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

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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Uncertainty analysis and multi-objective billet robust optimization for transitional region of multi-rib component under isothermal local loading forming

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2018年第1-4期97卷 1165-1179页

作者： Wei, Ke Fan, Xiaoguang Zhan, Mei Zeng, Xiang Jiang, Xueqi Northwestern Polytech Univ State Key Lab Solidificat Proc Sch Mat Sci & Engn POB 542 Xian 710072 Shaanxi Peoples R China

Isothermal local loading forming is promising to manufacture the large-scale Ti-alloy multi-rib component, but the folding, die underfilling, and strain concentration (SC) are undesired characteristics existing in transitional region due to the reciprocating material transfer between loading region and unloading region. The current research showed that the optimized billet could eliminate or improve these defects. However, it may also lead to unacceptable results due to the variation of the uncertainty factors, such as the manufacturing tolerance of the billet, the fluctuation of the stroke length, friction factor, and forming temperature. Aiming at this issue, an uncertainty analysis and the multi-objective robust optimization of the billet are performed based on 3D finite element simulation and dual-response surface model. Firstly, a valid FE model of the eigenstructure is established to represent the transitional region. Then, the significance analysis of the uncertainty factors is carried out and the significant uncertainty factors are obtained. Subsequently, a multi-objective robust optimization model concerning the mean and standard deviation of the die underfilling rate and average strain of SC zone under the condition of avoiding folding is established. Finally, the Pareto-optimal solutions are obtained by NSGA-II and the minimum distance selection method is employed to acquire the satisfied solution. The comparison results between the robust optimization and deterministic optimization showed that not only the folding is effectively avoided under the uncertainty factors, but also more robust die filling and deformation homogeneity can be achieved.

关键词： multi-rib component Isothermal local loading forming Transitional region Uncertainty analysis multi-objective robust optimization Dual-response surface model

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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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multi-objective robust design optimization of a two-dimensional tri-axial braided hollow pillar using an evolutionary algorithm

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COMPOSITE STRUCTURES 2019年 220卷 105-113页

作者： Yang, Jishi Sun, Dongyang Hu, Ning Ning, Huiming Zhang, Jianyu Ye, Wei Wu, Jian Chongqing Univ Coll Aerosp Engn Chongqing 400044 Peoples R China

In this work, multi-objective robust optimization of a two-dimensional tri-axial braided hollow pillar was presented. Two conflicting objectives, weight and cost, were simultaneously minimized under the constraint of mechanical safety requirements based on Probability theory. The material properties were taken into account with three design variables and two uncontrollable variables. The three design variables were the total fiber volume fraction, the relative volume fraction of carbon fiber in the total fiber volume fraction and the braid angle. The two uncontrollable variables were the fiber volume fraction of the carbon fiber tows and of the glass fiber tows. A mesoscopic analytical model of the two-dimensional tri-axial braided composites (2DTBC) was adopted to obtain the necessary mechanical parameters. Appropriate surrogate models were used to investigate the approximate relationship between the mechanical properties and the input variables, which could significantly reduce the calculation cost. The optimization problem was solved with Pareto optimal solutions through a multi-objective evolutionary solver. The results indicate that, in general, the uncertainty in the total fiber volume fraction was the main decisive factor in the robust optimization and mechanical analysis of the monolithic construction.

关键词： Two-dimensional tri-axial braided composites multi-objective robust optimization Hollow pillar Kriging model

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multi-objective robust design optimization of fatigue life for a welded box girder

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ENGINEERING optimization 2018年第8期50卷 1252-1269页

作者： Wu, Yaozhong Li, Weijia Fang, Jianguang Lan, Qiuhua Huazhong Univ Sci & Technol Sch Naval Architecture & Ocean Engn Wuhan Hubei Peoples R China Univ Technol Sydney Sch Civil & Environm Engn Ctr Built Infrastruct Res Sydney NSW Australia Huazhong Univ Sci & Technol Sch Energy & Power Engn Wuhan Hubei Peoples R China

To reduce the scatter of fatigue life for welded structures, a robust optimization method is presented in this study based on a dual surrogate modelling and multi-objective particle swam optimization algorithm. Considering the perturbations of material parameters and environment variables, the mean and standard deviation of fatigue life are fitted using dual surrogate modelling and selected as the objective function to be minimized. As an example, a welded box girder is presented to reduce the standard deviation of fatigue life. A set of non-dominated solutions is produced through a multi-objective particle swam optimization algorithm. A cognitive approach is used to select the optimum solution from the Pareto sets. As a comparative study, traditional single objective optimizations are also presented in this study. The results reduced the standard deviation of the fatigue life by about 16.5%, which indicated that the procedure improved the robustness of the fatigue life.

关键词： multi-objective robust optimization fatigue design dual surrogate model particle swarm optimization

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multi-objective robust DESIGN optimization AND KNOWLEDGE MINING OF A CENTRIFUGAL FAN THAT TAKES DIMENSIONAL UNCERTAINTY INTO ACCOUNT

MULTI-OBJECTIVE ROBUST DESIGN OPTIMIZATION AND KNOWLEDGE MIN...

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53rd ASME Turbo Expo 2008

作者： Sugimura, Kazuyuki Jeong, Shinkyu Obayashi, Shigeru Kimura, Takeshi Mechanical Engineering Research Laboratory Hitachi Ltd. Japan Institute of Fluid Science Tohoku University JPN Japan Hitachi Appliances Inc. Japan

ISBN: (纸本)9780791843161

A new design approach named MORDE (multi-objective robust design exploration), in which multi-objective robust optimization techniques and data mining techniques are combined, is proposed in this paper. We first developed a widely applicable design framework for multi-objective robust optimization. In this framework, probabilistic representation of design variables are introduced and Kriging models are used to approximate relations between design variables with uncertainty and multiple design objectives. A multi-objective genetic algorithm optimizes the mean and standard deviation of the responses. We then applied the framework to the real-world design problem of a centriftigal fan used in a washer-dryer. Taking dimensional uncertainty into account, we optimized the means and standard deviations of the resulting distributions of fan efficiency and turbulent noise level. Steady Reynolds-averaged Navier Stokes simulations were used to build Kriging models that approximate these objective functions. With the obtained non-dominated solutions, we demonstrated how to analyze features of solutions and select design candidates. We also attempted to acquire design knowledge by applying several data mining techniques. Self-organizing map was used to visualize and reuse the high dimensional design data. Decision tree analysis and rough set theory were used to extract design rules to improve the product's performance. We also discussed differences in types of rules, which were extracted by both methods.

关键词： multi-objective robust optimization genetic algorithm Kriging model data mining Self-organizing map decision tree rough set Taguchi method centrifugal fan

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multi-objective robust Design optimization for Crashworthiness Enhancement of Hybrid 2D Triaxially Braided Composite Tube Using Evolutionary Algorithms

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POLYMERS 2024年第17期16卷 2457页

作者： Sun, Dongyang Jiao, Yudu Tian, Yuanhao Gong, Youkun Li, Leilei Ning, Huiming Jiangsu Univ Sci & Technol Sch Naval Architecture & Ocean Engn Zhenjiang 212003 Peoples R China China State Shipbuilding Corp Lab Sci & Technol Marine Nav & Control Tianjin 300131 Peoples R China Chongqing Univ Coll Aerosp Engn Chongqing 400044 Peoples R China Southwest Technol & Engn Res Inst Chongqing 400039 Peoples R China Chongqing Polycomp Int Corp Chongqing 400084 Peoples R China

An innovative optimal design framework is developed aiming at enhancing the crashworthiness while ensuring the lightweight design of a hybrid two-dimensional triaxial braided composite (2DTBC) tube, drawing insights from the mesostructure of the composite material. To achieve these goals, we first compile the essential mechanical properties of the 2DTBC using a concentric cylinder model (CCM) and an analytical laminate model. Subsequently, a kriging surrogate model to elucidate the intricate relationship between design variables and macroscopic crashworthiness is developed and validated. Finally, employing multi-objective evolutionary optimization, we identify Pareto optimal solutions, highlighting that reducing the total fiber volume and increasing the glass fiber content in the total fiber volume are crucial for optimal crashworthiness and the lightweight design of the hybrid 2DTBC tube. By integrating advanced predictive modeling techniques with multi-objective evolutionary optimization, the proposed approach not only sheds light on the fundamental principles governing the crashworthiness of hybrid 2DTBC but also provides valuable insights for the design of robust and lightweight composite structures.

关键词： two-dimensional tri-axial braided composites crashworthiness surrogate methods genetic algorithm multi-objective robust optimization

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multi-objective robust CROSS-MARKET MIXED PORTFOLIO optimization UNDER HIERARCHICAL RISK INTEGRATION

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JOURNAL OF INDUSTRIAL AND MANAGEMENT optimization 2020年第2期16卷 759-775页

作者： Yang, Han Yue, Jia Huang, Nan-Jing Sichuan Univ Dept Math Chengdu 610064 Sichuan Peoples R China Southwestern Univ Finance & Econ Dept Econ Math Chengdu 610074 Sichuan Peoples R China

In this paper, we consider a multi-objective robust cross-market mixed portfolio optimization model under hierarchical risk integration in the international financial market consisting of finite sub-markets. It is difficult to describe the dependent structure accurately by the traditional copula theory because of the dependent structures of the risk assets in finite sub-markets are different usually. By employing the hierarchical risk integration method, we establish the multi-objective robust cross-market mixed portfolio model in which the worst-case value at risk is used as the risk measurement and the transaction costs, skewness and investment proportion limitation are all considered. We provide a new algorithm to calculate the worst-case value at risk of the cross-market mixed portfolio and give a numerical experiment to show the superiority of the model considered in this paper.

关键词： Cross-market mixed portfolio hierarchical risk integration multi-objective robust optimization worst-case value at risk

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multi-objective minmax robust combinatorial optimization with cardinality-constrained uncertainty

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2018年第2期267卷 628-642页

作者： Raith, Andrea Schmidt, Marie Schoebel, Anita Thom, Lisa Univ Auckland Dept Engn Sci Private Bag 92019 Auckland 1142 New Zealand Erasmus Univ Rotterdam Sch Management Dept Technol & Operat Management POB 1738 NL-3000 DR Rotterdam Netherlands Univ Gottingen Inst Numer & Angew Math Lotzestr 16-18 D-37083 Gottingen Germany

In this paper, we develop two approaches to find minmax robust efficient solutions for multi-objective combinatorial optimization problems with cardinality-constrained uncertainty. First, we extend an existing algorithm for the single-objective problem to multi-objective optimization. We propose also an enhancement to accelerate the algorithm, even for the single-objective case, and we develop a faster version for special multi-objective instances. Second, we introduce a deterministic multi-objective problem with sum and bottleneck functions, which provides a superset of the robust efficient solutions. Based on this, we develop a label setting algorithm to solve the multi-objective uncertain shortest path problem. We compare both approaches on instances of the multi-objective uncertain shortest path problem originating from hazardous material transportation. (C) 2017 Elsevier B.V. All rights reserved.

关键词： multiple objective programming robust optimization Combinatorial optimization multi-objective robust optimization Shortest path problem

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robust emergency logistics network design for pandemic emergencies under demand uncertainty☆

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TRANSPORTATION RESEARCH PART E-LOGISTICS AND TRANSPORTATION REVIEW 2025年 196卷

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

Pandemic emergencies often result in a surge in demand for emergency supplies in affected regions. To expedite the recovery process, ensuring prompt and reliable emergency supplies is crucial, yet the demand for these supplies often exhibits stochastic and time-varying characteristics as the emergency evolves. This paper introduces a two-echelon multi-period locationrouting allocation problem, with the objective of concurrent optimization of facility location, transportation routing, and the allocation of various types of emergency supplies. We integrate a constraint relationship equation that links supplies and cure rate into the established SEIR model to illustrate how emergency supplies counter the spread of the epidemic. In terms of the uncertain demand for various emergency supplies across multiple emergency periods, we quantify the nominal supply demand utilizing an enhanced SEIR model. On this basis, a set of uncertain demands for emergency supplies that are subject to random disturbances in real demand is established. We devise a multi-objective robust optimization model employing a budget-of-uncertainty robust approach to minimize total transportation time, total transportation cost, and shortage of emergency supplies. Subsequently, we develop a customized multi-objective discrete gray wolf algorithm aimed at enhancing solution efficiency. Our model is applied to a real-world case study in Shanghai during the 2022 COVID-19 pandemic. Results have proved that the algorithm is effective and feasible. Managerial insights are also provided.

关键词： Pandemic emergencies Emergency logistics multi-objective robust optimization Uncertainty Gray wolf optimizer

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