遗传算法在建筑结构优化设计中的应用研究
摘要
遗传算法是近年来在计算机科学领域和优化领域中受到广泛关注的一种拟生物进化理论的仿生学算法。在广泛阅读文献和调研的基础上，本文对遗传算法及其在结构优化设计应用中的相关内容进行了分析和综合，对结构优化设计的基本概念、主要特点进行了介绍，对遗传算法应用于结构优化设计时的数学建模、约束条件处理、初始种群的产生及其遗传算法控制参数的选择几个关键因素作了概要的分析与研究。
本文针对结构优化设计的特点，结合有限元结构分析原理，编制了基于简单遗传算法的结构优化设计程序，用于解决离散变量的框架结构优化设计。经过实例验证，该程序用于结构优化设计是可行的和高效的。
由于简单遗传算法仅擅长全局搜索，而局部搜索能力不足，要达到真正的最优解则要花费相当长的时间。针对简单遗传算法的缺点，本论文提出了对简单遗传算法进行改进—自适应遗传算法，并且编制了基于自适应遗传算法的结构优化程序，算例分析表明得出自适应遗传算法确实提高了遗传算法在应用于结构优化设计方面收敛性和计算速度。
在应用遗传算法时，初始种群的产生一般是随机的，它往往需要的编码长度很大，导致需要很大的种群规模或者很长的进化过程才能有较好的优化效果，这将耗费大量的计算时间和费用。如何确定恰当的种群规模是一个直接影响遗传算法效率的问题。由于没有这方面相关的文献资料，本文还针对群体规模对基本遗传算法的优化计算影响的问题结合三个算例进行了尝试性的对比计算，确定了较佳的群体规模。
Genetic Algorithm (GA) is one of the main directions in today's compute science. Its application in structural catches more and more attention. Based on a great many literature, this paper analyzes and summarizes the genetic algorithm for the design of structural optimization. The basic conceptions and primary characteristics are introduced in this paper. This paper discuss some primary factor when genetic algorithm applied on optimal design, for example the mathematical model、the constrained problem、the initial population and the controls parameter of genetic algorithm
Aimed at the characteristic of structural optimization and finite-element analysis, this paper accomplishes the optimal program based on the simple genetic algorithm. This program is present for optimizing structural systems with discrete design variables. The result shows that the program is feasible and effective.
Because simple genetic algorithm is good at the global search and short of the local search, searching the best optimized solution need to consume more time. Aimed at the shortage of GA, this paper improves the simple genetic algorithm and accomplishes the optimal program based on the adaptive genetic algorithm. The result shows that the adaptive genetic algorithm improves the convergence rate.
Generally, the genetic algorithm randomly generates the initial population. The coding of the variables that describe the problem is always large. In order to find the best optimal result, it needs the larger population and the longer course of optimization. That will spend much time and money, so the appropriate population size is a factor that affects the efficiency of genetic algorithm. Because no literature discusses that how to confirm the appropriate population size, this paper discusses how the population size affects GA's optimal course based on three examples. This paper confirms the better population size.
本文针对结构优化设计的特点，结合有限元结构分析原理，编制了基于简单遗传算法的结构优化设计程序，用于解决离散变量的框架结构优化设计。经过实例验证，该程序用于结构优化设计是可行的和高效的。
由于简单遗传算法仅擅长全局搜索，而局部搜索能力不足，要达到真正的最优解则要花费相当长的时间。针对简单遗传算法的缺点，本论文提出了对简单遗传算法进行改进—自适应遗传算法，并且编制了基于自适应遗传算法的结构优化程序，算例分析表明得出自适应遗传算法确实提高了遗传算法在应用于结构优化设计方面收敛性和计算速度。
在应用遗传算法时，初始种群的产生一般是随机的，它往往需要的编码长度很大，导致需要很大的种群规模或者很长的进化过程才能有较好的优化效果，这将耗费大量的计算时间和费用。如何确定恰当的种群规模是一个直接影响遗传算法效率的问题。由于没有这方面相关的文献资料，本文还针对群体规模对基本遗传算法的优化计算影响的问题结合三个算例进行了尝试性的对比计算，确定了较佳的群体规模。
Genetic Algorithm (GA) is one of the main directions in today's compute science. Its application in structural catches more and more attention. Based on a great many literature, this paper analyzes and summarizes the genetic algorithm for the design of structural optimization. The basic conceptions and primary characteristics are introduced in this paper. This paper discuss some primary factor when genetic algorithm applied on optimal design, for example the mathematical model、the constrained problem、the initial population and the controls parameter of genetic algorithm
Aimed at the characteristic of structural optimization and finite-element analysis, this paper accomplishes the optimal program based on the simple genetic algorithm. This program is present for optimizing structural systems with discrete design variables. The result shows that the program is feasible and effective.
Because simple genetic algorithm is good at the global search and short of the local search, searching the best optimized solution need to consume more time. Aimed at the shortage of GA, this paper improves the simple genetic algorithm and accomplishes the optimal program based on the adaptive genetic algorithm. The result shows that the adaptive genetic algorithm improves the convergence rate.
Generally, the genetic algorithm randomly generates the initial population. The coding of the variables that describe the problem is always large. In order to find the best optimal result, it needs the larger population and the longer course of optimization. That will spend much time and money, so the appropriate population size is a factor that affects the efficiency of genetic algorithm. Because no literature discusses that how to confirm the appropriate population size, this paper discusses how the population size affects GA's optimal course based on three examples. This paper confirms the better population size.
引文
[1] 张炳华，候昶. 土建结构优化设计，同济大学出版社，1998 1－2
[2] 汪树玉，刘国华，包志仁. 结构优化设计的现状与发展. 基建优化 1999,20(4) 3－14.
[3] 汪树玉，刘国华，包志仁. 结构优化设计的现状与发展(续). 基建优化 1999,20(5) 3－7.
[4] 钱令希 工程结构优化设计，水利电力出版社 1983 1－2.
[5] 谢祚水 结构优化设计概论，国防工业出版社 1997 1－2.
[6] 王小平，曹立明．遗传算法－理论、应用与软件实现，西安交通大学出版社 2002 1-68.
[7] 陈国良，王熙法等．遗传算法及其应用，人民邮电出版社, 1996 1-97.
[8] 陈永兵 遗传算法及其在结构工程优化中的应用研究(西北工业大学硕士论文) 陕西：西北工业大学图书馆，2001 52-53.
[9] Ghasemi M R, Hinton E, Wood R D. Optimization of trusses using genetic algorithms for discrete and continuous variables, Engineering Computations , 1999,16(3):272-301．
[10] Yeh I-Cheng. Hybrid genetic algorithms for optimization of truss structures. Computer-Aided Civil and Infrastructure Engineering, 1999(14):199-206．
[11] Hajela P, Yoo J, Lee J. GA based simulation of immune networks applications in structural optimization. Engineering Optimization, 1997,29:131-149．
[12] 易伟峰，刘霞．基于遗传算法的结构损伤诊断研究．工程力学，2001,18(2)：64-71.
[13] 沈成武，唐小兵，余开彪. 用频率识别平面刚架结构裂纹的遗传算法. 固体力学学报 2000,21(1): 79-84.
[14] M.I.Friswell, J.E.T Penny & S.D.Garvey. A combined genetic and eigensensitivity algorithm for the location of damage in structure. Compute & Structure , 1998,69(5):419-431．
[15] Jung-huai Chou, Jamshid Ghaboussi. Genetic algorithm in structural damage detection. Compute & Structure , 2001,79(14):1335-1353 ．
[16] E S Kameshki, M P Saka. Optimum design of nonlinear steel frames witn semi-rigid connections using a genetic algorithm, Compute & Structure , 2001,79(17):1593-1604．
[17] M S Hayalioglu. Optimum design of geometrically non-linear elastic-plastic steel frames via genetic algorithm, Compute & Structure , 2000,79(5):527-538.
[18] S.Pezeshk．Design Of Nonlinear Framed Structures Using Genetic Optimization．Journal of structural engineering, 2000(3) :382-388.
[19] Rajeev S, Krishnamoorthy C S. Genetic algorithm-based methodology for design optimization of reinforced concrete frames. Computer-aided civil and infrastructure engineering, 1999,14:63~74.
[20] Koumousis V K, Arsenis S J. Genetic algorithms in optimal detailed design of reinforced concrete members. Computer-aided civil and infrastructure engineering, 1998,13:43~52.
[21] Coello C C A, Christiansen A D,Santos Hernandez E. Asimple genetic algorithm for the design of reinforced concrete beams. Engineering with computers, 1997(13):185~196.
[22] 牟在根，张举兵，陈云周 结构优化设计的遗传算法研究 《工程力学》2002年增刊：605-608.
[23] Y. Arfiadi, M. N. S. Hadi. Optimal direct(static) output feedback controller using real coded genetic algorithms, Compute & Structure , 2001,79(17):1625-1634．
[24] J. C. Miles, G. M. Sisk, C. J. Moore. The conceptual design of commercial buildings using a genetic algorithm, Compute & Structure , 2001,79(17):1583-1592．
[25] 王光远．工程结构与系统抗震优化设计的实用方法，中国建筑工业出版社，1999 ,82-105．
[26] 张文修，梁怡 遗传算法的数学基础，西安交通大学出版社，2001 13-69.
[27] 潘正君，康立山，陈毓屏 演化计算 清华大学出版社，广西科学技术出版社 2000 16-35.
[28] 周明 孙树栋 遗传算法原理及应用 国防工业出版社，1999 1-64
[29] 段玉倩，贺家李. 遗传算法及其改进. 电力系统及其自动化学报，1998,10（1）:39-52.
[30] 张文元，吴知丰．遗传算法在建筑结构优化设计中的应用．哈尔滨建筑大学学报,1999,32(4):18-23.
[31] 唐文艳，顾元宪．遗传算法在结构优化中的研究进展．力学进展，2002,32(1):26-39．
[32] 贺拥军，齐冬莲等．遗传算法在双层圆柱面网壳结构优化中的应用．建筑结构，2002,32（3）:60-61．
[33] 邵军，程华，徐军. 遗传算法在结构可靠性优化中的应用. 四川建筑科学研究，2001,27(2):4-5.
[34] 鹿跃丽，周力平. 遗传算法用于工程结构优化设计的研究. 郑州工业大学学报,1998,19(2):35-39.
[35] 鹿跃丽，李菊丽，周力平. 遗传算法及其在工程结构优化设计中的应用.郑州轻工业学院学报,1997,12(3):61-64.
[36] 韩英仕，郭鹏飞，朱朝艳. 小生境遗传算法及在离散变量优化设计中的应用.《工程力学》增刊 2002：644-647.
[37] 郭鹏飞,韩英仕，朱朝艳. 离散变量结构的Fibonacci遗传算法.《工程力学》增刊 2002：672-675.
[38] 王坤，梁波. 基于遗传算法的输电铁塔结构优化. 《工程力学》增刊 2002：694-697.
[39] 赵更新. 杆系结构分析程序设计. 电子科技大学出版社，1998 108-157.
[2] 汪树玉，刘国华，包志仁. 结构优化设计的现状与发展. 基建优化 1999,20(4) 3－14.
[3] 汪树玉，刘国华，包志仁. 结构优化设计的现状与发展(续). 基建优化 1999,20(5) 3－7.
[4] 钱令希 工程结构优化设计，水利电力出版社 1983 1－2.
[5] 谢祚水 结构优化设计概论，国防工业出版社 1997 1－2.
[6] 王小平，曹立明．遗传算法－理论、应用与软件实现，西安交通大学出版社 2002 1-68.
[7] 陈国良，王熙法等．遗传算法及其应用，人民邮电出版社, 1996 1-97.
[8] 陈永兵 遗传算法及其在结构工程优化中的应用研究(西北工业大学硕士论文) 陕西：西北工业大学图书馆，2001 52-53.
[9] Ghasemi M R, Hinton E, Wood R D. Optimization of trusses using genetic algorithms for discrete and continuous variables, Engineering Computations , 1999,16(3):272-301．
[10] Yeh I-Cheng. Hybrid genetic algorithms for optimization of truss structures. Computer-Aided Civil and Infrastructure Engineering, 1999(14):199-206．
[11] Hajela P, Yoo J, Lee J. GA based simulation of immune networks applications in structural optimization. Engineering Optimization, 1997,29:131-149．
[12] 易伟峰，刘霞．基于遗传算法的结构损伤诊断研究．工程力学，2001,18(2)：64-71.
[13] 沈成武，唐小兵，余开彪. 用频率识别平面刚架结构裂纹的遗传算法. 固体力学学报 2000,21(1): 79-84.
[14] M.I.Friswell, J.E.T Penny & S.D.Garvey. A combined genetic and eigensensitivity algorithm for the location of damage in structure. Compute & Structure , 1998,69(5):419-431．
[15] Jung-huai Chou, Jamshid Ghaboussi. Genetic algorithm in structural damage detection. Compute & Structure , 2001,79(14):1335-1353 ．
[16] E S Kameshki, M P Saka. Optimum design of nonlinear steel frames witn semi-rigid connections using a genetic algorithm, Compute & Structure , 2001,79(17):1593-1604．
[17] M S Hayalioglu. Optimum design of geometrically non-linear elastic-plastic steel frames via genetic algorithm, Compute & Structure , 2000,79(5):527-538.
[18] S.Pezeshk．Design Of Nonlinear Framed Structures Using Genetic Optimization．Journal of structural engineering, 2000(3) :382-388.
[19] Rajeev S, Krishnamoorthy C S. Genetic algorithm-based methodology for design optimization of reinforced concrete frames. Computer-aided civil and infrastructure engineering, 1999,14:63~74.
[20] Koumousis V K, Arsenis S J. Genetic algorithms in optimal detailed design of reinforced concrete members. Computer-aided civil and infrastructure engineering, 1998,13:43~52.
[21] Coello C C A, Christiansen A D,Santos Hernandez E. Asimple genetic algorithm for the design of reinforced concrete beams. Engineering with computers, 1997(13):185~196.
[22] 牟在根，张举兵，陈云周 结构优化设计的遗传算法研究 《工程力学》2002年增刊：605-608.
[23] Y. Arfiadi, M. N. S. Hadi. Optimal direct(static) output feedback controller using real coded genetic algorithms, Compute & Structure , 2001,79(17):1625-1634．
[24] J. C. Miles, G. M. Sisk, C. J. Moore. The conceptual design of commercial buildings using a genetic algorithm, Compute & Structure , 2001,79(17):1583-1592．
[25] 王光远．工程结构与系统抗震优化设计的实用方法，中国建筑工业出版社，1999 ,82-105．
[26] 张文修，梁怡 遗传算法的数学基础，西安交通大学出版社，2001 13-69.
[27] 潘正君，康立山，陈毓屏 演化计算 清华大学出版社，广西科学技术出版社 2000 16-35.
[28] 周明 孙树栋 遗传算法原理及应用 国防工业出版社，1999 1-64
[29] 段玉倩，贺家李. 遗传算法及其改进. 电力系统及其自动化学报，1998,10（1）:39-52.
[30] 张文元，吴知丰．遗传算法在建筑结构优化设计中的应用．哈尔滨建筑大学学报,1999,32(4):18-23.
[31] 唐文艳，顾元宪．遗传算法在结构优化中的研究进展．力学进展，2002,32(1):26-39．
[32] 贺拥军，齐冬莲等．遗传算法在双层圆柱面网壳结构优化中的应用．建筑结构，2002,32（3）:60-61．
[33] 邵军，程华，徐军. 遗传算法在结构可靠性优化中的应用. 四川建筑科学研究，2001,27(2):4-5.
[34] 鹿跃丽，周力平. 遗传算法用于工程结构优化设计的研究. 郑州工业大学学报,1998,19(2):35-39.
[35] 鹿跃丽，李菊丽，周力平. 遗传算法及其在工程结构优化设计中的应用.郑州轻工业学院学报,1997,12(3):61-64.
[36] 韩英仕，郭鹏飞，朱朝艳. 小生境遗传算法及在离散变量优化设计中的应用.《工程力学》增刊 2002：644-647.
[37] 郭鹏飞,韩英仕，朱朝艳. 离散变量结构的Fibonacci遗传算法.《工程力学》增刊 2002：672-675.
[38] 王坤，梁波. 基于遗传算法的输电铁塔结构优化. 《工程力学》增刊 2002：694-697.
[39] 赵更新. 杆系结构分析程序设计. 电子科技大学出版社，1998 108-157.