JZUS - Journal of Zhejiang University SCIENCE

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. 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）

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References

[1] Ben-Haim, Y., 1995. A non-probabilistic measure of reliability of linear systems based on expansion of convex models. Structural Safety, 17(2):91-109.

[2] Boyd, J.P., 2011. The near-equivalence of five species of spectrally-accurate radial basis functions (RBFs): asymptotic approximations to the RBF cardinal functions on a uniform, unbounded grid. Journal of Computational Physics, 230(4):1304-1318.

[3] Bozkurt Gnen, G., Gnen, M., Grgen, F., 2012. Probabilistic and discriminative group-wise feature selection methods for credit risk analysis. Expert Systems with Applications, 39(14):11709-11717.

[4] Chen, S.M., Yang, M.W., Yang, S.W., 2012. Multicriteria fuzzy decision making based on interval-valued intuitionistic fuzzy sets. Expert Systems with Applications, 39(15):12085-12091.

[5] Cheng, J., Feng, Y.X., Tan, J.R., 2008. Optimization of injection mold based on fuzzy moldability evaluation. Journal of Materials Processing Technology, 208(1-3):222-228.

[6] Cheng, J., Liu, Z.Y., Tan, J.R., 2013. Multiobjective optimization of injection molding parameters based on soft computing and variable complexity method. The International Journal of Advanced Manufacturing Technology, 66(5-8):907-916.

[7] Deb, K., 2001. Multi-objective Optimization Using Evolutionary Algorithms. John Wiley & Sons,New York, USA :

[8] de Oliveira, M.A., Possamai, O., Valentina, L.V.O.D., 2013. Modeling the leadership–project performance relation: radial basis function, Gaussian and Kriging methods as alternatives to linear regression. Expert Systems with Applications, 40(1):272-280.

[9] Guo, X., Bai, W., Zhang, W.S., 2009. Confidence structural robust design and optimization under stiffness and load uncertainties. Computer Methods in Applied Mechanics and Engineering, 198(41-44):3378-3399.

[10] Hu, B.Q., Wang, S., 2006. A novel approach in uncertain programming part I: new arithmetic and order relation for interval numbers. Journal of Industrial and Management Optimization, 2(4):351-371.

[11] Ishibuchi, H., Tanaka, H., 1990. Multiobjective programming in optimization of the interval objective function. European Journal of Operational Research, 48(2):219-225.

[12] Jiang, C., Han, X., Liu, G.P., 2007. Optimization of structures with uncertain constraints based on convex model and satisfaction degree of interval. Computer Methods in Applied Mechanics and Engineering, 196(49-52):4791-4800.

[13] Jiang, C., Han, X., Guan, F.J., 2007. An uncertain structural optimization method based on nonlinear interval number programming and interval analysis method. Engineering Structures, 29(11):3168-3177.

[14] Jiang, C., Han, X., Liu, G.P., 2008. A nonlinear interval number programming method for uncertain optimization problems. European Journal of Operational Research, 188(1):1-13.

[15] Jiang, C., Han, X., Liu, G.P., 2008. A sequential nonlinear interval number programming method for uncertain structures. Computer Methods in Applied Mechanics and Engineering, 197(49-50):4250-4265.

[16] Jiang, C., Han, X., Liu, G.P., 2008. Uncertain optimization of composite laminated plates using a nonlinear interval number programming method. Computers and Structures, 86(17-18):1696-1703.

[17] Li, F.Y., Luo, Z., Sun, G.Y., 2013. Interval multi-objective optimisation of structures using adaptive Kriging approximations. Computers & Structures, 119(1):68-84.

[18] Li, F.Y., Luo, Z., Sun, G.Y., 2013. An uncertain multidisciplinary design optimization method using interval convex models. Engineering Optimization, 45(6):697-718.

[19] Li, X.G., Cheng, J., Liu, Z.Y., 2014. Robust optimization for dynamic characteristics of mechanical structures based on double renewal Kriging model. Journal of Mechanical Engineering, 50(3):165-173.

[20] Liu, B.D., Iwamura, K., 2001. Fuzzy programming with fuzzy decisions and fuzzy simulation-based genetic algorithm. Fuzzy Sets and Systems, 122(2):253-262.

[21] Luo, Y.J., Kang, Z., Luo, Z., 2009. Continuum topology optimization with non-probabilistic reliability constraints based on multi-ellipsoid convex model. Structural and Multidisciplinary Optimization, 39(3):297-310.

[22] Luo, Y.J., Li, A., Kang, Z., 2011. Reliability-based design optimization of adhesive bonded steel-concrete composite beams with probabilistic and non-probabilistic uncertainties. Engineering Structures, 33(7):2110-2119.

[23] Luo, Z., Chen, L.P., Yang, J.Z., 2006. Fuzzy tolerance multilevel approach for structural topology optimization. Computers & Structures, 84(3-4):127-140.

[24] Marler, R.T., Arora, J.S., 2004. Survey of multi-objective optimization methods for engineering. Structural and Multidisciplinary Optimization, 26(6):369-395.

[25] Qasem, S.N., Shamsuddin, S.M., 2011. Radial basis function network based on time variant multi-objective particle swarm optimization for medical diseases diagnosis. Applied Soft Computing, 11(1):1427-1438.

[26] Qasem, S.N., Shamsuddin, S.M., 2011. Memetic elitist Pareto differential evolution algorithm based radial basis function networks for classification problems. Applied Soft Computing, 11(8):5565-5581.

[27] Qasem, S.N., Shamsuddin, S.M., Zain, A.M., 2012. Multi-objective hybrid evolutionary algorithms for radial basis function neural network design. Knowledge-Based Systems, 27:475-497.

[28] Qiu, Z.P., Wang, X.J., 2003. Comparison of dynamic response of structures with uncertain non-probabilistic interval analysis method and probabilistic approach. International Journal of Solids and Structures, 40(20):5423-5439.

[29] Roy, R., Azene, Y.T., Farrugia, D., 2009. Evolutionary multi-objective design optimisation with real life uncertainty and constraints. CIRP Annals-Manufacturing Technology, 58(1):169-172.

[30] Salehghaffari, S., Rais-Rohani, M., Marin, E.B., 2013. Optimization of structures under material parameter uncertainty using evidence theory. Engineering Optimization, 45(9):1027-1041.

[31] Schuller, G.I., Jensen, H.A., 2008. Computational methods in optimization considering uncertainties–an overview. Computer Methods in Applied Mechanics and Engineering, 198(1):2-13.

[32] Sun, G.Y., Li, G.Y., Gong, Z.H., 2011. Radial basis functional model for multi-objective sheet metal forming optimization. Engineering Optimization, 43(12):1351-1366.

[33] Tootkaboni, M., Asadpoure, A., Guest, J.K., 2012. Topology optimization of continuum structures under uncertainty–a polynomial chaos approach. Computer Methods in Applied Mechanics and Engineering, 201-204:263-275.

[34] Wang, Z.J., Li, K.W., 2012. An interval-valued intuitionistic fuzzy multiattribute group decision making framework with incomplete preference over alternatives. Expert Systems with Applications, 39(18):13509-13516.

[35] Wang, Z.J., Li, K.W., Xu, J.H., 2011. A mathematical programming approach to multi-attribute decision making with interval-valued intuitionistic fuzzy assessment information. Expert Systems with Applications, 38(10):12462-12469.

[36] Wang, Z.L., Huang, H.Z., 2010. A unified framework for integrated optimization under uncertainty. Journal of Mechanical Design, 132(5):051008

[37] Wu, J.L., Luo, Z., Zhang, Y.Q., 2013. Interval uncertain method for multibody mechanical systems using Chebyshev inclusion functions. International Journal for Numerical Methods in Engineering, 95(7):608-630.

[38] Yao, W., Chen, X.Q., Luo, W.C., 2011. Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles. Progress in Aerospace Sciences, 47(6):450-479.

[39] Yilmaz, I., Kaynar, O., 2011. Multiple regression, ANN (RBF, MLP) and ANFIS models for prediction of swell potential of clayey soils. Expert Systems with Applications, 38(5):5958-5966.

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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

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