动态竞争策略的链式多智能体遗传算法的研究
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摘要
遗传算法(Genetic Algorithm)是根据生物进化理论和遗传变异理论提出的一种基于种群搜索的优化算法。由于其具有简单易行、鲁棒性强,以及不需要很多专业领域先验知识等特点,所以遗传算法在众多领域有良好的应用前景。但传统遗传算法有时会出现早收敛及搜索效率不高的现象,制约了它的进一步推广应用。
针对这两个不足,提出了一种链式智能体遗传算法CAGA(Chainlike Agents Genetic Algorithm)。该算法是一种单种群智能体遗传算法,采用实数编码,用生存在链式环境中的智能体代表候选解,通过智能体间的竞争与合作来搜索最优解。同时,该算法通过动态邻域竞争、邻域正交交叉、自适应变异等改进措施,提高智能体的搜索效率从而提高算法的优化性能。实验采用多个国际标准测试函数对该算法和其它几种改进遗传算法进行了多次函数优化性能测试。实验结果表明,该算法能有效防止早收敛现象,比其它多种改进GAs有较高的搜索效率。
对于一些复杂性和难度较大的应用问题,CAGA这种单种群智能体遗传算法仅采用一个种群进化,无法实现多种群并行搜索的性能,其算法的优化速度仍不能满足系统的实时性要求。基于此,本文进一步展开研究,提出了多子群协同链式智能体遗传算法(Multi-population Agents Genetic Algorithm,MPAGA)。该算法结合协同进化思想,采用了多子群并行搜索模式。其思路是:首先整个种群被划分为多个子群;其次,每个子群采用CAGA的方式进行进化,子群间通过共享智能体进行遗传信息的分享与传递,以实现多个子群协同寻找满意解的目的,有效提高了优化速度。本文采用多个国际标准的复杂测试函数对该算法的优化性能进行了测试。测试结果表明,与其它多种改进GAs相比,该算法不仅有较高质量的满意解,而且有较短的算法运行时间,能有效提高算法的优化速度。
此外,本文简短讨论了链式智能体遗传算法在特征选择中的应用。为了适应特征选择应用的需要,本文采用二进制编码作为搜索算法的编码方式,选用距离测度作为评价准则,并使用BP神经网络作为分类器对所选特征子集进行了分类测试。文末采用机器学习的经典数据集作为待分类数据集进行了多次测试。实验结果表明,与其它几种改进GAs相比,该算法能以较短的运算时间搜索到入选特征数较少但识别率较高的特征子集。
Genetic algorithm is a global optimization algorithm enlightened biological evolution theory. Because of its simplicity, robustness and no need for lots of prior knoeledge, genetic algorithm is applied in many fields. However, currently the algorithm has two severe disadvantages needing to be improved.
In order to improve the two disadvantages, one chain-like agent genetic algorithm (CAGA) is proposed in this paper. The CAGA adopts real coding, introduces agent standing for solution and living in chain-like environment, searchs global optima through the cooperation and competition of agents. The algorithm adopts dynamic neighborhood competition operator, neithborhood orthogonal crossover operator and neighborhood adaptive mutation operator to improve searching efficiency of agents, thereby improving optimization performance of the algorithm. Lots of benchmark test functions are used for comparing the optimization performance of CAGA and other representative GAs in the experiments. The experimental results show that CAGA can obtain higher optimization precision and can converge to the domain close to global optima rapidly.
The CAGA is an agent genetic algorithm with single population, it can not realize co-evolution with multi-population, so the optimization speed can not be improved greatly. Based on the reason, further research is done and Multi-population agents genetic algorithm (MPAGA) is proposed in this paper. This algorithm adopts parallel searching mode combining co-eovlution idea. The major process is: firstly the whole population is divided into many sub-populations. Then each sub-popualtion evolves as CAGA does. Sub-populations co-evolve and search global optima through the shared agents, thereby improving optimization speed. Lots of benchmark test functions are used for comparing the optimization performance of MPAGA and one popular agent genetic algorithm in the experiments. The experimental results show that MPAGA not only can improve optimization speed greatly, but also obtain satisfied optimization precision.
Besides, this paper briefly discusses the application of CAGA into feature selection problems. In order to use the algorithm in feature selection problems, the binary coding is used as coding strategy, distance measurement is used for evaluation criterion and BP neural network is used as classifier for classification test of feature subsets. In the experiments, several datasets is used for showing the performance of CAGA. The experimental results show that the CAGA can obtain less features, and higher classification accuracy compared with other popular GAs.
针对这两个不足,提出了一种链式智能体遗传算法CAGA(Chainlike Agents Genetic Algorithm)。该算法是一种单种群智能体遗传算法,采用实数编码,用生存在链式环境中的智能体代表候选解,通过智能体间的竞争与合作来搜索最优解。同时,该算法通过动态邻域竞争、邻域正交交叉、自适应变异等改进措施,提高智能体的搜索效率从而提高算法的优化性能。实验采用多个国际标准测试函数对该算法和其它几种改进遗传算法进行了多次函数优化性能测试。实验结果表明,该算法能有效防止早收敛现象,比其它多种改进GAs有较高的搜索效率。
对于一些复杂性和难度较大的应用问题,CAGA这种单种群智能体遗传算法仅采用一个种群进化,无法实现多种群并行搜索的性能,其算法的优化速度仍不能满足系统的实时性要求。基于此,本文进一步展开研究,提出了多子群协同链式智能体遗传算法(Multi-population Agents Genetic Algorithm,MPAGA)。该算法结合协同进化思想,采用了多子群并行搜索模式。其思路是:首先整个种群被划分为多个子群;其次,每个子群采用CAGA的方式进行进化,子群间通过共享智能体进行遗传信息的分享与传递,以实现多个子群协同寻找满意解的目的,有效提高了优化速度。本文采用多个国际标准的复杂测试函数对该算法的优化性能进行了测试。测试结果表明,与其它多种改进GAs相比,该算法不仅有较高质量的满意解,而且有较短的算法运行时间,能有效提高算法的优化速度。
此外,本文简短讨论了链式智能体遗传算法在特征选择中的应用。为了适应特征选择应用的需要,本文采用二进制编码作为搜索算法的编码方式,选用距离测度作为评价准则,并使用BP神经网络作为分类器对所选特征子集进行了分类测试。文末采用机器学习的经典数据集作为待分类数据集进行了多次测试。实验结果表明,与其它几种改进GAs相比,该算法能以较短的运算时间搜索到入选特征数较少但识别率较高的特征子集。
Genetic algorithm is a global optimization algorithm enlightened biological evolution theory. Because of its simplicity, robustness and no need for lots of prior knoeledge, genetic algorithm is applied in many fields. However, currently the algorithm has two severe disadvantages needing to be improved.
In order to improve the two disadvantages, one chain-like agent genetic algorithm (CAGA) is proposed in this paper. The CAGA adopts real coding, introduces agent standing for solution and living in chain-like environment, searchs global optima through the cooperation and competition of agents. The algorithm adopts dynamic neighborhood competition operator, neithborhood orthogonal crossover operator and neighborhood adaptive mutation operator to improve searching efficiency of agents, thereby improving optimization performance of the algorithm. Lots of benchmark test functions are used for comparing the optimization performance of CAGA and other representative GAs in the experiments. The experimental results show that CAGA can obtain higher optimization precision and can converge to the domain close to global optima rapidly.
The CAGA is an agent genetic algorithm with single population, it can not realize co-evolution with multi-population, so the optimization speed can not be improved greatly. Based on the reason, further research is done and Multi-population agents genetic algorithm (MPAGA) is proposed in this paper. This algorithm adopts parallel searching mode combining co-eovlution idea. The major process is: firstly the whole population is divided into many sub-populations. Then each sub-popualtion evolves as CAGA does. Sub-populations co-evolve and search global optima through the shared agents, thereby improving optimization speed. Lots of benchmark test functions are used for comparing the optimization performance of MPAGA and one popular agent genetic algorithm in the experiments. The experimental results show that MPAGA not only can improve optimization speed greatly, but also obtain satisfied optimization precision.
Besides, this paper briefly discusses the application of CAGA into feature selection problems. In order to use the algorithm in feature selection problems, the binary coding is used as coding strategy, distance measurement is used for evaluation criterion and BP neural network is used as classifier for classification test of feature subsets. In the experiments, several datasets is used for showing the performance of CAGA. The experimental results show that the CAGA can obtain less features, and higher classification accuracy compared with other popular GAs.
引文
[1] Holland J H. Adaptation in Natural and Artificial Systems [M]. Michigan: The University of Michigan Press, 1975.
[2]陈国良等.遗传算法及其应用[M].北京:人民邮电出版社,1996.
[3] J H Holland. Adaptation in nature and artificial system [M]. Cambridge MA: MIT Press, 1992.
[4] Z J Pan, L S Kang. an adaptive evolutionary algorithms for numerical optimization in simulated evolution and learning. lecture notes in artificial intelligence, X Yao, J H Kim, T Furuhashi, Eds Berlin, Germany: Springer-Verlag,1997, pp:27-34.
[5] X Yao, Y Liu, G Lin. Evolutionary programming made faster[J]. IEEE Transaction evolutionary computation, 1999, 3(3):82-102.
[6] H Muhlenbein, D Schlierkampvose. Predictive models for the breeder genetic algorithm[J]. Evolution comutation, 1993, 1(1):25-49.
[7]姚新,陈国良,徐惠敏.进化算法研究进展[J].计算机学报,1995,18(9):694-706.
[8]张文修,梁怡.遗传算法的数学基础[M].西安:西安交通大学出版社,2000.
[9] Mathias K E, Whitely L D. Transforming the Search Space with Gray Coding [J]. IEEE Transaction evolutionary computation, 1996, (48):319-524.
[10] Schraudolph N N, Belew R K. Dynamic Parameter Encoding for Genetic Algorithms. Machine Learning, 1992,9(1):9-21 .
[11] Michalewicz Z. Genetic Algorithms + Date Structure = Evolution Programs. Springer-Verlag [M]. Berlin. 1992.
[12] Wright A H. Genetic Algorithms for Real Parameter Optimization. Foundation of Genetic Algorithms . Morgan Kaufmann Sanmateo GA.1991:205-218.
[13]杨党林.排队“梯度”浮点数编码遗传算法[J]微电子学与计算机,2004,21(6):49-52
[14]杨淑媛,焦李成,刘芳.量子进化算法[J].工程数学学报,2006,23(2):235-246.
[15]陈辉,张家树.实数编码混沌量子遗传算法[J].控制与决策,2005,20(11):1300-1303.
[16]李阳阳,焦李成.量子克隆多播路由算法[J].软件学报,2007,18(9):2063-2069.
[17]王凌,吴昊,唐芳,郑大钟,金以慧.混合量子遗传算法及其性能分析[J].控制与决策,2005,20(2):156-160.
[18]唐飞,滕弘飞,刘峻,娄汉文.带有能力约束的二维装填布局问题[J].宇航学报,2000,21(2):50-57.
[19]雷德明.多维实数编码遗传算法[J].控制与决策,2000,15(2):239-241.
[20]姜大力,杨西龙.车辆路径问题的遗传算法研究[J].系统工程理论与实践,1999,19(1):26-30.
[21] Goldberg D E. Genetic Algorithms in Search, Optimization and Machine Learning [M]. Boston, MA: Addison-Wesley, 1989.
[22]张亮,王凌,郑大钟.随机优化问题基于假设检验的遗传算法[J].控制理论与应用,2004,21(6):885-889.
[23]钟伟才,刘静,焦李成.遗传算法中自适应伸缩搜索空间的方法[J].系统工程与电子技术,26(2):245-247.
[24]王凌,黄璇,郑大钟.一类带筛选策略的改进遗传算法及其性能分析[J].控制与决策,2004,19(11):1290-1297.
[25]覃俊,康立山.基于动态群体的聚集演化求解多峰函数优化问题[J].中南民族大学学报,2003,22(2):56-59.
[26] Shinn Ying Ho, Li Sun Shu, Jian Hung Chen. Intelligent Evolutionary Algorithms for Large Parameter Optimization Problems [A]. IEEE transactions on evolutionary computation [C], 1994, 8(6): 522-541.
[27] Chi-Hung Su, Tun Hsu Hou. Using multi-population intelligent genetic algorithm to find the pareto-optimal parameters for a nano-particle milling process [R].Expert Systems with Applications 34(2008):2502-2510.
[28]郝翔,李人厚.适用于复杂函数优化的多群体遗传算法[J].控制与决策,1998,13(3):263-266.
[29]郝翔,李人厚.一种快速有效的多模态函数寻优方法[J].控制理论与应用,1997,14(5):765-769.
[30]蔡良伟,张基宏,李霞.作业车间调度问题的多种群遗传算法[J].电子学报,2005,33(6):991-994.
[31]刘守生,于盛林,丁勇.基于均匀分割的多种群并行遗传算法[J].数据采集与处理,2003,18(2):142-145.
[32]易晗平,蒲超.非线性系统参数的多种群并行遗传优化[J].兵工自动化,2005,24(4):53-55.
[33]孙晓燕,巩敦卫.变种群规模合作型协同进化遗传算法及其在优化中的应用[J].控制与决策,2004,19(12):1437-1440.
[34] Davis L. Adaptive Operator Probability in Genetic Algorithms. In Proc.3rd In Conf Genetic Algorithms,1989:61-69.
[35] M. Srinivas, L M Patnaik. Adaptive Probabilities of Crossover and Mutation in Genetic Algorithms [A]. IEEE transactions on systems, man and cybernetics [C], 1994, 24 (4): 656-667.
[36] Whitley D, Starkweather D. A Distributed Genetic Algorithms[J]. Expt J Theory,1990,2:189-214.
[37]巩敦卫,孙晓燕,郭西进.一种新的优胜劣汰遗传算法[J].控制与决策,2002,17(6):908-911.
[38]张良杰,毛志宏,李衍达.遗传算法中突变算子的数学分析及改进策略[J].电子科学学刊,1996,18(6):590-595.
[39] Arabas J, Michalewicz Z, Mulawka J. GAVaPS-a Genetic Algorithm with Varying Population Size[C]. Proc. of the 1st IEEE Int Conf. on Evolutionary Computation (ICEC’94), Orlando, Florida, USA, IEEE press, 1994, 1:73-78.
[40]丁承民,张传生,刘贵忠.利用正交试验法优化配置遗传算法控制参数[R].西安交通大学电子与信息工程学院信息工程研究所研究报告,1996.
[41]张金奎,林萌宇,杨传忠,甘兴国,谢科.基于遗传算法的潮流多根求解方法[J].重庆大学学报(自然科学版),2000,23(1):56-59.
[42] Liu Li,Chen Xueyun.Reconfiguration of distribution networks based on fuzzy genetic algorithms[J]. Proceedings of the Chinese Society of Electrical Engineering,2000,20(2):66-69.
[43] Feng Q X, Francesco P. Theoretical Analysis of Evolutionary Algorithms with an Infinite Population Size in Continuous Space Part 1 and 2:Basic Properties of Selection and Mutation[J]. IEEE Trans Neural Networks , 1994,5(1):102-129.
[44]高汉平,康立山,杨族桥.基于自适应交叉、变异率的演化算法[J].黄冈师范学院学报,2003,23(3):57-59.
[45]陈文平,康立山.基于多父代杂交的多目标演化优化算法[J].计算机工程与应用,2003,39(10):79-82.
[46]李景治,康立山,方宁.多亲杂交算子及其在连续优化中的应用[J].计算机工程,2004,30(16):33-35.
[47]陈子仪,康立山.多父代杂交演化算法求解约束优化问题[J].武汉大学学报,2006,31(5):440-443.
[48]叶在福,单渊达.基于多种群遗传算法的输电系统扩展规划[J].电力系统自动化,2000,24(5):24-27.
[49] Xie Nan, Chen Yingjun. Improving strategies on genetic algorithm and its application to the optimum design of bridges under earthquake[J]. Engineering Mechanics Tsinghua University ,2000,17(3):31-36.
[50]汪俐,张玲.用网格实现交叉操作的遗传算法[J].计算机工程与科学,2000,22(1):18-22.
[51] Back T. Hoffmeister F. Extended Selection Mechanisms in Genetic Algorithms[J]. In Proc 4thInt Conf Genetic Algorithms, 1991:89-99.
[52] Maza M D L, Tidor B. An Analysis of Selection Procedures with Particular Paid to Proportion and Boltzmann Selection[J]. In Proc 7th Int Conf Genetic Algorithms, 1993:124-131.
[53] Back T .Selection pressure in evolutionary algorithm: a Characterization of selection mechanisms[C]. Proceeding of the First IEEE conference on Evolutionary computation, IEEE press, Orlando, FL.1994: 57-62.
[54] D T Pham, C Jin. Genetic Algorithms using gradient-like reproduction operator[J]. Electronics Letters, 1995, 31(18):1558-1559.
[55]徐锐,康立山,陈毓屏.对策论中最优策略搜索的协同进化演化算法[J].计算机工程与设计,2004,25(11):1966-1968,2011.
[56]谢大同,康立山,李悦乔.符号回归的一种新算法[J].系统仿真学报,2007,19(8):1667-1671.
[57]谢大同,康立山.函数优化的一种高效演化算法[J].计算机工程与应用,2007,43(4):44-46,57.
[58]祝安,康立山.冒泡择优遗传算法[J].计算机工程,2003,29(15):66-67,117.
[59]吴志健,康立山,邹秀芬.一种解函数优化问题的精英子空间演化算法[J].计算机应用,2003,23(2):13-15.
[60]覃俊,康立山,陈毓屏.演化算法的收敛性分析及算法改进[J].计算机工程与应用,2003,39(19):91-92,179.
[61]李彬彬,王凌,郑大钟.基于插值评估的遗传算法及其在参数估计中的应用[J].化工自动化及仪表,2004,31(6):14-17.
[62]王凌,李彬彬,郑大钟,金以慧.模型降阶和参数估计的一种快速遗传算法[J].控制与决策,2005,20(4):426-429,433.
[63] Storn R, Price K. Differential evolution—A simple and efficient adaptive scheme for global optimization over continuous spaces [R]. Berkeley: University of California, 2006.
[64]刘波,王凌,金以慧.差分进化算法研究进展[J].控制与决策,2007,22(7):721-729.
[65] Lampinen J. A bibliography of differential evolution algorithm [EB/OL]. http://www.lut.fi/~j lampine/debiblio.htm, 2002-10-14/2002-12-31.
[66] Weicai Zhong, Jing Liu, Mingzhi Xue, Licheng Jiao. A Multi-agent Genetic Algorithm for Global Numerical Optimization [J]. IEEE transactions on systems, man and cybernetics, 2004, 34(2): 1128-1141.
[67] Y.W.Leung, Y.Wang. An orthogonal genetic algorithm with quantization for global numerical optimization [J]. IEEE Transaction evolutionary computation, 2001, 1(5).41-53.
[68] Zbigniew Michalewicz David B.Fogel著.曹宏庆,李艳,董红斌,吴志健译.如何求解问题—现代启发式方法[M].中国水利水电出版社,2003.
[69]高鹰,谢胜利.基于聚类的多子群粒子群优化算法[J].计算机应用研究,2006,23(4):40-41.
[70]张丽萍,柴跃廷.遗传算法的现状及发展动向[J].信息与控制,2001,30(6):531-536.
[2]陈国良等.遗传算法及其应用[M].北京:人民邮电出版社,1996.
[3] J H Holland. Adaptation in nature and artificial system [M]. Cambridge MA: MIT Press, 1992.
[4] Z J Pan, L S Kang. an adaptive evolutionary algorithms for numerical optimization in simulated evolution and learning. lecture notes in artificial intelligence, X Yao, J H Kim, T Furuhashi, Eds Berlin, Germany: Springer-Verlag,1997, pp:27-34.
[5] X Yao, Y Liu, G Lin. Evolutionary programming made faster[J]. IEEE Transaction evolutionary computation, 1999, 3(3):82-102.
[6] H Muhlenbein, D Schlierkampvose. Predictive models for the breeder genetic algorithm[J]. Evolution comutation, 1993, 1(1):25-49.
[7]姚新,陈国良,徐惠敏.进化算法研究进展[J].计算机学报,1995,18(9):694-706.
[8]张文修,梁怡.遗传算法的数学基础[M].西安:西安交通大学出版社,2000.
[9] Mathias K E, Whitely L D. Transforming the Search Space with Gray Coding [J]. IEEE Transaction evolutionary computation, 1996, (48):319-524.
[10] Schraudolph N N, Belew R K. Dynamic Parameter Encoding for Genetic Algorithms. Machine Learning, 1992,9(1):9-21 .
[11] Michalewicz Z. Genetic Algorithms + Date Structure = Evolution Programs. Springer-Verlag [M]. Berlin. 1992.
[12] Wright A H. Genetic Algorithms for Real Parameter Optimization. Foundation of Genetic Algorithms . Morgan Kaufmann Sanmateo GA.1991:205-218.
[13]杨党林.排队“梯度”浮点数编码遗传算法[J]微电子学与计算机,2004,21(6):49-52
[14]杨淑媛,焦李成,刘芳.量子进化算法[J].工程数学学报,2006,23(2):235-246.
[15]陈辉,张家树.实数编码混沌量子遗传算法[J].控制与决策,2005,20(11):1300-1303.
[16]李阳阳,焦李成.量子克隆多播路由算法[J].软件学报,2007,18(9):2063-2069.
[17]王凌,吴昊,唐芳,郑大钟,金以慧.混合量子遗传算法及其性能分析[J].控制与决策,2005,20(2):156-160.
[18]唐飞,滕弘飞,刘峻,娄汉文.带有能力约束的二维装填布局问题[J].宇航学报,2000,21(2):50-57.
[19]雷德明.多维实数编码遗传算法[J].控制与决策,2000,15(2):239-241.
[20]姜大力,杨西龙.车辆路径问题的遗传算法研究[J].系统工程理论与实践,1999,19(1):26-30.
[21] Goldberg D E. Genetic Algorithms in Search, Optimization and Machine Learning [M]. Boston, MA: Addison-Wesley, 1989.
[22]张亮,王凌,郑大钟.随机优化问题基于假设检验的遗传算法[J].控制理论与应用,2004,21(6):885-889.
[23]钟伟才,刘静,焦李成.遗传算法中自适应伸缩搜索空间的方法[J].系统工程与电子技术,26(2):245-247.
[24]王凌,黄璇,郑大钟.一类带筛选策略的改进遗传算法及其性能分析[J].控制与决策,2004,19(11):1290-1297.
[25]覃俊,康立山.基于动态群体的聚集演化求解多峰函数优化问题[J].中南民族大学学报,2003,22(2):56-59.
[26] Shinn Ying Ho, Li Sun Shu, Jian Hung Chen. Intelligent Evolutionary Algorithms for Large Parameter Optimization Problems [A]. IEEE transactions on evolutionary computation [C], 1994, 8(6): 522-541.
[27] Chi-Hung Su, Tun Hsu Hou. Using multi-population intelligent genetic algorithm to find the pareto-optimal parameters for a nano-particle milling process [R].Expert Systems with Applications 34(2008):2502-2510.
[28]郝翔,李人厚.适用于复杂函数优化的多群体遗传算法[J].控制与决策,1998,13(3):263-266.
[29]郝翔,李人厚.一种快速有效的多模态函数寻优方法[J].控制理论与应用,1997,14(5):765-769.
[30]蔡良伟,张基宏,李霞.作业车间调度问题的多种群遗传算法[J].电子学报,2005,33(6):991-994.
[31]刘守生,于盛林,丁勇.基于均匀分割的多种群并行遗传算法[J].数据采集与处理,2003,18(2):142-145.
[32]易晗平,蒲超.非线性系统参数的多种群并行遗传优化[J].兵工自动化,2005,24(4):53-55.
[33]孙晓燕,巩敦卫.变种群规模合作型协同进化遗传算法及其在优化中的应用[J].控制与决策,2004,19(12):1437-1440.
[34] Davis L. Adaptive Operator Probability in Genetic Algorithms. In Proc.3rd In Conf Genetic Algorithms,1989:61-69.
[35] M. Srinivas, L M Patnaik. Adaptive Probabilities of Crossover and Mutation in Genetic Algorithms [A]. IEEE transactions on systems, man and cybernetics [C], 1994, 24 (4): 656-667.
[36] Whitley D, Starkweather D. A Distributed Genetic Algorithms[J]. Expt J Theory,1990,2:189-214.
[37]巩敦卫,孙晓燕,郭西进.一种新的优胜劣汰遗传算法[J].控制与决策,2002,17(6):908-911.
[38]张良杰,毛志宏,李衍达.遗传算法中突变算子的数学分析及改进策略[J].电子科学学刊,1996,18(6):590-595.
[39] Arabas J, Michalewicz Z, Mulawka J. GAVaPS-a Genetic Algorithm with Varying Population Size[C]. Proc. of the 1st IEEE Int Conf. on Evolutionary Computation (ICEC’94), Orlando, Florida, USA, IEEE press, 1994, 1:73-78.
[40]丁承民,张传生,刘贵忠.利用正交试验法优化配置遗传算法控制参数[R].西安交通大学电子与信息工程学院信息工程研究所研究报告,1996.
[41]张金奎,林萌宇,杨传忠,甘兴国,谢科.基于遗传算法的潮流多根求解方法[J].重庆大学学报(自然科学版),2000,23(1):56-59.
[42] Liu Li,Chen Xueyun.Reconfiguration of distribution networks based on fuzzy genetic algorithms[J]. Proceedings of the Chinese Society of Electrical Engineering,2000,20(2):66-69.
[43] Feng Q X, Francesco P. Theoretical Analysis of Evolutionary Algorithms with an Infinite Population Size in Continuous Space Part 1 and 2:Basic Properties of Selection and Mutation[J]. IEEE Trans Neural Networks , 1994,5(1):102-129.
[44]高汉平,康立山,杨族桥.基于自适应交叉、变异率的演化算法[J].黄冈师范学院学报,2003,23(3):57-59.
[45]陈文平,康立山.基于多父代杂交的多目标演化优化算法[J].计算机工程与应用,2003,39(10):79-82.
[46]李景治,康立山,方宁.多亲杂交算子及其在连续优化中的应用[J].计算机工程,2004,30(16):33-35.
[47]陈子仪,康立山.多父代杂交演化算法求解约束优化问题[J].武汉大学学报,2006,31(5):440-443.
[48]叶在福,单渊达.基于多种群遗传算法的输电系统扩展规划[J].电力系统自动化,2000,24(5):24-27.
[49] Xie Nan, Chen Yingjun. Improving strategies on genetic algorithm and its application to the optimum design of bridges under earthquake[J]. Engineering Mechanics Tsinghua University ,2000,17(3):31-36.
[50]汪俐,张玲.用网格实现交叉操作的遗传算法[J].计算机工程与科学,2000,22(1):18-22.
[51] Back T. Hoffmeister F. Extended Selection Mechanisms in Genetic Algorithms[J]. In Proc 4thInt Conf Genetic Algorithms, 1991:89-99.
[52] Maza M D L, Tidor B. An Analysis of Selection Procedures with Particular Paid to Proportion and Boltzmann Selection[J]. In Proc 7th Int Conf Genetic Algorithms, 1993:124-131.
[53] Back T .Selection pressure in evolutionary algorithm: a Characterization of selection mechanisms[C]. Proceeding of the First IEEE conference on Evolutionary computation, IEEE press, Orlando, FL.1994: 57-62.
[54] D T Pham, C Jin. Genetic Algorithms using gradient-like reproduction operator[J]. Electronics Letters, 1995, 31(18):1558-1559.
[55]徐锐,康立山,陈毓屏.对策论中最优策略搜索的协同进化演化算法[J].计算机工程与设计,2004,25(11):1966-1968,2011.
[56]谢大同,康立山,李悦乔.符号回归的一种新算法[J].系统仿真学报,2007,19(8):1667-1671.
[57]谢大同,康立山.函数优化的一种高效演化算法[J].计算机工程与应用,2007,43(4):44-46,57.
[58]祝安,康立山.冒泡择优遗传算法[J].计算机工程,2003,29(15):66-67,117.
[59]吴志健,康立山,邹秀芬.一种解函数优化问题的精英子空间演化算法[J].计算机应用,2003,23(2):13-15.
[60]覃俊,康立山,陈毓屏.演化算法的收敛性分析及算法改进[J].计算机工程与应用,2003,39(19):91-92,179.
[61]李彬彬,王凌,郑大钟.基于插值评估的遗传算法及其在参数估计中的应用[J].化工自动化及仪表,2004,31(6):14-17.
[62]王凌,李彬彬,郑大钟,金以慧.模型降阶和参数估计的一种快速遗传算法[J].控制与决策,2005,20(4):426-429,433.
[63] Storn R, Price K. Differential evolution—A simple and efficient adaptive scheme for global optimization over continuous spaces [R]. Berkeley: University of California, 2006.
[64]刘波,王凌,金以慧.差分进化算法研究进展[J].控制与决策,2007,22(7):721-729.
[65] Lampinen J. A bibliography of differential evolution algorithm [EB/OL]. http://www.lut.fi/~j lampine/debiblio.htm, 2002-10-14/2002-12-31.
[66] Weicai Zhong, Jing Liu, Mingzhi Xue, Licheng Jiao. A Multi-agent Genetic Algorithm for Global Numerical Optimization [J]. IEEE transactions on systems, man and cybernetics, 2004, 34(2): 1128-1141.
[67] Y.W.Leung, Y.Wang. An orthogonal genetic algorithm with quantization for global numerical optimization [J]. IEEE Transaction evolutionary computation, 2001, 1(5).41-53.
[68] Zbigniew Michalewicz David B.Fogel著.曹宏庆,李艳,董红斌,吴志健译.如何求解问题—现代启发式方法[M].中国水利水电出版社,2003.
[69]高鹰,谢胜利.基于聚类的多子群粒子群优化算法[J].计算机应用研究,2006,23(4):40-41.
[70]张丽萍,柴跃廷.遗传算法的现状及发展动向[J].信息与控制,2001,30(6):531-536.