Journal of Zhejiang University

Journal of Zhejiang University SCIENCE A 2014 Vol.15 No.10 P.774-788

Interval multiobjective optimization of structures based on radial basis function, interval analysis, and NSGA-II*

Author(s): Jin Cheng¹,Gui-fang Duan¹,Zhen-yu Liu²,Xiao-gang Li¹,Yi-xiong Feng¹,Xiao-hai Chen³
Affiliation(s): 1. 1. State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China more
Corresponding email(s): gfduan@zju.edu.cn
Key Words: Interval multiobjective optimization, Uncertainty, Radial basis function (RBF), Interval analysis method, Non-dominated sorting genetic algorithm (NSGA-II)

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Jin Cheng, Gui-fang Duan, Zhen-yu Liu, Xiao-gang Li, Yi-xiong Feng, Xiao-hai Chen. Interval multiobjective optimization of structures based on radial basis function, interval analysis, and NSGA-II[J]. Journal of Zhejiang University Science A, 2014, 15(10): 774-788.

@article{title="Interval multiobjective optimization of structures based on radial basis function, interval analysis, and NSGA-II",
author="Jin Cheng, Gui-fang Duan, Zhen-yu Liu, Xiao-gang Li, Yi-xiong Feng, Xiao-hai Chen",
journal="Journal of Zhejiang University Science A",
volume="15",
number="10",
pages="774-788",
year="2014",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A1300311"
}

%0 Journal Article
%T Interval multiobjective optimization of structures based on radial basis function, interval analysis, and NSGA-II
%A Jin Cheng
%A Gui-fang Duan
%A Zhen-yu Liu
%A Xiao-gang Li
%A Yi-xiong Feng
%A Xiao-hai Chen
%J Journal of Zhejiang University SCIENCE A
%V 15
%N 10
%P 774-788
%@ 1673-565X
%D 2014
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A1300311

TY - JOUR
T1 - Interval multiobjective optimization of structures based on radial basis function, interval analysis, and NSGA-II
A1 - Jin Cheng
A1 - Gui-fang Duan
A1 - Zhen-yu Liu
A1 - Xiao-gang Li
A1 - Yi-xiong Feng
A1 - Xiao-hai Chen
J0 - Journal of Zhejiang University Science A
VL - 15
IS - 10
SP - 774
EP - 788
%@ 1673-565X
Y1 - 2014
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A1300311

Abstract
Chinese Summary
Academic Network
Reviewer Comment

Abstract: To improve the multiple performance indices of practical engineering structures under uncertainties, an interval constrained multiobjective optimization model was constructed with structural performance indices included in objectives and constraints being functions of the interval uncertain parameters. An algorithm integrating radial basis function (RBF), interval analysis, and non-dominated sorting genetic algorithm (NSGA-II) was put forward to locate the Pareto-optimal solutions to the interval multiobjective optimization model. A series of RBFs were constructed based on the Latin hypercube experimental design (LHED) and finite element analysis (FEA), which were then integrated with interval analysis to compute the interval bounds of the objective and constraint functions under the fluctuation of uncertain parameters. Then the fitness of every individual during the NSGA-II-based optimization could be obtained. The case study on the optimization of the mechanical performance of a press slider with uncertain material properties demonstrated the feasibility and validity of the proposed methodology.

基于径向基函数、区间分析和非支配排序遗传算法的结构区间多目标优化

研究目的：为改善实际工程结构在不确定性条件下的多性能指标，提供一种高效的区间多目标优化方法。
创新要点：建立一个目标和约束均为区间不确定性参数函数的区间约束多目标优化模型，提出并实现基于径向基函数、区间分析和非支配排序遗传算法（NSGA-II）的区间多目标优化算法。
研究方法：首先，利用区间序关系将每个区间目标转换为同时优化其中点和半径的确定性双目标，利用区间可能度法将区间约束转换为确定性约束，并在此基础上，利用加权法和罚函数法将每个区间目标的约束优化问题转换为相应的无约束优化问题；然后，利用拉丁超立方实验设计和有限元分析构建预测各待优化结构性能指标值的径向基函数；最后，将径向基函数、区间分析法与NSGA-II相结合，快速求出转换后确定性无约束多目标优化问题的所有Pareto最优解，并通过考虑材料不确定性的高速压力机滑块机构设计实例验证该方法的有效性。
重要结论：目标和约束均为不确定性参数函数的区间多目标优化模型能有效反映实际工程中同时改善结构多性能指标的需求。基于径向基函数、区间分析和NSGA-II相结合的区间多目标优化算法将传统区间优化模型求解中的嵌套优化过程简化为单层遗传优化过程，大大提高了求解效率，并可获得多目标优化问题的所有Pareto最优解。
区间多目标优化；不确定性；径向基函数；区间分析法；非支配排序遗传算法（NSGA-II）