基于初始种群改进策略的经验遗传-单纯形算法
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摘要
为提高初始种群的多样性,加快经验遗传-单纯形算法搜索效率,对算法初始种群的随机生成方式进行了改进.首先对问题搜索空间进行均匀划分,然后应用均匀试验设计对划分的子区间进行选择,最后在选择的子空间内分别产生随机数,由此获得在搜索空间内均匀分散的个体,增加初始种群的多样性.将该方法应用到典型测试函数的寻优计算中,比较和分析结果表明:在种群规模相同的情况下,相比于随机初始种群,均匀设计得到的改进初始种群可提高优化求解的寻优效率.
To obtain the initial population individual with diversity and speed up the search efficiency of the empirical genetic-simplex algorithm( EGSA),an improved method of initial population's generation for EGSA is described in this paper. First,the searching space of an optimization problem was meshed into several uniform subspaces; Second,uniform design was utilized to select the subspaces; Finally random numbers were generated in the selected subspaces that became individuals of the initial population finally. Therefore,the initial population that dispersed in the search space uniformly were obtained,increasing the diversity of the initial population. Classical test functions were selected and calculated by the proposed method for comparison. Testing results show that under the condition of the same population size,the initial population obtained by uniform design can improve the optimization efficiency of EGSA compared with random initial population.
To obtain the initial population individual with diversity and speed up the search efficiency of the empirical genetic-simplex algorithm( EGSA),an improved method of initial population's generation for EGSA is described in this paper. First,the searching space of an optimization problem was meshed into several uniform subspaces; Second,uniform design was utilized to select the subspaces; Finally random numbers were generated in the selected subspaces that became individuals of the initial population finally. Therefore,the initial population that dispersed in the search space uniformly were obtained,increasing the diversity of the initial population. Classical test functions were selected and calculated by the proposed method for comparison. Testing results show that under the condition of the same population size,the initial population obtained by uniform design can improve the optimization efficiency of EGSA compared with random initial population.
引文
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[12]陈理国,蔡之华.改进的正交遗传算法及其在函数优化中的应用[J].计算机工程与设计,2008,29(13):3413-3415.CHEN Li-guo,CAI Zhi-hua.Application of improving orthogonal-based genetic algorithm in function optimization[J].Computer Engineering and Design,2008,29(13):3413-3415.(in Chinese)
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[14]江洁,王主丁,张宗益,等.基于有效生成初始种群的电网无功规划优化遗传算法[J].电网技术,2009,33(8):60-65.JIANG Jie,WANG Zhu-ding,ZHANG Zong-yi,et al.Effective initial population generationbased genetic algorithm for optimal capacitor placement inradial distribution networks[J].Power System Technology,2009,33(8):60-65.(in Chinese)
[15]李志西,杜双奎.试验优化设计与统计分析[M].北京:科学出版社,2010.
[16]方开泰,马长兴.正交与均匀试验设计[M].北京:科学出版社,2001.
[17]张晓缋,戴冠中,徐乃平.遗传算法种群多样性的分析研究[J].控制理论与引用,1998,15(1):17-23.ZHANG Xiao-hui,DAI Guan-zhong,XU Nai-ping.Analysis of population diversity of genetic algorithm[J].Control Theory and Applications,1998,15(1):17-23.(in Chinese)
[18]方开泰.均匀试验设计的理论、方法和应用——历史回顾[J].数理统计与管理,2004,23(3):69-80.FANG Kai-tai.The theory,method and application of uniform design—a history review[J].Application of Statistics and Management,2004,23(3):69-80.(in Chinese)
[19]方开泰.均匀设计[J].战术导弹技术,1994(2):56-69.FANG Kai-tai.Uniform design[J].Tactical Missile Technology,1994(2):56-69.(in Chinese)
[20]杜修力,韩玲,姜丽萍.高效寻优的经验遗传算法[J].北京工业大学学报,2006,32(11):992-995.DU Xiu-li,HAN Ling,JIANG Li-ping.An efficient global optimization algorithm empirical genetic algorithm[J].Journal of Beijing University of Technology,2006,32(11):992-995.(in Chinese)
[21]潘正君,康立山,陈毓平.演化计算[M].北京:清华大学出版社,南宁:广西科学技术出版社,1998.
[2]韩炜.一种全局-局部优化算法及其在桩基承载力反演中的应用[D].哈尔滨:中国地震局工程力学研究所,2000.HAN Wei.A global-local optimization algorithm and its applicationin the pile bearing capacity inversion[D].Harbin:Institute of Engineering Mechanics,China Earthquake Engineering Bureau,2000.(in Chinese)
[3]MONTANA D J,DAVIS L.Training feedforward neural networks using genetic algorithms[C]∥Proceedings of the International Joint Conference on Artificial Intelligence.Michigan:Morgan Kaufmann Publishers,Inc,1989:762-767.
[4]王凌,郑大钟.一种GASA混合优化策略[J].控制理论与应用,2001,18(4):552-554.WANG Ling,ZHENG Da-zhong.A kind of GASA hybrid optimization strategy[J].Control Theory and Applications,2001,18(4):552-554.(in Chinese)
[5]杜修力,王智慧,李立云,等.土钉结构稳定验算的经验遗传-单纯形算法[J].岩土工程学报,2007,29(4):598-602.DU Xiu-li,WANG Zhi-hui,LI Li-yun,et al.Interior stablility analysis method of soil-nail structure based on empirical genetic-simplex algorithm[J].Chinese Journal of Geotechnical Engineering,2007,29(4):598-602.(in Chinese)
[6]李敏强,寇继松,林丹,等.遗传算法的基本理论与应[M].北京:科学出版社,2002.
[7]何大阔,王福利,贾明兴.遗传算法初始种群与操作参数的均匀设计[J].东北大学学报:自然科学版,2005,26(9):828-831.HE Da-kuo,WANG Fu-li,JIA Ming-xing.Uniform design of tinitial population and operationalparameters of genetic algorithm[J].Journal of Northeastern University:Natural Science,2005,26(9):828-831.(in Chinese)
[8]唐世浩,朱启疆.遗传算法中初始种群与交叉、变异率对解的影响及其解决方案[J].科技通报,2001,17(3):1-7.TANG Shi-hao,ZHU Qi-jiang.Effects of the initial population,crossover and mutation rate to the results of genetic algorithms and a possible solution scheme[J].Bulletin of Science and Technology,2001,17(3):1-7.(in Chinese)
[9]DIAZ-GOMEZ P A,HOUGEN D F.Initial population for genetic algorithms:a metric approach[J].Lecture Notes in Computer Science,2013,7902:435-444.
[10]LEUNG Yiu-wing,WANG Yu-ping.Multi-objective programming using uniform design and genetic algorithm[J].IEEE Transactions on Systems Man and Cybernetics,2000,30(3):293-304.
[11]LEUNG Yiu-wing,WANG Yu-ping.An orthogonal genetic algorithm with quantization for global numerical optimization[J].IEEE Transactions on Evolutionary Computation,2001,5(1):41-53.
[12]陈理国,蔡之华.改进的正交遗传算法及其在函数优化中的应用[J].计算机工程与设计,2008,29(13):3413-3415.CHEN Li-guo,CAI Zhi-hua.Application of improving orthogonal-based genetic algorithm in function optimization[J].Computer Engineering and Design,2008,29(13):3413-3415.(in Chinese)
[13]张建勇,李军.具有同时配送和回收需求的车辆路径问题的混合遗传算法[J].中国公路学报,2006,19(4):118-122.ZHANG Jian-yong,LI Jun.Hyrid genetic algorithm tovehicle routing problem with simultaneous delivery and pick-up[J].China Journal of Highway and Transport,2006,19(4):118-122.(in Chinese)
[14]江洁,王主丁,张宗益,等.基于有效生成初始种群的电网无功规划优化遗传算法[J].电网技术,2009,33(8):60-65.JIANG Jie,WANG Zhu-ding,ZHANG Zong-yi,et al.Effective initial population generationbased genetic algorithm for optimal capacitor placement inradial distribution networks[J].Power System Technology,2009,33(8):60-65.(in Chinese)
[15]李志西,杜双奎.试验优化设计与统计分析[M].北京:科学出版社,2010.
[16]方开泰,马长兴.正交与均匀试验设计[M].北京:科学出版社,2001.
[17]张晓缋,戴冠中,徐乃平.遗传算法种群多样性的分析研究[J].控制理论与引用,1998,15(1):17-23.ZHANG Xiao-hui,DAI Guan-zhong,XU Nai-ping.Analysis of population diversity of genetic algorithm[J].Control Theory and Applications,1998,15(1):17-23.(in Chinese)
[18]方开泰.均匀试验设计的理论、方法和应用——历史回顾[J].数理统计与管理,2004,23(3):69-80.FANG Kai-tai.The theory,method and application of uniform design—a history review[J].Application of Statistics and Management,2004,23(3):69-80.(in Chinese)
[19]方开泰.均匀设计[J].战术导弹技术,1994(2):56-69.FANG Kai-tai.Uniform design[J].Tactical Missile Technology,1994(2):56-69.(in Chinese)
[20]杜修力,韩玲,姜丽萍.高效寻优的经验遗传算法[J].北京工业大学学报,2006,32(11):992-995.DU Xiu-li,HAN Ling,JIANG Li-ping.An efficient global optimization algorithm empirical genetic algorithm[J].Journal of Beijing University of Technology,2006,32(11):992-995.(in Chinese)
[21]潘正君,康立山,陈毓平.演化计算[M].北京:清华大学出版社,南宁:广西科学技术出版社,1998.
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