A multi-objective optimization mathematical model is established, aiming to minimize the operating cost and carbon dioxide emission during a certain time. The multi-objective planning problem is used to guide solutions to building heating problems in Northern China. Subsequently, for a specific example, the NSGA2 algorithm is used to solve the calculation. Based on the compromise solution of the two optimization objectives, the optimal operation strategy is determined: the amount of heat generated or stored by each device on a typical day. The optimal operating strategy is as follows. In the low heat load period (9:00-16:00), which coincides with the sunny period, the heat production of the solar collectors and the wind turbine heaters exceeds the heat load, and the storage device stores surplus heat. During peak hours (0:00-9:00, 16:00-24:00), the solar collectors are not activated because the solar irradiance is nearly zero. And at this point, the heat production by the wind turbine heaters fluctuates greatly, and the air source heat pump turns out to be the main heating equipment and the heat storage device to release heat when necessary.

Research on a lightweight unmanned sightseeing vehicle frame based on multi-condition and multi-objective optimization

A design method for a lightweight unmanned sightseeing vehicle frame was proposed based on multi-condition and multi-objective optimization to improve the vehicle’s range and reduce its production cost. First, a finite element model of the frame is established, and its static and dynamic characteristics are analyzed. Then, the wall thickness of the middle beam of the frame was selected as the design variable, and its sensitivity was analyzed. Sample points were generated from the design variables using the Latin hypercube sampling method, and the corresponding response values of the sample points were calculated. A Kriging approximation model was established using the sample points and response values and replaced the actual model for optimization. Finally, a multi-condition and multi-objective optimization mathematical model of the frame was established with the minimum mass, maximum first-order natural frequency, and the minimum stresses under full load bending and torsion conditions as the objectives. The multi-objective genetic algorithm was used for the lightweight design by comparing the fuzzy matter element and analytic hierarchy process methods to select the optimal design and to verify the rationality of the final design scheme. The results show that this method results in an optimized frame meeting the strength requirements under various working conditions and reducing the frame mass by 5.4%.

Characteristics analysis and optimization design of bridge crane based on improved particle swarm optimization algorithm

Large redundant metal structures have high stability with large cost. An excellent mechanical structure should have the lower weight when satisfying its stability. Aiming at the large redundancy of the main beam metal structure of the double-beam bridge crane, the paper extracts six important parameters to determine its quality, and the corresponding value is set. The orthogonal test table is designed to calculate the strength and stiffness. In order to avoid resonance, the fixed vibration frequency and excitation frequency are calculated. The experimental results are fitted to obtain the six parameters of the quality, strength, stiffness, and natural frequency. Moreover, particle swarm optimization algorithm is used to solve the multi-objective optimization mathematical model with the design quality as the goal and the stiffness, strength, and easy resonance interval as constraints. In view of the long calculation time and poor convergence of particle swarm optimization algorithm, a module that limits the particle forward speed is added and the generation conditions of particles are redefined. The improved particle swarm algorithm shows that the first-order vibration frequency of the main beam increases from 18 Hz to 27.55 Hz. It improves the stability of the overall structure and avoids resonance with the motor frequency. Under the condition of satisfying the stability of the main beam, the quality of the main beam is reduced from 1.23 tons to 0.53 tons, with a reduction of 6%.

Multiobjective Optimization Management of Construction Engineering Based on Ant Colony Algorithm

In order to solve the problems of extensive management, the construction stage often faces the extension of construction period, excessive cost, and large amount of carbon emission and this paper proposes a multiobjective optimization management method of construction engineering based on ant colony algorithm. Firstly, taking the installation process of laminated plate components as an example, this paper combs the construction process and the consumption types of labor, materials, machinery, or equipment in each process in detail. Then, combined with the idea of multiobjective optimization, the multiobjective optimization mathematical model of construction process is constructed, and the construction data obtained from field investigation are summarized and analyzed to obtain the cost, construction period, and carbon emission of each process under different execution modes. The experimental results show that the ant colony algorithm is used to find the comprehensive optimal process execution mode combination of “cost duration carbon emission.” After optimization, the installation cost of laminated plate components is reduced by 1.55%, the construction period is reduced by 3.52%, and the carbon emission is reduced by 7.36%. The feasibility and rationality of multiobjective optimization in this paper are verified by experiments, which can effectively guide the optimization management of construction process.

Model Matematika Optimasi Multi-Objektif Penurunan Beban Limbah Biochemical Oxygen Demand pada Instalasi Pengolahan Air Limbah

The increase in community activities causes the amount of wastewater to increase. This wastewater comes from industrial production processes and from the community activities which are domestic wastewater. Domestic wastewater must be treated before being discharged to water sources because it contains pathogenic organisms. The place for treating domestic wastewater is Wastewater Treatment Plant (WWTP). The main purpose of WWTP is to degrade the Biochemical Oxygen Demand (BOD) and pathogenic organisms. This study develops a multi-objective optimization mathematical model for reducing the BOD load in the WWTP. This optimization model has three objective functions, namely maximizing the BOD load that is treated in the pond minimizing the difference between the BOD reduction efficiency value in the WWTP with the reference efficiency value and minimizing the power used by the aerator. The simulation results show that the maximum BOD load that can be treated in facultative ponds I and II is 1,589.688 Kg/day while for facultative ponds III and IV is 1,727.158 Kg/day. The efficiency value of reducing BOD load is influenced by the residence time variable, where the efficiency value of reducing the BOD load for facultative ponds I and II by 54% while for facultative ponds III and IV by 57%. The power used by the aerator is influenced by the treated BOD load variable, the aerator power in facultative ponds I and II is 49.67775 Kwh while in facultative ponds III and IV it is 53.97369 Kwh.

Reliability analysis of autonomous underwater vehicle aft pressure shell for optimal design and strength

The lightweight design of the autonomous underwater vehicle (AUV) is a means to improve its resistance. In order to meet reliability requirements of AUV, the lightweight optimization design of aft pressure shell (APS) with sandwich structure is studied. A multi-objective optimization mathematical model is established for the mass and maximum stress as objectives and the strength as constraint condition, which is efficiently adopted by NSGA-II based on Kriging surrogate model. In the reliability analysis, the statistical distributions of the yield strength and the maximum stress is obtained according to the random variable sample and finite element method and then the stress-strength interference model is established. The result shows that the APS with sandwich structure meets the strength requirements and the maximum stress appears near outer skin. The thickness of the sandwich structure has a great influence on the mass and maximum stress. The reliability index of the optimized APS is 5.02, which satisfies three sigma level of random variables and ensures safety and reliability of AUV. The analysis provides reference and technical support for lightweight of pressure shell.

Multiobjective Optimization for Planning the Service Areas of Smart Parcel Locker Facilities in Logistics Last Mile Delivery

The planning of the location service areas of smart parcel locker facilities became a critical aspect of logistics last mile delivery. In e-commerce, the efficiency of delivering merchandise from retailer warehouses to customers determines the competitiveness of retailers and delivery operators. The considerable increases in e-commerce transactions and safety concerns under the COVID-19 (Coronavirus disease 2019) pandemic made home delivery services even more inefficient than before, which resulted in the considerable increase in social costs. In numerous countries, smart parcel lockers were adopted to increase delivery efficiency, decrease the risk of COVID-19 infection, and reduce the burden on society. This study proposed a multiobjective optimization mathematical model for investigating the planning of the location service areas of smart parcel locker facilities, and then the optimization mathematical model was solved using a combination of the Taguchi method (TA) and nondominant sorting genetic algorithm II (NSGA-II). Finally, this composite approach was applied to a case study in producing favorable solutions for facility location service area planning.

Optimization of the transmission characteristics of an HMCVT for a high-powered tractor based on an improved NSGA-II algorithm

The hydro-mechanical continuously variable transmission (HMCVT) is a critical component of the power transmission system in a tractor. However, the complexity of the operating conditions imposes high requirements on the transmission characteristics. To improve the powerful performance and economy of HMCVTs and satisfy the operational demands of high-powered tractors, a new optimization design method for the characteristic parameters of an HMCVT is proposed. First, the characteristics of an HMCVT are modeled, and the influence of the structural parameters on the transmission characteristics is analyzed. Then, HMCVT performance evaluation indexes are formulated. In accordance with the speed regulation of system, power performance, and economy characteristics, a multi-objective optimization mathematical model is established, and an improved fast non-dominated sorting genetic algorithm (INSGA-II) is designed. The introduction of a normal distribution crossover operator (NDX) and an improved adaptive adjustment mutation operator not only ensures the population diversity but also improves the Pareto solution convergence properties during the process of genetic evolution. The superiority of INSGA-II is verified by comparison with a traditional multi-objective genetic algorithm. Finally, the optimization results show that the torque ratio is increased by approximately 2.81%, 14.32%, 2.31%, and 15.07% in HM1, HM2, HM3, and HM4 respectively. The transmission efficiency is increased by approximately 3.48% and 1.97% in HM1 (HM3) and HM2 (HM4). Also, INSGA-II finds the optimal solution with a faster speed and shorter optimization time than MULGA. This research can serve as a reference for the design and optimization of HMCVTs for high-powered tractors.

Integrated Optimization Method of IPPS under TOU and Tiered Electricity Price

Energy-saving production is one of the issues that must be paid attention to by today’s manufacturing enterprises. Aiming at the problem of integrated process planning and scheduling (IPPS) in the manufacturing process, considering Time-of-Use (TOU) and tiered electricity price, this paper systematically studies the energy-saving scheduling problem in order to reduce the power consumption in processing and production. To establish the multiobjective optimization mathematical model of the problem, the load balancing problem of the equipment is considered, the minimization of the power consumption and the maximum load of the equipment are taken as the optimization objectives. Then, considering the constraints of resource and multiprocess, the switching strategy of the equipment in idle time is introduced, including shutdown and restart operations. In order to solve the model easily, a multiobjective firefly algorithm (MOFA) based on five-layer coding is designed, and the elite strategy is introduced to protect the excellent firefly individuals in the iterative population. Finally, through a specific example, the Pareto solution set is obtained, which provides a reference scheme for decision-makers, and verifies the correctness of the model and the effectiveness of the algorithm.

Underground space optimization of smart city based on information processing technology

This study explores the underground space optimization method of smart city based on information processing technology to save space optimization operation time. Taking coordinate of intersection point, radius of intersection point, mileage of vertical slope change point and elevation of slope change point as design variables, taking total cost of underground space construction of smart city as objective function and taking plane, vertical section, horizontal and vertical combination and environmental impact as constraint conditions, a multi-objective optimization mathematical model of underground space of smart city was constructed. Parete genetic algorithm in information processing technology was used to solve the multi-objective optimization mathematical model of the underground space of smart city, realize the automatic search for the optimal scheme of the underground space of smart city, and complete the intelligent optimization process of the underground space construction scheme of smart city. The results show that the method obtained from this study can effectively optimize the underground space of smart city and obtain the optimal subway laying line, save space and optimize operation time and improve the convergence of the method.