演化计算在参数估计中的应用
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摘要
演化计算是模拟自然界的演化过程，特别是生物物种演化过程的随机优化技术，具有自组织、自适应和自学习等智能特征，基于种群的搜索机制使其适合大规模并行。演化计算在不同的科学领域得到了广泛的应用，其中演化非线性参数估计是演化计算的应用方向之一。
本文主要研究演化计算在参数估计中的应用，提出了一个新的演化算法，大量的计算实例表明，该算法是一个通用性好、搜索效率高、收敛速度快的有效算法。用演化算法解决了物理学中密立根油滴实验数据处理问题，用求一组小数最大公约数的方法，直接获得了电子电量，与传统的方法相比，使用本文算法所得到的结果更能反映实验的真实性。
第一章对演化计算作了全面的概述，介绍了演化计算的起源与发展、分支流派及特点，概述了演化计算的算法框架，介绍编码方式、遗传算子的设计、选择策略，研究现状及趋势。
第二章介绍参数估计问题，并讨论模型参数估计的经典算法及已有的一些改进算法，从保持种群多样性与动态调整搜索区间的角度，提出了一个新的演化算法。
第三章结合具体问题利用新算法来求解模型参数估计问题，并与已有算法的结果进行了比较，实验结果表明新算法是一个性能优良的有效算法。
第四章将演化算法应用于求解一组数的最大公约数，并用于解决实际问题。实验结果表明了算法的有效性和可行性。
第五章对全文做了总结，总结了本文的主要研究结果同时指出了今后的工作展望。
Evolutionary computation simulates the evolutionary process of nature, especially the creature species that evolves on stochastic optimization technique. It has characteristics such as self-organization, self-adaptive, self-learning and so on. The population-based searching mechanism makes it suitable run parallel in large scale. Evolutionary computation has found vast application to many science fields, of which evolutionary non-linear parameter evaluation is one direction.
The main content of this thesis is discussing how to improve evolutionary algorithm and raising a new evolutionary algorithm and using this new algorithm to parameter evaluation. A large number of computation shows that the new algorithm is a universal, searching-efficiently, converging-quickly algorithm. Data handle problem of the physics experiment of the R. A. Millikan oil drop is solved with evolving algorithm. Getting the greatest common divisor of the minimal data, we will directly obtain electronic quantity and reflect the result of the experiment.
In chapter one, the paper have described the overall concept, introduced the origination and the development, the branch of the school and the character of the evolution algorithm, depicted the frame of the algorithm, the method of coding, the design of crossover and mutation, selection strategy, the current situation and trend of research of evolution algorithm.
In chapter two, the paper have introduced the problem of parameter estimation, discussed the classical algorithm of the parameter estimation model and some unproved algorithm, In order to keep variety and dynamic adjust-searching area, we put forward to a new evolving algorithm.
In chapter three, we settled a model's parameter estimation with this new algorithm, the effect acquired with the new algorithm is better than that acquired with the other algorithms. The result shows that the new algorithm is a one with quality and affectivity.
In chapter four, we utilized evolution algorithm to get greatest common divisor of a set of numbers, and solved the concrete problem, the result proves that the new algorithm is affectivity and feasibility.
Chapter 5 summarizes the main work of the thesis and describes the work of future.
本文主要研究演化计算在参数估计中的应用，提出了一个新的演化算法，大量的计算实例表明，该算法是一个通用性好、搜索效率高、收敛速度快的有效算法。用演化算法解决了物理学中密立根油滴实验数据处理问题，用求一组小数最大公约数的方法，直接获得了电子电量，与传统的方法相比，使用本文算法所得到的结果更能反映实验的真实性。
第一章对演化计算作了全面的概述，介绍了演化计算的起源与发展、分支流派及特点，概述了演化计算的算法框架，介绍编码方式、遗传算子的设计、选择策略，研究现状及趋势。
第二章介绍参数估计问题，并讨论模型参数估计的经典算法及已有的一些改进算法，从保持种群多样性与动态调整搜索区间的角度，提出了一个新的演化算法。
第三章结合具体问题利用新算法来求解模型参数估计问题，并与已有算法的结果进行了比较，实验结果表明新算法是一个性能优良的有效算法。
第四章将演化算法应用于求解一组数的最大公约数，并用于解决实际问题。实验结果表明了算法的有效性和可行性。
第五章对全文做了总结，总结了本文的主要研究结果同时指出了今后的工作展望。
Evolutionary computation simulates the evolutionary process of nature, especially the creature species that evolves on stochastic optimization technique. It has characteristics such as self-organization, self-adaptive, self-learning and so on. The population-based searching mechanism makes it suitable run parallel in large scale. Evolutionary computation has found vast application to many science fields, of which evolutionary non-linear parameter evaluation is one direction.
The main content of this thesis is discussing how to improve evolutionary algorithm and raising a new evolutionary algorithm and using this new algorithm to parameter evaluation. A large number of computation shows that the new algorithm is a universal, searching-efficiently, converging-quickly algorithm. Data handle problem of the physics experiment of the R. A. Millikan oil drop is solved with evolving algorithm. Getting the greatest common divisor of the minimal data, we will directly obtain electronic quantity and reflect the result of the experiment.
In chapter one, the paper have described the overall concept, introduced the origination and the development, the branch of the school and the character of the evolution algorithm, depicted the frame of the algorithm, the method of coding, the design of crossover and mutation, selection strategy, the current situation and trend of research of evolution algorithm.
In chapter two, the paper have introduced the problem of parameter estimation, discussed the classical algorithm of the parameter estimation model and some unproved algorithm, In order to keep variety and dynamic adjust-searching area, we put forward to a new evolving algorithm.
In chapter three, we settled a model's parameter estimation with this new algorithm, the effect acquired with the new algorithm is better than that acquired with the other algorithms. The result shows that the new algorithm is a one with quality and affectivity.
In chapter four, we utilized evolution algorithm to get greatest common divisor of a set of numbers, and solved the concrete problem, the result proves that the new algorithm is affectivity and feasibility.
Chapter 5 summarizes the main work of the thesis and describes the work of future.
引文
[1] 潘正君，康立山，陈毓屏，演化计算，清华大学出版社，1998．
[2] Holland J. H., Adaptation in Natural and Artificial Systems, The University of Michigan Press, 1975.
[3] Fogel L. J., Owens A. J. and Walsh M. J., Artificial Intelligence through Simulated Evolution, John Wiley, New York, 1966.
[4] Fogel L. J., Owens A. J. and Walsh M. J., Artificial Intelligence through Simulated Evolution, John Wiley, New York, 1966.
[5] Koza J. R., Genetic Programming: On the Programming of Computer by Means of Nature Selection, Cambridge, MA, The MIT Press, 1992.
[6] Koza J. R., Genetic Programming Ⅱ: Automatic Discovery of Reusable Programs, Cambridge, MA, The MIT Press, 1994.
[7] Goldberg D. E., Genetic Algorithms in Search, Optimization and Machine Learning, Addison Wesley, Reading, MA, 1989.
[8] Fogel D. B., Evolutionary Programming for Training Neural Networks. International Joint Conference On Neural Networks'90, Washington: D. C., I-601-I-605, 1990.
[9] Fogel D. B., Evolving Neural Networks, Biol. Cybern, 63: 487-493. 1990,
[10] Saravanan N. and Fogel D. B., Evolving Neuron Controllers Using Evolutionary Programming. In [31], 217-222, 1994
[11] 陈文平，演化计算在优化领域中的应用，武汉大学硕士学位论文，2003．
[12] 蒋华，演化计算及其在图论中的应用，武汉大学硕士学位论文，2003．
[13] 丁承民，张传生，遗传算法纵横谈，信息与控制，26(1)：40-47．1997，
[14] 胡国四，韩生廉，遗传算法适值函数的定义方法，控制与决策，14(6)：694-697．1999
[15] 黄昱申，韩生廉，胡国四，遗传算法非效率操作的改进方法，控制与决策，15(2)：251-253．2000
[16] Srinivas M. and Patnaik L. M., Adaptive Probabilities of Crossover and Mutation in Gas, IEEE Trans. On SMC, 24(4): 656-667. 1994
[17] 杨艳丽，史维祥，一种新的优化算法—遗传算法的设计，液压气动与密封，Vol 86 No．2 pp13-15，2001
[18] 王小平，曹立明，遗传算法一理论、应用与软件实现，1998．
[19] 张晓绩，方浩，戴冠中，遗传算法的编码机制研究，信息与控制，1997．
[20] 周激流，丁晶，金菊良，一种新型遗传算法及其在暴雨强度公式参数优化中的应用研究，四川大学学报，Vol．37 No．4，pp543-546，2000．
[21] (美)Z．米凯利维茨，演化程序—遗传算法和数据编码的结合，科学出版社，2000．
[22] Booker L. B., Improving Search in Genetic Algorithm, in [32], pp:61-73.
[23] 方开泰，张金延，非线性回归模型参数估计的一个新算法，应用数学学报，Vol．16(3)，366--377，1993
[24] 张圣佩，潘守清，马清茂，大学物理实验，武汉工业大学出版社，1990．
[25] 石玉，提高实数遗传算法数值优化效率的研究，南京航空航天大学博士学位论文，2002．
[26] 曹志浩等，矩阵计算和方程求根，北京：高等教育出版社，1984．
[27] 陶云刚，误差理论与数据分析，北京：航空工业出版社，1997．
[28] 王正明，易东云，测量数据建模与参数估计，长沙：国防科技大学出版社，1996．
[29] 罗智华，李金萍，最大公约数的倍数和表示，张家口师专学报，No．2 1995
[30] 龙作友，王丰，大学物理实验，湖北科学技术出版社，2003．
[31] Michalewicz Z, Schaffer J D, Schwefel H P, Fogel D B and Kitano H(Eds.). Proc. of the 1st IEEE Int'l. Conf. on Evolutionary Computation(ICEC'94). Orlando, Florida, USA, IEEE press, 1994
[32] Davis, L, (Editor), Genetic Algorithms and Simulated Annealing, Morgan Kaufrnann Publishers., San Mateo, CA, 1987
[2] Holland J. H., Adaptation in Natural and Artificial Systems, The University of Michigan Press, 1975.
[3] Fogel L. J., Owens A. J. and Walsh M. J., Artificial Intelligence through Simulated Evolution, John Wiley, New York, 1966.
[4] Fogel L. J., Owens A. J. and Walsh M. J., Artificial Intelligence through Simulated Evolution, John Wiley, New York, 1966.
[5] Koza J. R., Genetic Programming: On the Programming of Computer by Means of Nature Selection, Cambridge, MA, The MIT Press, 1992.
[6] Koza J. R., Genetic Programming Ⅱ: Automatic Discovery of Reusable Programs, Cambridge, MA, The MIT Press, 1994.
[7] Goldberg D. E., Genetic Algorithms in Search, Optimization and Machine Learning, Addison Wesley, Reading, MA, 1989.
[8] Fogel D. B., Evolutionary Programming for Training Neural Networks. International Joint Conference On Neural Networks'90, Washington: D. C., I-601-I-605, 1990.
[9] Fogel D. B., Evolving Neural Networks, Biol. Cybern, 63: 487-493. 1990,
[10] Saravanan N. and Fogel D. B., Evolving Neuron Controllers Using Evolutionary Programming. In [31], 217-222, 1994
[11] 陈文平，演化计算在优化领域中的应用，武汉大学硕士学位论文，2003．
[12] 蒋华，演化计算及其在图论中的应用，武汉大学硕士学位论文，2003．
[13] 丁承民，张传生，遗传算法纵横谈，信息与控制，26(1)：40-47．1997，
[14] 胡国四，韩生廉，遗传算法适值函数的定义方法，控制与决策，14(6)：694-697．1999
[15] 黄昱申，韩生廉，胡国四，遗传算法非效率操作的改进方法，控制与决策，15(2)：251-253．2000
[16] Srinivas M. and Patnaik L. M., Adaptive Probabilities of Crossover and Mutation in Gas, IEEE Trans. On SMC, 24(4): 656-667. 1994
[17] 杨艳丽，史维祥，一种新的优化算法—遗传算法的设计，液压气动与密封，Vol 86 No．2 pp13-15，2001
[18] 王小平，曹立明，遗传算法一理论、应用与软件实现，1998．
[19] 张晓绩，方浩，戴冠中，遗传算法的编码机制研究，信息与控制，1997．
[20] 周激流，丁晶，金菊良，一种新型遗传算法及其在暴雨强度公式参数优化中的应用研究，四川大学学报，Vol．37 No．4，pp543-546，2000．
[21] (美)Z．米凯利维茨，演化程序—遗传算法和数据编码的结合，科学出版社，2000．
[22] Booker L. B., Improving Search in Genetic Algorithm, in [32], pp:61-73.
[23] 方开泰，张金延，非线性回归模型参数估计的一个新算法，应用数学学报，Vol．16(3)，366--377，1993
[24] 张圣佩，潘守清，马清茂，大学物理实验，武汉工业大学出版社，1990．
[25] 石玉，提高实数遗传算法数值优化效率的研究，南京航空航天大学博士学位论文，2002．
[26] 曹志浩等，矩阵计算和方程求根，北京：高等教育出版社，1984．
[27] 陶云刚，误差理论与数据分析，北京：航空工业出版社，1997．
[28] 王正明，易东云，测量数据建模与参数估计，长沙：国防科技大学出版社，1996．
[29] 罗智华，李金萍，最大公约数的倍数和表示，张家口师专学报，No．2 1995
[30] 龙作友，王丰，大学物理实验，湖北科学技术出版社，2003．
[31] Michalewicz Z, Schaffer J D, Schwefel H P, Fogel D B and Kitano H(Eds.). Proc. of the 1st IEEE Int'l. Conf. on Evolutionary Computation(ICEC'94). Orlando, Florida, USA, IEEE press, 1994
[32] Davis, L, (Editor), Genetic Algorithms and Simulated Annealing, Morgan Kaufrnann Publishers., San Mateo, CA, 1987