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A novel multi-objective robust optimization method based on improved Gray Wolf optimizer and Kriging model

PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART C-JOURNAL OF MECHANICAL ENGINEERING SCIENCE 2025年第6期239卷 1872-1892页

作者： Zhang, Hang Li, Yonghua Shi, Shanshan Xia, Qing Chai, Min Dalian Jiaotong Univ Coll Locomot & Rolling Stock Engn Dalian Peoples R China Dalian Jiaotong Univ Sch Mech Engn Dalian Peoples R China

A novel multi-objective robust optimization method for mechanical structure products is introduced. Firstly, the method introduces Bernoulli Dynamic Adaptive Gray Wolf Optimizer (BDAGWO) to address inherent limitations within the original Gray Wolf Optimizer (GWO), such as falling into local optimal solutions and low convergence rate. Subsequently, BDAGWO is utilized to search optimal correlation coefficients of Kriging. The proposed surrogate model exhibits high fitting accuracy on different test cases, with coefficients of determination reaching above 0.99 on the test set, and mean relative error, mean absolute error, mean absolute percentage error and root mean squared error are all close to 0. To solve multi-objective optimization problems, an improved NSGA-II is introduced to amplify search capabilities. Then based on robust optimization method, combine BDAGWO-Kriging and improved NSGA-II to establish a multi-objective robust optimization framework with high accuracy and high solution efficiency. The proposed method is implemented to an EMU bogie frame, demonstrating that the robust optimization scheme reduces the maximum equivalent stress and mass, and exhibits lower fluctuation compared to deterministic optimization. This substantiates the method's effectiveness and provides an optimization approach of large and complex mechanical products.

关键词： Gray Wolf optimizer Kriging model NSGA-II multi-objective robust optimization Bogie frame

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multi-objective robust optimization Reconstruction Algorithm for Electrical Capacitance Tomography

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APPLIED SCIENCES-BASEL 2025年第9期15卷

作者： Yang, Xuejie Lei, Jing Liu, Qibin China Nucl Power Engn Co Ltd Beijing 100840 Peoples R China North China Elect Power Univ Sch Energy Power & Mech Engn Beijing 102206 Peoples R China Chinese Acad Sci Inst Engn Thermophys Beijing 100190 Peoples R China

Electrical capacitance tomography holds significant potential for multiphase flow parameter measurements, but its application has been limited by the challenge of reconstructing high-quality images, especially under complex and uncertain conditions. We propose an innovative multi-objective robust optimization model to alleviate this limitation. This model integrates advanced optimization methods, multimodal learning, and measurement physics, structured as a nested upper-level optimization problem and lower-level optimization problem to tackle the challenges of complex image reconstruction. By integrating supervised learning methodologies with optimization principles, our framework synchronously achieves parameter tuning and performance enhancement. Utilizing the regularization theory, the multimodal learning prior image, sparsity prior, and measurement physics are incorporated into a novel lower-level optimization problem. To enhance the inference accuracy of the prior image, a new multimodal neural network leveraging multimodal data is developed. An innovative nested algorithm that mitigates computational difficulties arising from the interactions between the upper- and lower-level optimization problems is proposed to solve the proposed multi-objective robust optimization model. Qualitative and quantitative evaluation results demonstrate that the proposed method surpasses mainstream imaging algorithms, enhancing the automation level of the reconstruction process and image quality while exhibiting exceptional robustness. This study pioneers a novel imaging framework for enhancing overall reconstruction performance.

关键词： imaging method multi-objective robust optimization multimodal learning information fusion electrical capacitance tomography

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multi-objective robust optimization of the sustainable helical milling process of the aluminum alloy Al 7075 using the augmented-enhanced normalized normal constraint method

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JOURNAL OF CLEANER PRODUCTION 2017年 152卷 474-496页

作者： Dutra Pereira, Robson Bruno Leite, Rodrigo Reis Alvim, Aline Cunha de Paiva, Anderson Paulo Ferreira, Joao Roberto Paulo Davim, J. Univ Fed Sao Joao del Rei Dept Mech Engn 170 Frei Orlando Sq BR-36880000 Sao Joao Del Rei MG Brazil Univ Fed Itajuba Inst Ind Engn & Management 1303 BPS Ave BR-37500903 Itajuba MG Brazil Univ Aveiro Dept Mech Engn Campus Santiago P-3810193 Aveiro Portugal

Helical milling is an eco-friendly hole-making process considering energy economy, tool inventory reduction, tool life cycle increase, set-up and non-productive times reduction due to tools changes and better borehole quality. In order to achieve the best results in terms of the sustainable manufacturing aspects energy, quality, and productivity, the present paper proposes to optimize the multi-objective helical milling process of the aluminum alloy Al 7075. With consideration to sustainable objectives, the axial cutting force component, related to energy consumption, the total roundness, related to borehole geometrical quality, and the material removal rate, related to productivity, were taken into account. The process factors axial and tangential feed per tooth and cutting velocity were selected, besides the noise factor tool overhang length, allowing to optimize bias and variance of cutting force and roundness together with the deterministic response material removal rate. In order to achieve a complete exploitation of the Pareto frontier, the new multi-objective optimization method augmented enhanced normalized normal constraint method was proposed. It was obtained a set of Pareto optimal solutions for the mean square error of the axial cutting force, mean square error of the total roundness, and material removal rate, achieving the trade-off among energy, quality, and productivity. Therefore, different optimization scenarios were obtained, allowing to the experimenter the possibility of choice, guaranteeing a sustainable hole-making process. Furthermore, besides allowing the possibility of choosing different solutions, the TOPSIS decision-making approach was performed so that the best compromise solution was found among the Pareto optimal solutions. The helical milling of the aluminum alloy Al 7075 is presented as a green machining process. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Helical milling Sustainable manufacturing multi-objective robust optimization Mean square error Augmented-enhanced normalized normal constraint

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multi-objective robust optimization of foam-filled tapered multi-cell thin-walled structures

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STRUCTURAL AND multiDISCIPLINARY optimization 2015年第6期52卷 1051-1067页

作者： Yin, Hanfeng Fang, Hongbing Xiao, Youye Wen, Guilin Qing, Qixiang Univ N Carolina Dept Mech Engn & Engn Sci Charlotte NC 28223 USA Hunan Univ Key Lab Adv Design & Simulat Tech Special Equipme Minist Educ Changsha 410082 Hunan Peoples R China

Foam-filled multi-cell thin-walled structure has recently gained attentions for its excellent energy absorption capacity. Tapered thin-walled structure is less likely to fail by global buckling, and is more capable of bearing oblique impact loads. Thus, foam-filled tapered multi-cell thin-walled structure (FTMTS) may be an extremely excellent energy absorber candidate in future vehicle body. This paper focuses on the crashworthiness of four kinds of axisymmetric FTMTSs with different cell numbers. According to our study, we find that FTMTSs have very excellent energy absorption capacity as well as strong capacity of avoiding global buckling. According to our investigation, it was found that the crashworthiness of FTMTS was largely affected by design parameters such as geometric sizes and foam density. In order to find optimal designs of FTMTSs, it is very essential to carry out crashworthiness optimization for FTMTSs. However, the conventional deterministic design is likely to become less meaningful or even unacceptable when considering the uncertainties of design parameters due to the manufacturing or installation deviation. In order to overcome this drawback, a multi-objective robust optimization procedure which employs Kriging metamodels, multi-objective particle swarm optimization (MOPSO) algorithm, "k-sigma" robust design theory and Monte Carlo simulation (MCS) was developed. The comparison of the Pareto fronts obtained by the developed multi-objective robust optimization procedure and the traditional multi-objective deterministic optimization algorithm shows that the robust optimization result is more reliable than the deterministic optimization result. The robust optimal design of FTMTS not only has very excellent crashworthiness but also has very high reliability when considering the uncertainty of design parameters.

关键词： multi-objective robust optimization Monte Carlo simulation Crashworthiness Thin-walled structure Foam-filled structure Tapered energy absorber

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multi-objective robust optimization of foam-filled bionic thin-walled structures

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THIN-WALLED STRUCTURES 2016年 109卷 332-343页

作者： Yin, Hanfeng Xiao, Youye Wen, Guilin Gan, Nianfei Chen, Can Dai, Jinle Hunan Univ State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China Hunan Univ Key Lab Adv Design & Simulat Tech Special Equipme Minist Educ Changsha 410082 Hunan Peoples R China

Bio-inspired design has drawn increased attention in recent years for the excellent structural properties of biological system. In our recent work, a bionic thin-walled structure (BTS), which was inspired from the structural characteristic of horsetail, was found to have excellent crashworthiness (Yin et al., 2015) [1]. In order to further improve the crashworthiness of the BTS, a foam-filled bionic thin-walled structure (FBTS) was investigated using the software LS-DYNA in this study. And, the FBTS was optimized by a multi-objective deterministic optimization (MDO) method. The MDO result indicates that the FBTS performed better than the corresponding traditional structure. However, the deterministic optimal design is likely to become unacceptable when considering the uncertainties of design parameters. To solve this problem, a multi-objective robust optimization (MRO) method which employs ensemble metamodel, NSGA-II, "3-sigma" robust design and Monte Carlo simulation (MCS) was developed. Then, the FBTS was optimized by this MRO method. The comparison of the Pareto fronts of the MDO and MRO shows that the robust optimal FBTS is more reliable than the deterministic optimal FBTS. The robust optimal FBTS not only has excellent crashworthiness but also has high reliability. Therefore, the robust optimal FBTS is a kind of excellent and reliable energy absorber in impact engineering.

关键词： Bionic thin-walled structure Foam-filled Crashworthiness Ensemble metamodel Monte Carlo simulation multi-objective robust optimization

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multi-objective robust optimization method for the modified epoxy resin sheet molding compounds of the impeller

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JOURNAL OF COMPUTATIONAL DESIGN AND ENGINEERING 2016年第3期3卷 179-190页

作者： Qu, Xiaozhang Liu, Guiping Duan, Shuyong Yang, Jichu Hunan Univ State Key Lab Adv Designand Mfg Vehicle Body Changsha 410082 Hunan Peoples R China Zhuzhou Lince Grp Co Ltd Zhengzhou 412001 Peoples R China

A kind of modified epoxy resin sheet molding compounds of the impeller has been designed. Through the test, the non-metal impeller has a better environmental aging performance, but must do the waterproof processing design. In order to improve the stability of the impeller vibration design, the influence of uncertainty factors is considered, and a multi-objective robust optimization method is proposed to reduce the weight of the impeller. Firstly, based on the fluid-structure interaction,the analysis model of the impeller vibration is constructed. Secondly, the optimal approximate model of the impeller is constructed by using the Latin hypercube and radial basis function, and the fitting and optimization accuracy of the approximate model is improved by increasing the sample points. Finally, the micro multi-objective genetic algorithm is applied to the robust optimization of approximate model, and the Monte Carlo simulation and Sobol sampling techniques are used for reliability analysis. By comparing the results of the deterministic, different sigma levels and different materials, the multi-objective optimization of the SMC molding impeller can meet the requirements of engineering stability and lightweight. And the effectiveness of the proposed multi-objective robust optimization method is verified by the error analysis. After the SMC molding and the robust optimization of the impeller, the optimized rate reached 42.5%, which greatly improved the economic benefit, and greatly reduce the vibration of the ventilation system. (C) 2016 Society of CAD/CAM Engineers. Publishing Services by Elsevier.

关键词： multi-objective robust optimization Impeller SMC molding Micro multi-objective genetic algorithm Radial basis function Fluid-structure interaction

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multi-objective robust optimization of active distribution networks considering uncertainties of photovoltaic

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2021年 133卷

作者： Xu, Tao Ren, Yi Guo, Lingxu Wang, Xiaoxue Liang, Lemeng Wu, Yuhan Tianjin Univ Key Lab Smart Grid Minist Educ Tianjin Peoples R China State Grid Tianjin Elect Power Co Tianjin Peoples R China Hebei Univ Technol State Key Lab Reliabil & Intelligence Elect Equip Tianjin Peoples R China

The conventional single objective optimization cannot meet the requirements for the optimal operation of active distribution networks (ADNs) with multiple uncertainties brought by the distributed generation (DG), diverse demand responses and flexible topologies etc. In addition, the contradictions among multiple objectives, the tradeoff between the robustness, conservative, and deterioration of performance, as well as the computation cost have challenged the solution of multi-objective optimization, in particular for the ADNs with multiple uncertainties along with complicated operation scenarios. Considering the uncertainties of distributed photovoltaic (PV), a multi-objective robust optimization strategy for ADNs is proposed in this paper to maximize the utilization of renewables and to minimize the network losses at the same time. By constructing the uncertainty set of predicted PV's maximum outputs, the extreme scenarios of the uncertainty set are chosen to establish constraints, and reduce the dimension of calculation. Then, the multi-objective optimization algorithm can obtain the Pareto fronts under various ranges of uncertainty sets while satisfying the physical and operating constraints of the ADNs, the influence of various ranges of uncertainty set on the Pareto front is taken into consideration. The effectiveness and robustness of the proposed model are verified on a modified IEEE 33 bus system, and the scalability is tested on a 141 bus distribution network.

关键词： Active distribution networks multi-objective robust optimization Distributed photovoltaic Uncertainty set

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multi-objective robust optimization of staff scheduling for emergency under stochastic demand

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EXPERT SYSTEMS WITH APPLICATIONS 2024年 254卷

作者： Hu, Yucong Liu, Qingyang Li, Sitong Wu, Weitiao South China Univ Technol Sch Civil Engn & Transportat Guangzhou 510641 Peoples R China

Large-scale centralized emergency rescue staff scheduling under emergencies has always been a challenge. With a specific focus on nucleic acid testing amid the COVID-19 pandemic, this study introduces a model that considers dynamic changes in staff supply at rescue points, the varying demand at sampling points over time, and their impact on the spread of the epidemic. We quantified the emergency weight of sampling points by the demand and the regional risk degree and adopted robust optimization with base constraint. With the objectives of minimum comprehensive service distance, maximum weighted value of demand satisfaction rate, and minimum loss caused by unmet demand, a multi-stage, multi-medical rescue point medical staff scheduling model for nucleic acid sampling points with the influence caused by uncertain demand disturbance was built, and an improved NSGA-II-HC algorithm was designed to solve the optimization problem under the influence of demand disturbances. The testing results proved that the NSGA-II-HC algorithm can tackle the issue of insufficient uniformity and diversity in the solution set of NSGA-II while multi-objective Particle Swarm optimization (MOPSO) failed to do so. Taking the epidemic data of Guangzhou city in May 2021 as a case study, our model and algorithm are verified to be feasible. We offer a scheme selection strategy according to the loss degree of two conflicting objectives, the comprehensive service distance and shortage loss. The results suggest that, compared with the demand deterministic model, the decision mechanism under the robust model can reduce the deviation from the optimization objective due to the demand disruption.

关键词： Public health event Sampling crew scheduling multi-objective robust optimization Non-dominated sorting genetic algorithm COVID-19

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multi-objective robust optimization design of a front-end underframe structure for a high-speed train

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ENGINEERING optimization 2019年第5期51卷 753-774页

作者： Peng, Yong Hou, Lin Che, Quanwei Xu, Ping Li, Fan Cent S Univ Sch Traff & Transportat Engn Minist Educ Key Lab Traff Safety Track Changsha Hunan Peoples R China Cent S Univ State Key Lab High Performance Complex Mfg Changsha Peoples R China Cent S Univ Joint Int Res Lab Key Technol Rail Traff Safety Changsha Peoples R China CRRC Qingdao Sifang Co Ltd Qingdao Peoples R China Cent S Univ Natl & Local Joint Engn Res Ctr Safety Technol Ra Changsha Hunan Peoples R China Hunan Univ State Key Lab Adv Design & Mfg Vehicle Body Changsha Hunan Peoples R China

A multi-objective robust design optimization of a front-end underframe structure for application in high-speed trains is proposed and the structural parameter uncertainty is considered. A finite element model of the structure is developed and verified by dynamic impact experiments. The sensitivity analysis demonstrates that the thicknesses of the centre sill have significant influences on structural crushing behaviours. The specific energy absorption and the initial peak crushing force (F-p) are taken as optimization objectives. Compared with the baseline structure, the 6-sigma robust design shows that the F-p and the structural mass are reduced by 54.86% and 13.06%, respectively, and the robust optimum is more reliable. The 6-sigma robust optimal solution has an efficient energy-absorbing capacity while satisfying the design constraint. Thus, 6-sigma robust optimization can be applied for high-speed trains.

关键词： multi-objective robust optimization crashworthiness front-end underframe structure

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multi-objective robust optimization of a solar power tower plant under uncertainty

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ENERGY 2022年 238卷

作者： Luo, Yan Wang, Zhiyuan Zhu, Jiamin Lu, Tao Xiao, Gang Chu, Fengming Wang, Ruixing Beijing Univ Chem Technol Sch Mech & Elect Engn Beijing 100029 Peoples R China Zhejiang Univ State Key Lab Clean Energy Utilizat Hangzhou 310027 Peoples R China Chinese Acad Sci Inst Mech Key Lab Mech Fluid Solid Coupling Syst Beijing 100190 Peoples R China Univ Chinese Acad Sci Sch Engn Sci Beijing 100049 Peoples R China

The optimal design of a molten salt solar power tower (SPT) plant is sensitive to the variations of uncertainties, such as solar radiation, which result in dispersion of the model output. To mitigate the impacts of uncertainties on the thermo-economic performance of SPT plant, this study develops an uncertainty-based multi-objective robust optimization design method for the case of a SPT plant in Sevilla with the expected value (i.e. the average energy cost) and the standard deviation (i.e. the dispersion of the model output) of the levelized cost of energy (LCOE) as the objectives. The Monte Carlo (MC) simulation and simulated annealing (SA) algorithm are combined to solve the robust optimization problem. The results of Pareto frontier indicate that a trade-off is needed through decision-making. The final optimal solution is determined with expectation of LCOE of 23.09 c/kWhe and standard deviation of LCOE of 1.25 c/kWhe. Compared with the deterministic optimal design, the standard deviation of LCOE of the multi-objective robust optimum is reduced by 17.22 %, which turns out to be less sensitive to the uncertainties. Moreover, the Sobol' global sensitivity analysis results show that the direct solar radiation, heliostat field cost and receiver cost are the most sensitive to LCOE. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： Solar power tower plant system Uncertainty propagation multi-objective robust optimization Global sensitivity analysis Levelized cost of energy

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