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multi-objective robust optimization Reconstruction Algorithm for Electrical Capacitance Tomography

APPLIED SCIENCES-BASEL 2025年第9期15卷 4778-4778页

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

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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 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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Free vibration analysis and multi-objective robust optimization of three-dimensional pyramidal truss core sandwich plates with interval uncertain parameters

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EUROPEAN JOURNAL OF MECHANICS A-SOLIDS 2024年 108卷

作者： Chen, Yugeng Zhong, Rui Wang, Qingshan Chen, Liming Qin, Bin Cent South Univ Coll Mech & Elect Engn Changsha 410083 Peoples R China Cent South Univ State Key Lab Precis Mfg Extreme Serv Performance Changsha 410083 Peoples R China Cent South Univ Sch Traff & Transportat Engn Key Lab Traff Safety Track Minist Educ Changsha 410075 Peoples R China Cent South Univ Joint Int Res Lab Key Technol Rail Traff Safety Changsha 410075 Peoples R China Cent South Univ Natl & Local Joint Engn Res Ctr Safety Technol Rai Changsha 410075 Peoples R China

In this study, the free vibration analysis and multi-objective robust optimization of three-dimensional pyramidal truss core sandwich plates with interval uncertain parameters are fulfilled. The numerical model for free vibration of the plate is derived by combining the three-dimensional elasticity theory and Rayleigh-Ritz method, and the validity of the model is illustrated by numerical results. On this basis, considering various uncertainties within the plate, a new uncertainty-propagation analysis method is constructed by integrating the numerical model, interval-analysis model, kriging model and optimization. The one-dimensional and multi-source uncertainty-propagation analysis of the fundamental frequency is finished using this method, and the accuracy is proved by comparing with Monte Carlo simulation results. Meanwhile, to minimize the effects of uncertainties on the performance of plates at the design stage, an objective multi-objective robust optimization model with the objectives of maximizing the fundamental frequency and minimizing the robustness factor is established. Finally, an improved pelican optimization algorithm is proposed by introducing the improved opposition-based learning strategy, tracking strategy with step control and convergence strategy. And the Pareto front and corresponding design schemes applicable to different working environments are obtained without repeating the optimization.

关键词： Three-dimensional pyramidal truss core sandwich plates Interval uncertainty Free vibration multi-objective robust optimization Improved pelican optimization algorithm

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

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ENERGY 2022年第PartA期238卷 121716-121716页

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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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 107197-107197页

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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Smart charging and discharging of electric vehicles based on multi-objective robust optimization in smart cities

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APPLIED ENERGY 2023年第1期343卷

作者： Yao, Zhaosheng Wang, Zhiyuan Ran, Lun Beijing Inst Technol Sch Management & Econ Beijing 100081 Peoples R China

The combination of low-carbon electricity and electric vehicles brings considerable economic and environmen-tal benefits but also introduces challenges due to the complexity and uncertainty of system synergies in smart cities. To fully exploit the advantages of photovoltaic power generation and electric vehicles and to release the potential of electric vehicles as distributed energy storage facilities, this paper develops a multi-objective robust optimization framework that accounts for the benefits of multiple parties of smart charging and discharging systems and depicts a bounded uncertainty set based on partial statistical information from real data. The original model is scalarized and linearized using efficient methods such as max-ordering scalarization and the robust augmented weighted Tchebycheff to facilitate the solution. Moreover, a smart charging and discharging scheduling strategy based on a convergent demand response strategy is proposed to achieve better demand -side management. A case study, based on real data from Car2go and the solar radiation intensity in Portland, Oregon, shows that (1) The methodological framework effectively addresses the smart scheduling issue that considers the interests of multiple parties in complex systems with uncertainty, in contrast to conventional methods. (2) The designed convergent demand response strategy promotes photovoltaic power generation and charging demand synergy and achieves regulation effects such as peak shaving and valley filling. (3) The proposed method and strategy yield good results in multiple aspects, such as charging costs, load regulation, and clean energy utilization, while enhancing the economic and environmental benefits.

关键词： Smart charging and discharging multi-objective robust optimization Photovoltaic power generation Demand-side management Economic and environmental benefits

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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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An interval-based multi-objective robust design optimization for vehicle dynamics

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MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES 2023年第12期51卷 7076-7101页

作者： Centeno Drehmer, Luis Roberto Gomes, Herbert Martins Paucar Casas, Walter Jesus Univ Fed Santa Maria Dept Mech Engn Campus Cachoeira SulAv Presidente Vargas 1958 BR-96506302 Cachoeira Do Sul RS Brazil Univ Fed Rio Grande do Sul Dept Mech Engn Porto Alegre RS Brazil

This study presents an Interval-based multi-objective robust Design optimization (IB-MORDO) algorithm applied to a vehicle dynamic problem. The proposed algorithm optimizes a full 15 degrees-of-freedom (15-DOF) vehicle model, subjected to a double-lane change (DLC) maneuver under random road profiles, to attain driver comfort and safety. This study does not make assumptions about uncertain parameter statistics;instead, the uncertainties are quantified using a non-probabilistic x-cut level interval analysis. These uncertainties are applied to the system parameters and design variables to ensure robust results. After the optimization process, the root mean square (RMS) vertical acceleration at the driver's seat resulted in a robust solution of 1.041 m/s(2) and a parameter interval radius (IR) equals to 0.631 m/s(2), whereas the RMS lateral acceleration at the driver's seat resulted in a solution of 1.908 m/s(2) with an interval radius of 0.168 m/s(2). Unlike the robust optimization, the algorithm proposed herein considers uncertainties at system parameters and design variables without assuming any statistical data.

关键词： multi-objective robust optimization uncertainty quantification alpha-cut level method multibody system dynamics Pareto frontier

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An Efficient multi-objective robust optimization Method by Sequentially Searching From Nominal Pareto Solutions

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JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING 2021年第4期21卷 041010-041010页

作者： Xia, Tingting Li, Mian Shanghai Jiao Tong Univ Univ Michigan Shanghai Jiao Tong Univ Joint Inst Shanghai 200030 Peoples R China Shanghai Jiao Tong Univ Dept Automat Shanghai 200240 Peoples R China

multi-objective optimization problems (MOOPs) with uncertainties are common in engineering design. To find robust Pareto fronts, multi-objective robust optimization (MORO) methods with inner-outer optimization structures usually have high computational complexity, which is a critical issue. Generally, in design problems, robust Pareto solutions lie somewhere closer to nominal Pareto points compared with randomly initialized points. The searching process for robust solutions could be more efficient if starting from nominal Pareto points. We propose a new method sequentially approaching to the robust Pareto front (SARPF) from the nominal Pareto points where MOOPs with uncertainties are solved in two stages. The deterministic optimization problem and robustness metric optimization are solved in the first stage, where nominal Pareto solutions and the robust-most solutions are identified, respectively. In the second stage, a new single-objective robust optimization problem is formulated to find the robust Pareto solutions starting from the nominal Pareto points in the region between the nominal Pareto front and robust-most points. The proposed SARPF method can reduce a significant amount of computational time since the optimization process can be performed in parallel at each stage. Vertex estimation is also applied to approximate the worst-case uncertain parameter values, which can reduce computational efforts further. The global solvers, NSGA-II for multi-objective cases and genetic algorithm (GA) for single-objective cases, are used in corresponding optimization processes. Three examples with the comparison with results from the previous method are presented to demonstrate the applicability and efficiency of the proposed method.

关键词： multi-objective robust optimization robust Pareto front nominal Pareto front robustness metric vertex estimation computer-aided design model-based systems engineering multidisciplinary optimization

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