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multiobjective robust optimization method for drawbead design in sheet metal forming

MATERIALS & DESIGN 2010年第4期31卷 1917-1929页

作者： Sun, Guangyong Li, Guangyao Gong, Zhihui Cui, Xiangyang Yang, Xujing Li, Qing Univ Sydney Sch Aerosp Mech & Mech Engn Sydney NSW 2006 Australia Hunan Univ State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China

It is recognized that fracture and wrinkling in sheet metal forming can be eliminated via an appropriate drawbead design. Although deterministic multiobjective optimization algorithms and finite element analysis (FEA) have been applied in this respect to improve formability and shorten design cycle, the design could become less meaningful or even unacceptable when considering practical variation in design variables and noises of system parameters. To tackle this problem, we present a multiobjective robust optimization methodology to address the effects of parametric uncertainties on drawbead design, where the six sigma principle is adopted to measure the variations, a dual response surface method is used to construct surrogate model and a multiobjective particle swarm optimization is developed to generate robust Pareto solutions. In this paper, the procedure of drawbead design is divided into two stages: firstly, equivalent drawbead restraining forces (DBRF) are obtained by developing a multiobjective robust particle swarm optimization, and secondly the DBRF model is integrated into a single-objective particle swarm optimization (PSO) to optimize geometric parameters of drawbead. The optimal design showed a good agreement with the physical drawbead geometry and remarkably improve the formability and robust. Thus, the presented method provides an effective solution to geometric design of drawbead for improving product quality. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： multiobjective robust optimization Sheet metal forming Particle swarm optimization Multicriteria Dual response surface method Drawbead design

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Passenger Evacuation Path Planning in Subway Station Under Multiple Fires Based on multiobjective robust optimization

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2022年第11期23卷 21915-21931页

作者： Yang, Xiaoxia Zhang, Rui Li, Yongxing Pan, Fuquan Qingdao Univ Technol Sch Informat & Control Engn Qingdao 266520 Peoples R China Qingdao Univ Technol Sch Mech & Automot Engn Qingdao 266520 Peoples R China Beijing Univ Technol Beijing Key Lab Traff Engn Beijing 100124 Peoples R China

The optimization of passenger evacuation path in subway station under emergencies directly affects the evacuation efficiency. Aiming at the evacuation scenario of passengers in subway station under multiple fires, a path planning method based on multi-objective robust optimization is established in this paper. The shortest total evacuation time, the minimum total risk and the minimum total congestion cost are taken as the objectives where the robustness of travel time and risk is also considered. NSGA-II algorithm is used to solve the model, the optimal Pareto solution under a certain robust control parameter is obtained according to the principle of minimizing the total cost function, and the overall optimization degree of route is obtained by using the evaluation index. Taking Qingdao May 4th Square subway station of China as a verification example, a fire diffusion model is built by using Pyrosim, and a passenger evacuation system is built by using Pathfinder. The multi-objective robust path optimization model of passenger evacuation is applied to the built passenger evacuation system under fires. The simulation results show that the overall optimization degree of route can reach 12.8% , when the time and risk robust control parameters are 30 and 30, respectively. The method can be used to guide the passenger evacuation in subway stations under multiple hazard sources and improve the safety index of passenger travel.

关键词： Subway station multiobjective robust optimization path planning evacuation network efficiency passenger evacuation fire

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Decision maker iterative-based framework for multiobjective robust optimization

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NEUROCOMPUTING 2017年 242卷 113-130页

作者： Sabioni, Claret Laurente de Oliveira Ribeiro, Marcos Felipe de Vasconcelos, Joao Antonio Univ Fed Minas Gerais Dept Elect Engn Av Antonio Carlos 6627 BR-31270901 Belo Horizonte MG Brazil

In design optimization problems, the robustness of a solution is essential to be considered when it is going to be implemented or used in real world. robustness can be defined in different ways, but in this work, it is considered as the property of a solution's performance to be as insensitive as possible to perturbations in that solution. Optimizing both quality and robustness is generally addressed as a multiobjective problem. This paper presents a complete framework aided by decision maker, which can be used to solve robust optimization problems with one or more objectives. Decision maker actively takes part of the process, defining a priori the robustness metric, and specifying iteratively a robustness factor that joins quality and robustness metrics into a single fitness function. The framework is very flexible allowing decision maker not only to specify the right robustness level for him, but also to exchange metrics and algorithms if he wants. The framework was tested and validated using two single-objective robust benchmarking functions, and in one new multiobjective robust function, created to challenge the framework, which tries to seek the most robust Pareto optimal front according to decision maker preferences. (C) 2017 Elsevier B.V. All rights reserved.

关键词： robust optimization multiobjective robust optimization Decision making robustness metric Evolutionary algorithm

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Crashworthiness design of vehicle by using multiobjective robust optimization

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STRUCTURAL AND MULTIDISCIPLINARY optimization 2011年第1期44卷 99-110页

作者： Sun, Guangyong Li, Guangyao Zhou, Shiwei Li, Hongzhou Hou, Shujuan Li, Qing Univ Sydney Sch Aerosp Mech & Mechatron Engn Sydney NSW 2006 Australia Hunan Univ State Key Lab Adv Technol Vehicle Design & Mfg Changsha 410082 Hunan Peoples R China

Although deterministic optimization has to a considerable extent been successfully applied in various crashworthiness designs to improve passenger safety and reduce vehicle cost, the design could become less meaningful or even unacceptable when considering the perturbations of design variables and noises of system parameters. To overcome this drawback, we present a multiobjective robust optimization methodology to address the effects of parametric uncertainties on multiple crashworthiness criteria, where several different sigma criteria are adopted to measure the variations. As an example, a full front impact of vehicle is considered with increase in energy absorption and reduction of structural weight as the design objectives, and peak deceleration as the constraint. A multiobjective particle swarm optimization is applied to generate robust Pareto solution, which no longer requires formulating a single cost function by using weighting factors or other means. From the example, a clear compromise between the Pareto deterministic and robust designs can be observed. The results demonstrate the advantages of using multiobjective robust optimization, with not only the increase in the energy absorption and decrease in structural weight from a baseline design, but also a significant improvement in the robustness of optimum.

关键词： multiobjective robust optimization Crashworthiness Particle swarm optimization Multicriteria Dual response surface method

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Crashworthiness analysis and multiobjective robust optimization of two-stage variable thickness expansion tube under impact loading

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STRUCTURAL AND MULTIDISCIPLINARY optimization 2022年第6期65卷 178-178页

作者： Jin, Xihong Lu, Jun Guan, Weiyuan Gao, Guangjun CRRC Zhuzhou Locomot Co Ltd Zhuzhou 412001 Peoples R China State Key Lab Heavy Duty AC Dr Elect Locomot Syst Zhuzhou 412001 Peoples R China Cent South Univ Minist Educ Key Lab Traff Safety Track Changsha 410075 Peoples R China Cent South Univ Natl & Local Joint Engn Res Ctr Safety Technol Ra Changsha 410075 Peoples R China

Improving the crashworthiness performance of the expansion tube of the coupler system using the limited deformation space at the vehicle end is of vital significance for the collision safety of trains. Nevertheless, an optimal design could become less meaningful or even unacceptable when some uncertainties are present. To address the issue, this paper firstly proposes a two-stage variable thickness expansion tube for the coupler system and investigates its crashworthiness performance through the impact test and finite element (FE) simulation. Associated with the verified FE model, parametric studies are performed to evaluate the effects of design variables on specific energy absorption (SEA), maximum crushing force (F-max) and crushing force efficiency (CFE). The results show that variation in thickness (t(1), t(2)) of different stages for the expansion tube has a significant effect on CFE, but they have no obvious effects on the SEA. Meanwhile, r(in) and alpha have a significant effect on SEA, while they have a smaller effect on CFE. Furthermore, a multiobjective robust optimization process is developed to address the effects of parametric uncertainties of the expansion tube on design optimization, which comprises a sampling approach, surrogate model, six-sigma-based robust design, the non-dominated sorting genetic algorithm II, Monte Carlo verification and technique for order preference by similarity to ideal solution. It is found that the reliability of constraints (F-max, F-m) of multiobjective robust optimization is increased from 87.0 to 94.4% in the case of two objectives (max [CFE, SEA]) and from 90.0 to 93.3% in the case of three objectives (max [CFE, SEA,- F-max]) compared to those in the deterministic optimization, respectively. Meanwhile, CFE and SEA values in the cases of two objectives (max [CFE, SEA]) and three objectives (max [CFE, SEA,- F-max]) are improved by 17.95%, 5.30% and 16.57%, 15.62% compared to the original structure, respectively. Thus, i

关键词： Expansion tube Variable thickness Crashworthiness design multiobjective robust optimization

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multiobjective robust shape and topology optimization of plane frames using order statistics

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STRUCTURAL AND MULTIDISCIPLINARY optimization 2021年第1期63卷 75-94页

作者： Shen, Wei Ohsaki, Makoto Yamakawa, Makoto Kyoto Univ Dept Architecture & Architectural Engn Nishikyo Ku Kyoto 6158540 Japan Tokyo Univ Sci Dept Architecture Katsushika Ku 6-3-1 Niijuku Tokyo 1258585 Japan

This paper presents a worst-case approach to robust optimization of plane frame structures under variation in uncertain parameters. The optimization procedure is first implemented without considering uncertainty, resulting in an optimal structure that may be unstable without bending stiffness. Based on such optimal solution, we then take variation in uncertain parameters into consideration and estimate the quantile response or trimmed mean of order statistics, where the quantile response is used as a relaxation of worst value of structural response. In order to obtain robust optimal solutions at various robustness levels, a multiobjective optimization problem is formulated and solved to simultaneously minimize the several order statistics or trimmed means with different orders. It is demonstrated in the numerical examples that the optimal distribution of cross-sectional areas of elements vary with the change of robustness level, and the convergence by using trimmed mean as estimation of quantile response is better than that of the simple order statistics.

关键词： Plane frame structure multiobjective robust optimization Order statistics Genetic algorithm

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multiobjective multistage robust integer optimization model and algorithm for oilfield development planning

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COMPUTERS & INDUSTRIAL ENGINEERING 2021年 159卷 107497-107497页

作者： Yan, Sen Ji, Xiaoyu Fang, Yanjun Sun, Hongguo Renmin Univ China Sch Business Beijing 100872 Peoples R China Daqing Oilfield Co Ltd Explorat & Dev Res Inst Daqing 163712 Peoples R China

This paper discusses the long-term planning problem of oilfield development. The planning aims to deploy the workload of stimulation treatments with uncertain indicators. And the uncertainties of initial stimulation effect, annual effect error and new recoverable reserves are considered. With their uncertainty sets and the adaptability of decisions, a multiobjective multistage robust integer optimization model is constructed. In this model, the total development cost is minimized and the total new recoverable reserves is maximized. And the model makes decisions on the workload of each stimulation treatment in each year under constraints of annual oil production and workload balance. In addition, an algorithm for solving multiobjective multistage robust integer optimization model is proposed, which can obtain the finitely adaptive robust efficient solution set. Finally, a numerical example of long-term oilfield development planning is presented. The planning model with given uncertainty sets is solved, to verify the validity of the proposed model and algorithm.

关键词： Oilfield development planning multiobjective robust optimization Multistage robust optimization Integer programming optimization algorithm

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The price of multiobjective robustness: Analyzing solution sets to uncertain multiobjective problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2021年第2期291卷 782-793页

作者： Schoebel, Anita Zhou-Kangas, Yue Tech Univ Kaiserslautern Fac Math Kaiserslautern Germany Tech Univ Kaiserslautern Fraunhofer Inst Ind Math ITWM Kaiserslautern Germany Univ Jyvaskyla Fac Informat Technol POB 35 FI-40014 Jyvaskyla Finland

Defining and finding robust efficient solutions to uncertain multiobjective optimization problems has been an issue of growing interest recently. Different concepts have been published defining what a "robust efficient" solution is. Each of these concepts leads to a different set of solutions, but it is difficult to visualize and understand the differences between these sets. In this paper we develop an approach for comparing such sets of robust efficient solutions, namely we analyze their outcomes under the nominal scenario and in the worst case using the upper set-less order from set-valued optimization. Analyzing the set of nominal efficient solutions, the set of minmax robust efficient solutions and different sets of lightly robust efficient solutions gives insight into robustness and nominal objective function values of these sets of solutions. Among others we can formally prove that lightly robust efficient solutions are good compromises between nominal efficient solutions and minmax robust efficient solutions. In addition, we also propose a measure to quantify the price of robustness of a single solution. Based on the measure, we propose two strategies which can be used to support a decision maker to find solutions to a multiobjective optimization problem under uncertainty. All our results are illustrated by examples. (C) 2020 Elsevier B.V. All rights reserved.

关键词： multiobjective robust optimization Decision making Uncertainty Price of robustness

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Decision making in multiobjective optimization problems under uncertainty: balancing between robustness and quality

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OR SPECTRUM 2019年第2期41卷 391-413页

作者： Zhou-Kangas, Yue Miettinen, Kaisa Univ Jyvaskyla Fac Informat Technol POB 35 Agora Jyvaskyla 40014 Finland

As an emerging research field, multiobjective robust optimization employs minmax robustness as the most commonly used concept. Light robustness is a concept in which a parameter, tolerable degradations, can be used to control the loss in the objective function values in the most typical scenario for gaining in robustness. In this paper, we develop a lightly robust interactive multiobjective optimization method, LiRoMo, to support a decision maker to find a most preferred lightly robust efficient solution with a good balance between robustness and the objective function values in the most typical scenario. In LiRoMo, we formulate a lightly robust subproblem utilizing an achievement scalarizing function which involves a reference point specified by the decision maker. With this subproblem, we compute lightly robust efficient solutions with respect to the decision maker's preferences. With LiRoMo, we support the decision maker in understanding the lightly robust efficient solutions with an augmented value path visualization. We use two measures price to be paid for robustness' and gain in robustness' to support the decision maker in considering the trade-offs between robustness and quality. As an example to illustrate the advantages of the method, we formulate and solve a simple investment portfolio optimization problem.

关键词： multiobjective robust optimization Interactive methods Light robust efficiency Handling uncertainty Trade-off between robustness and quality Decision support

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Nondeterministic multiobjective optimization of 3D printed ceramic tissue scaffolds

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JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS 2023年 138卷 105580页

作者： Entezari, Ali Liu, Nai-Chun Zhang, Zhongpu Fang, Jianguang Wu, Chi Wan, Boyang Swain, Michael Li, Qing Univ Technol Sydney Sch Biomed Engn Sydney NSW 2007 Australia Univ Sydney Sch Aerosp Mech & Mechatron Engn Sydney NSW 2008 Australia Western Sydney Univ Sch Comp Engn & Math Penrith NSW 2751 Australia Univ Technol Sydney Sch Civil & Environm Engn Sydney NSW 2007 Australia

Despite significant advances in the design optimization of bone scaffolds for enhancing their biomechanical properties, the functionality of these synthetic constructs remains suboptimal. One of the main challenges in the structural optimization of bone scaffolds is associated with the large uncertainties caused by the manufacturing process, such as variations in scaffolds' geometric features and constitutive material properties after fabrication. Unfortunately, such non-deterministic issues have not been considered in the existing optimization frameworks, thereby limiting their reliability. To address this challenge, a novel multiobjective robust optimization approach is proposed here such that the effects of uncertainties on the optimized design can be minimized. This study first conducted computational analyses of a parameterized ceramic scaffold model to determine its effective modulus, structural strength, and permeability. Then, surrogate models were constructed to formulate explicit mathe-matical relationships between the geometrical parameters (design variables) and mechanical and fluidic prop-erties. The Non-Dominated Sorting Genetic Algorithm II (NSGA-II) was adopted to generate the robust Pareto solutions for an optimal set of trade-offs between the competing objective functions while ensuring the effects of the noise parameters to be minimal. Note that the nondeterministic optimization of tissue scaffold presented here is the first of its kind in open literature, which is expected to shed some light on this significant topic of scaffold design and additive manufacturing in a more realistic way.

关键词： Tissue scaffold Additive manufacturing Nondeterministic design multiobjective robust optimization Bioceramics Uncertainty Direct ink writing (robocasting)

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