基于GP的结构参数混合优化方法及其应用
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摘要
本文在分析遗传算法(GA)在结构优化与参数优化方面的基础之上,提出基于遗传编程(GP)的结构参数混合优化方法,利用遗传编程的树形结构编码方式,分析了结构和参数协同优化对结果的影响。考虑到参数搜索的随机性,通常有优秀参数的拓扑结构会占据整个种群,导致进化的早熟收敛。为了平衡进化中拓扑搜索和参数搜索,必须对初始胚胎与参数进行科学的设置。
结合功率键合图和遗传编程,采用键合图表示电路系统,研究了基于两种不同胚胎键合图的模拟电路进化设计方法:一个可修改点胚胎进化和三个可修改点胚胎进化,该方法利用遗传编程开放式拓扑搜索的特点,模拟一组4特征值问题,使用键合图和遗传编程对这两种初始胚胎分别进行进化,分别实现了结构及参数协同优化,并总结了两种初始胚胎结构对进化设计结果的影响。分析其进化过程中的结构参数变化,得出由三个可修改点胚胎进化的电路优于由一个可修改点胚胎进化的电路,三个可修改点胚胎进化具有更平衡的结构。
最后,以8特征值设置问题为测试对象,采用三个可修改点初始胚胎模型初始化种群,进化设计模拟带阻滤波器。实验结果表明,基于遗传编程的结构与参数混合优化的方法,可以设计出功能达到既定目标的模拟带阻滤波器,这进一步证明了该方法的可行性与有效性。
With the analysis of genetic algorithm to optimize structure and parameters, a kind of collaborative optimization method based on genetic programming to optimize structure and parameters is proposed, and the influence of collaborative optimization between structure and parameter on evolution is analyzed by applying the tree structure coding of genetic programming. Considering the stochastic of parameters searching, the topology with optimal parameters dominates the whole population, which will leads to prematurely convergence. In order to balance the topology and parameter searching on the evolution, it is very essential to initial the embryo and parameters scientifically.
In this research, analog circuit is presented by Bond graph. Combining the Bond graph with genetic programming, the method of analog circuit automation design based on two different Bond graph embryos with one-modified site or three-modified site is investigated, which makes good use of open-ended topology search of genetic programming. Simulating a group data of 4-eigenvalue replace problems, those two different Bond graph embryos are adopted to initial individual for evolving analog circuit, and the collaborative optimization between structure and parameter is realized separately, then some conclusions about the influence of different Bond graph embryos on evolutionary design are summarized. By analyzing the change of parameter on the evolutionary process, it is strongly demonstrated that analog circuit traced from the Bond graph embryo with three-modified site is superior to those analog circuit designed by the Bond graph embryo with one-modified site, which has more balance structures compared to the latter.
Finally, using the eight-eigenvalues replace as benchmark problem, the bond graph embryo with three-modified site is used to initial the evolutionary population to synthesize the analogue band-stop filter. The results strongly show that this technique of structure and parameter hybrid optimization based on genetic programming can synthesize analogue band-stop filter, which is well demonstrated the feasibility and validity, and has good performance.
结合功率键合图和遗传编程,采用键合图表示电路系统,研究了基于两种不同胚胎键合图的模拟电路进化设计方法:一个可修改点胚胎进化和三个可修改点胚胎进化,该方法利用遗传编程开放式拓扑搜索的特点,模拟一组4特征值问题,使用键合图和遗传编程对这两种初始胚胎分别进行进化,分别实现了结构及参数协同优化,并总结了两种初始胚胎结构对进化设计结果的影响。分析其进化过程中的结构参数变化,得出由三个可修改点胚胎进化的电路优于由一个可修改点胚胎进化的电路,三个可修改点胚胎进化具有更平衡的结构。
最后,以8特征值设置问题为测试对象,采用三个可修改点初始胚胎模型初始化种群,进化设计模拟带阻滤波器。实验结果表明,基于遗传编程的结构与参数混合优化的方法,可以设计出功能达到既定目标的模拟带阻滤波器,这进一步证明了该方法的可行性与有效性。
With the analysis of genetic algorithm to optimize structure and parameters, a kind of collaborative optimization method based on genetic programming to optimize structure and parameters is proposed, and the influence of collaborative optimization between structure and parameter on evolution is analyzed by applying the tree structure coding of genetic programming. Considering the stochastic of parameters searching, the topology with optimal parameters dominates the whole population, which will leads to prematurely convergence. In order to balance the topology and parameter searching on the evolution, it is very essential to initial the embryo and parameters scientifically.
In this research, analog circuit is presented by Bond graph. Combining the Bond graph with genetic programming, the method of analog circuit automation design based on two different Bond graph embryos with one-modified site or three-modified site is investigated, which makes good use of open-ended topology search of genetic programming. Simulating a group data of 4-eigenvalue replace problems, those two different Bond graph embryos are adopted to initial individual for evolving analog circuit, and the collaborative optimization between structure and parameter is realized separately, then some conclusions about the influence of different Bond graph embryos on evolutionary design are summarized. By analyzing the change of parameter on the evolutionary process, it is strongly demonstrated that analog circuit traced from the Bond graph embryo with three-modified site is superior to those analog circuit designed by the Bond graph embryo with one-modified site, which has more balance structures compared to the latter.
Finally, using the eight-eigenvalues replace as benchmark problem, the bond graph embryo with three-modified site is used to initial the evolutionary population to synthesize the analogue band-stop filter. The results strongly show that this technique of structure and parameter hybrid optimization based on genetic programming can synthesize analogue band-stop filter, which is well demonstrated the feasibility and validity, and has good performance.
引文
[1]李建红.汽车车身复杂钣金件的拓扑优化设计[J].汽车工程,2003,25.
[2]张卫红,王敏.拓扑优化技术在汽车工业的应用[J].昆明理工大学学报,2005,30(1):77-81.
[3]李金鹏,韩英仕,李基波.遗传算法原理及在结构优化设计中的应用[J].辽宁工学院学报,2004,24(3):56-60.
[4]郭鹏飞,韩英仕.离散变量结构优化设计的拟满应力遗传算法[J].工程力学,2003,20(2):95-99.
[5]郭鹏飞.离散变量结构优化的斐波那契遗传算法[J].辽宁工学院学报,2003,23(4):1-4.
[6]张明辉,王尚锦.遗传算法在结构形状优化中的应用[J].机械科学与技术,2001,20(6):824-826.
[7]石连拴,孙焕纯.离散变量结构形状优化设计的综合算法[J].力学学报,1999,31(6):731-738.
[8]吕大刚,王光远.基于遗传算法的抗震结构智能优化设计[J].地震工程与工程振动,1999,19(2):15-20
[9]刘永清,桑正中,遗传算法在潜土逆转旋耕刀参数优化中的应用[J],农业机械学报.2002,32(1):34-37
[10]袁玉萍,胡亮,周志坚,基于遗传算法对支持向量机模型中参数优化[J],计算机工程与设计.2008,29(19):5016-5018
[11]杨洁,郑宁,刘董,罗时贵,基于遗传算法的SVM带权特征和模型参数优化.2008,25(9):115-118
[12]何学文,付静,汪峰锁,孙林,基于Fisher判别准则的故障分类器核函数参数优化研究[J],机床与液压.2008,36(11):189-191
[13]于信伟,麻晓红,李晓豁,基于遗传算法的连续采煤机滚筒参数优化设计.2008,27(5):748-750
[14]邱琳等,基于遗传算法的直线同步电机优化设计,大电机技术,2003.11
[15]王锋,屈梁生.用遗传编程方法提取和优化机械故障的声音特征.西安交通大学学报,2002.12
[16]李少波,胡建军等.基于遗传编程(GP)与键合图的机电系统自动设计[J].系统仿真学报,2002.11:1513-1516.
[17]Bendsoe M P,Kikuchi N.Generating Optimal Topologies in Structure Design Using a Homogenization Met hod[J].Computer Methods in Applied Mechanics and Engineering,1988,71:197-224.
[18]Bendsoe M P,Sigmund O.Topology Optimization:Theory,Methods and Applications[J].Springer,2003.
[19]Fukushima J,et.al.Shape and Topology Optimization of a Car Body with Multiple Loading conditions[J].SAE Technical Paper Series,1992,920777:1-3.
[20]Thomas H,Zhou M,Schramm U.Issues of Commercial Optimization Software Development [J].Struct Multidisc Optim,2002,(23):97-110.
[21]Volvo Car Coporation.Industrial Case Studies[Z].IVS Activities,2002.
[22]Kita E,H Tanie H.Topology and Shape Optimization of Continuum Structures Using GA and BEM[J].Structural Optimization,1999,(17):130-139.
[23] Yamakawa Hiroshi. Studies on multi disciplinary optimization for topology, shape of structural systems and designs of control systems using genetic algorithm[A]. "Gu Y X.Proceedings of the First China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems[C]. Xi'an: Xidian University Press, 1999. 109-116.
[24] Sufimoto Masahiro, Yamakawa Hiroshi. A study on simultaneous optimization by parallel genetic algorithms [A]. Gu Y X. Proceedings of the First China- Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems [C]. Xi'an: Xidian University Press, 1999. 241 -248.
[25] Hajela P, Lee E, Cho H. Genetic algorithms in topologic design of grillage structure[J].Computer-Aided Civil and Infrastructure Engineering, 1998, (13): 13-22.
[26] Soh Chee-Kiong, Yang Jiaping. Optimal layout of bridge trusses by genetic algorithms[J].Computer Aided Civil and Infrastructure Engineering, 1998, (13): 247-254.
[27] Burczynski Tadeusz, Koko Grzegorz. Topology optimization using boundary elements and genetic algorithms [A]. Idelsohn S, Ouate E, Drorkiu E, eds.Computational Mechanics New Trends and Applications[C]. Baecelona: MNE. 1998. 1-12.
[28] Koza, John R., Forrest H, Andre, David, and Keane, Martin A.2000. Automatic design of analog electrical circuits using genetic programming In Cartwright, Hugh(editor). Intelligent Data Analysis in Science. Oxford: Oxford University Press. Chapter 8. Pages 172-202.
[29] Koza, John R., Keane, Martin A. Yu, Jessen, Bennett, Forrest H, and Mydlowec, William. 2000. Automatic creation of human-competitive programs and controllers by means of genetic programming. Genetic Programming and Evolvable Machines. 1 (1-2): 124-164.
[30] J.Hu, Shaobo Li, Structure Fitness Sharing(SFS) for Evolutionary Design by Genetic Programming, Proceedings of the Genetic and Evolutionary Computation Conference,GECCO-2002, New York. July 2002, PP780-787.
[31] Jianjun Hu. Sustainable Evolutionary Algorithms and Scalable Evolutionary Synthesis of Dynamic Systems. 2004.
[32] Janos Madar Janos Abonyi and Ferenc Szeifert, Genetic Programming for the Identification of Nonlinear Input-Output Models, American Chemical Society ,2005.03.18
[33] Katya Rodriguez-Vazquez Peter J. Fleming,Evolution of mathematical models of chaotic system based on mutiobjective genetic programming , Knowledge and Information Systems,2004.10
[34] K.Rodriguez-Vazquez, C.M.Fonseca,and P.J.Fleming, Identifying the Structure of Nonlinear Dynamic System Using Multiobjective Genetic Programming, IEEE. 2004
[35] Chang YS, Kim BY , Nonlinear model for ECG R-R interval variation using genetic programming approach, FUTURE GENERATION COMPUTER SYSTEMS 21(7):1117-1123,JUL2005
[36] McConaghy T,Leung H,Varadan V, Functional reconstruction of dynamical systems from time series using genetic programming, 26TH ANNUAL CONFERENCE OF THE IEEE INDUSTRIAL ELECTRONICS SOCIETY, VOLS 1-4-21ST CENTURY TECHNOLOGIES AND INDUSTRIAL OPPORTUNITIES : 2031-2034, 2000
[37] Friedberg R. M., Dunham, B., & North, J. H.. A learning machine: Part II. IBM Journal of Research and Development, 1959, 3(8):282-287.
[38] Cramer, N. L. (1985). A representation for the Adaptive Generation of Simple Sequential Programs. In Proc. of an International Conference on Genetic Algorithms and the Applications, Grefenstette, John J. (ed.), CMU.
[39] Koza, J.R. (1992), Genetic Programming: On the Programming of Computers by Means of Natural Selection, MIT Press.
[40] Jianjun Hu. Sustainable Evolutionary Algorithms and Scalable Evolutionary Synthesis of Dynamic Systems: [Ph. D. Dissertation]. East Lansing; Michigan State University, 2004.
[41] Stanley, K.O & Miikkulainen, R. Evolving Neural Networks through augmenting topologies.Evolutionary Computation, 2002, 10(2):99-127.
[42] Stanley, K.O & Risto Miikkulainen. A Taxonomy for Artificial Embryogeny. Artificial Life,2003, 9(2):93-130.
[43] Lohn J D,Colombano S P. A circuit representation technique for automated circuit design [J]. IEEE Trans On Evolutionary Computation. 1999. 3(3): 205—219.
[44] Li Shao-bo, Chen Xi, Hu Jian-jun, Sustainable HFC Genetic Algorithms based with Adaptive Migration Structure[C], IEEE International Conference on Wireless Communications,Networking and Mobile Computing. 2007: 653 - 657.
[45] Li Shao-bo, Hu Jian-jun. Evolving Vibration Absorbers Based on Genetic Programming and Bond Graphs [C]. Proceedings of the 2006 International Conference on Computational Intelligence and Security (CIS'2006) . IEEE Press, 2006.10: 202-207.
[46] Koza J R, Bennett F H, Andre D, Keane M A, Dunlap F. Automated Synthesis of Analog Electrical Circuits by Means of Genetic Programming [J]. IEEE Trans on Evolutionary.Computation. 1997. 1(2): 109-128.
[47] Yuehui Chen and Bo Yang and Ajith Abraham. Flexible neural trees ensemble for stock index modeling. Neurocomputing, 2007. 70(4-6): 697-703.
[48] Tay E, Flowers W, Barrus J. Automated Generation and Analysis of Dynamic System Designs [J]. Research in Engineering Design, 1998. 10: 15-29.
[49] Ajith Abraham and Ravi Jain and Johnson Thomas and Sang Yong Hana. D-SCIDS:Distributed soft computing intrusion detection system[J]. Journal of Network and Computer Applications. 2007. 30(1): 81-98.
[50] Yao X, Higuichi T. Promises and Challenges of Evolvable Hardware(J]. IEEE Trans On Systems Man and Cybernetics—Part C: Applications and Reviews. 1999.
[51] Koza J R, Bennett F H, Andre D, Keane M A, Dunlap F. Automated Synthesis of Analog Electrical Circuits by Means of Genetic Programming [J]. IEEE Trans on Evolutionary.Computation. 1997. 1(2): 109-128.
[2]张卫红,王敏.拓扑优化技术在汽车工业的应用[J].昆明理工大学学报,2005,30(1):77-81.
[3]李金鹏,韩英仕,李基波.遗传算法原理及在结构优化设计中的应用[J].辽宁工学院学报,2004,24(3):56-60.
[4]郭鹏飞,韩英仕.离散变量结构优化设计的拟满应力遗传算法[J].工程力学,2003,20(2):95-99.
[5]郭鹏飞.离散变量结构优化的斐波那契遗传算法[J].辽宁工学院学报,2003,23(4):1-4.
[6]张明辉,王尚锦.遗传算法在结构形状优化中的应用[J].机械科学与技术,2001,20(6):824-826.
[7]石连拴,孙焕纯.离散变量结构形状优化设计的综合算法[J].力学学报,1999,31(6):731-738.
[8]吕大刚,王光远.基于遗传算法的抗震结构智能优化设计[J].地震工程与工程振动,1999,19(2):15-20
[9]刘永清,桑正中,遗传算法在潜土逆转旋耕刀参数优化中的应用[J],农业机械学报.2002,32(1):34-37
[10]袁玉萍,胡亮,周志坚,基于遗传算法对支持向量机模型中参数优化[J],计算机工程与设计.2008,29(19):5016-5018
[11]杨洁,郑宁,刘董,罗时贵,基于遗传算法的SVM带权特征和模型参数优化.2008,25(9):115-118
[12]何学文,付静,汪峰锁,孙林,基于Fisher判别准则的故障分类器核函数参数优化研究[J],机床与液压.2008,36(11):189-191
[13]于信伟,麻晓红,李晓豁,基于遗传算法的连续采煤机滚筒参数优化设计.2008,27(5):748-750
[14]邱琳等,基于遗传算法的直线同步电机优化设计,大电机技术,2003.11
[15]王锋,屈梁生.用遗传编程方法提取和优化机械故障的声音特征.西安交通大学学报,2002.12
[16]李少波,胡建军等.基于遗传编程(GP)与键合图的机电系统自动设计[J].系统仿真学报,2002.11:1513-1516.
[17]Bendsoe M P,Kikuchi N.Generating Optimal Topologies in Structure Design Using a Homogenization Met hod[J].Computer Methods in Applied Mechanics and Engineering,1988,71:197-224.
[18]Bendsoe M P,Sigmund O.Topology Optimization:Theory,Methods and Applications[J].Springer,2003.
[19]Fukushima J,et.al.Shape and Topology Optimization of a Car Body with Multiple Loading conditions[J].SAE Technical Paper Series,1992,920777:1-3.
[20]Thomas H,Zhou M,Schramm U.Issues of Commercial Optimization Software Development [J].Struct Multidisc Optim,2002,(23):97-110.
[21]Volvo Car Coporation.Industrial Case Studies[Z].IVS Activities,2002.
[22]Kita E,H Tanie H.Topology and Shape Optimization of Continuum Structures Using GA and BEM[J].Structural Optimization,1999,(17):130-139.
[23] Yamakawa Hiroshi. Studies on multi disciplinary optimization for topology, shape of structural systems and designs of control systems using genetic algorithm[A]. "Gu Y X.Proceedings of the First China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems[C]. Xi'an: Xidian University Press, 1999. 109-116.
[24] Sufimoto Masahiro, Yamakawa Hiroshi. A study on simultaneous optimization by parallel genetic algorithms [A]. Gu Y X. Proceedings of the First China- Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems [C]. Xi'an: Xidian University Press, 1999. 241 -248.
[25] Hajela P, Lee E, Cho H. Genetic algorithms in topologic design of grillage structure[J].Computer-Aided Civil and Infrastructure Engineering, 1998, (13): 13-22.
[26] Soh Chee-Kiong, Yang Jiaping. Optimal layout of bridge trusses by genetic algorithms[J].Computer Aided Civil and Infrastructure Engineering, 1998, (13): 247-254.
[27] Burczynski Tadeusz, Koko Grzegorz. Topology optimization using boundary elements and genetic algorithms [A]. Idelsohn S, Ouate E, Drorkiu E, eds.Computational Mechanics New Trends and Applications[C]. Baecelona: MNE. 1998. 1-12.
[28] Koza, John R., Forrest H, Andre, David, and Keane, Martin A.2000. Automatic design of analog electrical circuits using genetic programming In Cartwright, Hugh(editor). Intelligent Data Analysis in Science. Oxford: Oxford University Press. Chapter 8. Pages 172-202.
[29] Koza, John R., Keane, Martin A. Yu, Jessen, Bennett, Forrest H, and Mydlowec, William. 2000. Automatic creation of human-competitive programs and controllers by means of genetic programming. Genetic Programming and Evolvable Machines. 1 (1-2): 124-164.
[30] J.Hu, Shaobo Li, Structure Fitness Sharing(SFS) for Evolutionary Design by Genetic Programming, Proceedings of the Genetic and Evolutionary Computation Conference,GECCO-2002, New York. July 2002, PP780-787.
[31] Jianjun Hu. Sustainable Evolutionary Algorithms and Scalable Evolutionary Synthesis of Dynamic Systems. 2004.
[32] Janos Madar Janos Abonyi and Ferenc Szeifert, Genetic Programming for the Identification of Nonlinear Input-Output Models, American Chemical Society ,2005.03.18
[33] Katya Rodriguez-Vazquez Peter J. Fleming,Evolution of mathematical models of chaotic system based on mutiobjective genetic programming , Knowledge and Information Systems,2004.10
[34] K.Rodriguez-Vazquez, C.M.Fonseca,and P.J.Fleming, Identifying the Structure of Nonlinear Dynamic System Using Multiobjective Genetic Programming, IEEE. 2004
[35] Chang YS, Kim BY , Nonlinear model for ECG R-R interval variation using genetic programming approach, FUTURE GENERATION COMPUTER SYSTEMS 21(7):1117-1123,JUL2005
[36] McConaghy T,Leung H,Varadan V, Functional reconstruction of dynamical systems from time series using genetic programming, 26TH ANNUAL CONFERENCE OF THE IEEE INDUSTRIAL ELECTRONICS SOCIETY, VOLS 1-4-21ST CENTURY TECHNOLOGIES AND INDUSTRIAL OPPORTUNITIES : 2031-2034, 2000
[37] Friedberg R. M., Dunham, B., & North, J. H.. A learning machine: Part II. IBM Journal of Research and Development, 1959, 3(8):282-287.
[38] Cramer, N. L. (1985). A representation for the Adaptive Generation of Simple Sequential Programs. In Proc. of an International Conference on Genetic Algorithms and the Applications, Grefenstette, John J. (ed.), CMU.
[39] Koza, J.R. (1992), Genetic Programming: On the Programming of Computers by Means of Natural Selection, MIT Press.
[40] Jianjun Hu. Sustainable Evolutionary Algorithms and Scalable Evolutionary Synthesis of Dynamic Systems: [Ph. D. Dissertation]. East Lansing; Michigan State University, 2004.
[41] Stanley, K.O & Miikkulainen, R. Evolving Neural Networks through augmenting topologies.Evolutionary Computation, 2002, 10(2):99-127.
[42] Stanley, K.O & Risto Miikkulainen. A Taxonomy for Artificial Embryogeny. Artificial Life,2003, 9(2):93-130.
[43] Lohn J D,Colombano S P. A circuit representation technique for automated circuit design [J]. IEEE Trans On Evolutionary Computation. 1999. 3(3): 205—219.
[44] Li Shao-bo, Chen Xi, Hu Jian-jun, Sustainable HFC Genetic Algorithms based with Adaptive Migration Structure[C], IEEE International Conference on Wireless Communications,Networking and Mobile Computing. 2007: 653 - 657.
[45] Li Shao-bo, Hu Jian-jun. Evolving Vibration Absorbers Based on Genetic Programming and Bond Graphs [C]. Proceedings of the 2006 International Conference on Computational Intelligence and Security (CIS'2006) . IEEE Press, 2006.10: 202-207.
[46] Koza J R, Bennett F H, Andre D, Keane M A, Dunlap F. Automated Synthesis of Analog Electrical Circuits by Means of Genetic Programming [J]. IEEE Trans on Evolutionary.Computation. 1997. 1(2): 109-128.
[47] Yuehui Chen and Bo Yang and Ajith Abraham. Flexible neural trees ensemble for stock index modeling. Neurocomputing, 2007. 70(4-6): 697-703.
[48] Tay E, Flowers W, Barrus J. Automated Generation and Analysis of Dynamic System Designs [J]. Research in Engineering Design, 1998. 10: 15-29.
[49] Ajith Abraham and Ravi Jain and Johnson Thomas and Sang Yong Hana. D-SCIDS:Distributed soft computing intrusion detection system[J]. Journal of Network and Computer Applications. 2007. 30(1): 81-98.
[50] Yao X, Higuichi T. Promises and Challenges of Evolvable Hardware(J]. IEEE Trans On Systems Man and Cybernetics—Part C: Applications and Reviews. 1999.
[51] Koza J R, Bennett F H, Andre D, Keane M A, Dunlap F. Automated Synthesis of Analog Electrical Circuits by Means of Genetic Programming [J]. IEEE Trans on Evolutionary.Computation. 1997. 1(2): 109-128.