基于区间的不确定多目标优化方法及应用

中国机械工程 ›› 2011, Vol. 22 ›› Issue (9): 1100-1106.

基于区间的不确定多目标优化方法及应用

李新兰;姜潮;韩旭

湖南大学汽车车身先进设计制造国家重点实验室,长沙,410082

出版日期:2011-05-10 发布日期:2011-05-17
基金资助:
国家自然科学基金资助项目(10802028)；国家重点基础研究发展计划(973计划)资助项目(2010CB832705)；国家科技重大专项(2010ZX0417-013-005)；湖南大学汽车车身先进设计制造国家重点实验室自主课题(60870003)
National Natural Science Foundation of China（No. 10802028）;

National Program on Key Basic Research Project (973 Program)（No. 2010CB832705）;
National Science and Technology Major Project ( No. 2010ZX0417-013-005)

An Uncertainty Multi-objective Optimization Based on Interval Analysis and Its Application

Li Xinlan;Jiang Chao;Han Xu

State Key Laboratory of Advanced Design & Manufacturing for Vehicle Body,Hunan University,Changsha,410082

Online:2011-05-10 Published:2011-05-17
Supported by:

National Natural Science Foundation of China（No. 10802028）;

National Program on Key Basic Research Project (973 Program)（No. 2010CB832705）;
National Science and Technology Major Project ( No. 2010ZX0417-013-005)

摘要/Abstract

摘要：

基于非线性区间分析方法，提出了一种区间多目标优化方法。利用非线性区间分析方法求出每一个目标函数和约束在每一设计矢量下的上下界，采用目标函数的中点值来计算多目标优化问题的非劣解，同时，通过数学转换模型区间可能度处理约束问题，将非线性区间多目标优化问题转化为确定性多目标优化问题，利用微型多目标遗传算法(μMOGA)对转换后的确定性多目标问题进行求解。最后,将该方法应用于数值算例以及十杆桁架结构和商用车车架，计算结果证明了该方法的有效性和工程实用性。



关键词:

多目标优化, 不确定性, 区间, 车架

Abstract:

An interval multi-objective optimization method was suggested based on non-linear interval analysis methods. The upper and lower bounds of every objective and constraint functions for each vector were calculated,by using the center value of the interval objective function,the non-dominated solution of the multi-objective optimization problems was calculated,with the interval possibility degrees,the nonlinear interval multi-objective problems were changed into the deterministic multi-objective problems.The μMOGA was used to calculate the converted deterministic multi-objective problems. Finally,the method was applied to one numerical example and two engineering problems about ten truss structure and commercial automobile frame optimization. The results of these examples demonstrate the efficiency and engineering practicability of the presented method. 

中图分类号:

TP18

李新兰, 姜潮, 韩旭.

基于区间的不确定多目标优化方法及应用

[J]. 中国机械工程, 2011, 22(9): 1100-1106.

LI Xin-Lan, JIANG Chao, HAN Xu.

An Uncertainty Multi-objective Optimization Based on Interval Analysis and Its Application

[J]. China Mechanical Engineering, 2011, 22(9): 1100-1106.

参考文献

[1]Zadeh L. Optimality and Non--scalar--valued Performance Criteria[J]. IEEE Transactions on Automatic Control, 1963,59 (8) : 59-60.
[2]Deb K. Multi--objective Optimization Using Evolutionary Algorithms[M]. London: John Wiley & Sons, 2001.
[3]Moh J S, Chiang D Y. Improved Simulated Annealing Search for Structural Optimization[J]. AIAA J. ,2000,38(10) :1965-1973.
[4]刘桂萍[1],韩旭[1],姜潮[1].基于微型多目标遗传算法的薄板冲压成形变压边力优化[J].中国机械工程,2007,18(21):2614-2617.
[5]Ahbas M,Bellahcene F. Cutting Plane Method for Multiple Objective Stochastic Integer Linear Programming[J]. European Journal of Operational Research,2006,168(3) :967-984.
[6]Liu B D, Iwamura K. Fuzzy Programming with Fuzzy Decisions and Fuzzy Simulation-- based Genetic Algorithm[J]. Fuzzy Sets and Systems, 2001, 122:253-262.
[7]Ishibuehi H, Tanaka H. Multi--objective Programming in Optimization of the Interval Objective Funetion[J]. European Journal of Operational Research,1990,48(2) :219-225.
[8]Jiang C, Han X, Liu G R. Optimization of Structures with Uncertain Constraints Based on Convex Model and Satisfaction Degree of Interval[J]. Computer Methods in Applied Mechanics and Engineering, 2007,196:4791-4800.
[9]Jiang C, Han X, Liu G R, et al. A Nonlinear Interval Number Programming Method for Uncertain Optimization Problems[J]. European Journal of Operational Research, 2008,188 ( 1 ) : 1-13.
[10]Jiang C, Han X, Guan F J, et al. An Uncertain Structural Optimization Method Based on Nonlinear Interval Number Programming and Interval Analysis Method [J]. Engineering Structures, 2007,29(11) :3168-3177.
[11]Jiang C, Han X, Liu G P. A Sequential Nonlinear Interval Number Programming Method for Uncertain Structures[J]. Computer Methods in Applied Mechanics and Engineering, 2008,197 :4250-4265.
[12]姜潮.基于区间的不确定性优化理论与算法 [D].湖南大学,2008:
[13]Qiu Z P. Comparison of Static Response of Structures Using Convex Models and Interval Analysis Method[J]. International Journal for Numerical Methods in Engineering, 2003,56 : 1735-1753.
[14]邱志平著.非概率集合理论凸方法及其应用[M],2005:246.
[15]Guo X,Bai W,Zhang W S, et al. Confidence Structural Robust Design and Optimization under Stiffness and Load Uncertainties[J]. Computer Methods in Applied Mechanics and Engineering, 2009, 198(41/44) :3378-3399.
[16]亢战[1],罗阳军[1].基于凸模型的结构非概率可靠性优化[J].力学学报,2006,38(6):807-815.
[17]Luo Y J,Zhan K,Zhen L,et al. Continuum Topology Optimization with Non- probability Constraints Based on Multi--ellipsoid Convex Model[J]. Structural and Multidiseiplinary Optimization, 2009,39 : 297-310.
[18]李方义[1],李光耀[1],郑刚[1].基于区间的不确定多目标优化方法研究[J].固体力学学报,2010,31(1):86-93.
[19]张勇[1],巩敦卫[1],郝国生[1],蒋余庆[1].含区间参数多目标系统的微粒群优化算法[J].自动化学报,2008,34(8):921-928.
[20]刘桂萍.基于微型遗传算法的多目标优化方法及应用研究 [D].湖南大学,2007: