结构优化设计的改进交叉熵支持向量机方法
|
摘要
针对工程优化设计中隐式函数和高计算量困难,提出了支持向量机与改进交叉熵算法的组合优化算法。采用在设计变量空间内分布更为均匀的拉丁重心Voronoi结构抽样方法(Latinized centroidal Voronoi tessellation,LCVT)获得试验点,进而利用支持向量机得到高精度的代理模型。同时采用改进交叉熵方法,引入"全局精英样本"与"局部精英样本"概念,构建新的参数更新策略,以充分提取迭代过程中的隐含的有用信息。同时增加变异操作避免陷入局部最优。通过2个数值算例验证改进交叉熵支持向量机方法优于传统交叉熵支持向量机方法,利用1个工程算例验证改进交叉熵支持向量机方法在工程领域的可行性。
Aiming at the difficulties of implicit functions and high computation cost in engineering design optimization,a combined method is proposed in this paper,which takes advantage of support vector machine(SVM) and cross entropy method(CE). Used the 'Latinized' centroidal Voronoi tessellation(LCVT) which can generate much uniform supporting points in the design variable space,a high accurate surrogate model is obtained by SVM. At the same time,the traditional cross entropy method is improved by the concepts of "global elite samples"and the "local elites samples"and a new parameter updating strategy for extracting the useful information in iteration history.To avoid trapping in the local optimum,a mutation operation is also included in the proposed method. Two numerical examples are used to illustrate the performance of the improved method superior to that of the traditional one. Finally,an engineering example is employed to demonstrate the feasibility of the proposed method in the field of engineering.
Aiming at the difficulties of implicit functions and high computation cost in engineering design optimization,a combined method is proposed in this paper,which takes advantage of support vector machine(SVM) and cross entropy method(CE). Used the 'Latinized' centroidal Voronoi tessellation(LCVT) which can generate much uniform supporting points in the design variable space,a high accurate surrogate model is obtained by SVM. At the same time,the traditional cross entropy method is improved by the concepts of "global elite samples"and the "local elites samples"and a new parameter updating strategy for extracting the useful information in iteration history.To avoid trapping in the local optimum,a mutation operation is also included in the proposed method. Two numerical examples are used to illustrate the performance of the improved method superior to that of the traditional one. Finally,an engineering example is employed to demonstrate the feasibility of the proposed method in the field of engineering.
引文
[1]Koroglu S A,Ergin A.A Decomposition Method for Surrogate Models of Large Scale Structures[J].Journal of Marine Science and Technology,2016,21(2):325-333
[2]Vapnik V N.The Nature of Satistical Learning Theory[M].Pringer,1995:988-999
[3]Suykens J A K,Vandewalle J.Least Squares Support Vector Machine Classifiers[M].Kluwer Academic Publishers,1999:293-300
[4]Rubinstein R Y.Optimization of Computer Simulation Models with Rare Events[J].European Journal of Operational Research,1997,99(1):89-112
[5]Rubinstein R.The Cross-Entropy Method for Combinatorial and Continuous Optimization[J].Methodology and Computing in Applied Probability,1999,1(2):127-190
[6]Chepuri K,Homem De Mello.Solving the Vehicle Routing Problem with Stochastic Demands Using the Cross-Entropy Method[J].Annals of Operations Research,2005,134(1):153-181
[7]Santosa B.Application of the Cross-Entropy Method to Dual Lagrange Support Vector Machine[C]∥International Conference on Advanced Data Mining And Applications,2009
[8]Ghidey H.Reliability-Based Design Optimization with Cross-Entropy Method[D].2015
[9]任超,张航,李洪双.随机优化的改进交叉熵方法[J].北京航空航天大学学报,2018,44(1):205-214Ren Chao,Zhang Hang,Li Hongshuang.Stochastic Optimization Method Based on Improved Cross Entropy[J].Journal of Beijing University of Aeronautics and Astronautics,2018,44(1):205-214(in Chinese)
[10]Rubinstein R Y.Cross-Entropy and Rare Events for Maximal Cut and Partition Problems[J].ACM Trans on Modeling&Computer Simulation,2002,12(1):27-53
[11]Rubinstein R Y.A Stochastic Minimum Cross-Entropy Method for Combinatorial Optimization and Rare-Event Estimation[J].Methodology&Computing in Applied Probability,2005,7(1):5-50
[12]Botev Z I,Kroese D P.The Generalized Cross Entropy Method with Applications to Probability Density Estimation[J].Methodology&Computing in Applied Probability,2007,13(1):1-27
[13]Romero V J.Comparison of Pure and“Latinized”Centroidal Voronoi Tessellation against Various Other Statistical Sampling Methods[J].Reliability Engineering&System Safety,2006,91(10/11):1266-1280
[14]Jones D R,Schonlau M,Welch W J.Efficient Global Optimization of Expensive Black-Box Functions[J].Journal of Global Optimization,1998,13(4):455-492
[15]Liang J J,Runarsson T P,Mezura-Montes E,et al.Problem Definitions and Evaluation Criteria for the CEC 2006 Special Session on Constrained Real-Parameter Optimization[J].International Journal of Computer Assisted Radiology&Surgery,2005(2):1-24
[16]陈小前.飞行器不确定性多学科设计优化理论与应用[M].北京:科学出版社,2013Chen Xiaoqian.Theory and Application of Uncertainty-Based Multidisciplinary Design Optimization for Flight Vehicles[M].Beijin,Science Press,2013(in Chinese)
[17]Schmit A L,Miura H.Approximation Concepts for Efficient Structural Synthesis[J].AIAA Journal,1976,12(24):8508-8523
[18]Gellatly R A,Berke L.Optimal Structural Design[R].Flight Dynamics Laboratory,1971
[19]Gellatly R A.Development of Procedures for Large Scale Automated Minimum Weight Structural Design[R].Flight Dynamics Laboratory,1966
[2]Vapnik V N.The Nature of Satistical Learning Theory[M].Pringer,1995:988-999
[3]Suykens J A K,Vandewalle J.Least Squares Support Vector Machine Classifiers[M].Kluwer Academic Publishers,1999:293-300
[4]Rubinstein R Y.Optimization of Computer Simulation Models with Rare Events[J].European Journal of Operational Research,1997,99(1):89-112
[5]Rubinstein R.The Cross-Entropy Method for Combinatorial and Continuous Optimization[J].Methodology and Computing in Applied Probability,1999,1(2):127-190
[6]Chepuri K,Homem De Mello.Solving the Vehicle Routing Problem with Stochastic Demands Using the Cross-Entropy Method[J].Annals of Operations Research,2005,134(1):153-181
[7]Santosa B.Application of the Cross-Entropy Method to Dual Lagrange Support Vector Machine[C]∥International Conference on Advanced Data Mining And Applications,2009
[8]Ghidey H.Reliability-Based Design Optimization with Cross-Entropy Method[D].2015
[9]任超,张航,李洪双.随机优化的改进交叉熵方法[J].北京航空航天大学学报,2018,44(1):205-214Ren Chao,Zhang Hang,Li Hongshuang.Stochastic Optimization Method Based on Improved Cross Entropy[J].Journal of Beijing University of Aeronautics and Astronautics,2018,44(1):205-214(in Chinese)
[10]Rubinstein R Y.Cross-Entropy and Rare Events for Maximal Cut and Partition Problems[J].ACM Trans on Modeling&Computer Simulation,2002,12(1):27-53
[11]Rubinstein R Y.A Stochastic Minimum Cross-Entropy Method for Combinatorial Optimization and Rare-Event Estimation[J].Methodology&Computing in Applied Probability,2005,7(1):5-50
[12]Botev Z I,Kroese D P.The Generalized Cross Entropy Method with Applications to Probability Density Estimation[J].Methodology&Computing in Applied Probability,2007,13(1):1-27
[13]Romero V J.Comparison of Pure and“Latinized”Centroidal Voronoi Tessellation against Various Other Statistical Sampling Methods[J].Reliability Engineering&System Safety,2006,91(10/11):1266-1280
[14]Jones D R,Schonlau M,Welch W J.Efficient Global Optimization of Expensive Black-Box Functions[J].Journal of Global Optimization,1998,13(4):455-492
[15]Liang J J,Runarsson T P,Mezura-Montes E,et al.Problem Definitions and Evaluation Criteria for the CEC 2006 Special Session on Constrained Real-Parameter Optimization[J].International Journal of Computer Assisted Radiology&Surgery,2005(2):1-24
[16]陈小前.飞行器不确定性多学科设计优化理论与应用[M].北京:科学出版社,2013Chen Xiaoqian.Theory and Application of Uncertainty-Based Multidisciplinary Design Optimization for Flight Vehicles[M].Beijin,Science Press,2013(in Chinese)
[17]Schmit A L,Miura H.Approximation Concepts for Efficient Structural Synthesis[J].AIAA Journal,1976,12(24):8508-8523
[18]Gellatly R A,Berke L.Optimal Structural Design[R].Flight Dynamics Laboratory,1971
[19]Gellatly R A.Development of Procedures for Large Scale Automated Minimum Weight Structural Design[R].Flight Dynamics Laboratory,1966