粒子群算法参数设置对新安江模型模拟结果的影响研究
|
摘要
合理的粒子群算法(Particle Swarm Optimization Algorithm,PSO)的参数设置,可以提高算法的优化效率、避免陷入局部最优值,但常用参数设置对于特定优化问题,如新安江模型模拟,不具普适性。为分析种群规模pop、惯性权重w、学习因子c1和c2以及速度位置相关系数m这5个粒子群参数对新安江模型模拟结果的影响,对每个参数取5个不同水平,应用L25(56)正交表,设计了正交试验。通过对试验结果进行分析,得出了参数对PSO算法性能的影响能力和最优的参数组合方案(pop=80,w=1.3~0.4线性递减,c1=1.85,c2=2.5,m=0.05)。通过极差分析和方差分析,得出参数pop和w对模型模拟结果具有高显著性,其他三个参数对模型模拟结果不显著。将不同PSO参数组合应用于新安江模型模拟,证明了合理的PSO算法参数设置可以有效提高新安江模型模拟精度。通过对各因素分别进行趋势分析,得到了因素取值变化趋势与模型结果变化趋势的相关关系。本文提出的方法为如何寻找某一特定应用情景下的PSO算法参数组合提供了一种借鉴。
The reasonable parameter settings in the particle swarm optimization algorithm can improve the optimization efficiency and avoid falling into the local optimum.However,common parameter settings are not universally applicable to specific optimization problems,such as the simulation of Xin′anjiang model.In this study,we conducted orthogonal tests to study the influence of 5 particle swarm parameters on the simulation results of Xin′anjiang model.Through the analysis of the test results,we revealed the influence of parameters on the performance of PSO algorithm and obtained the optimum parameters(pop=80,w=linear regression from 1.3 to 0.4,c1=1.85,c2=2.5,m=0.05).Through range analysis and variance analysis,we found that the parameters pop and w are highly significant to the simulation results,and the other three parameters are not significant to the simulation results.The different PSO parameter sets were applied to Xin′anjiang model simulation,and proved that the reasonable PSO algorithm parameter setting can effectively improve the simulation accuracy of Xin′anjiang model.Through the trend analysis of each factor,we obtained the relationship between the change trend of the factor value and the change trend of the model result.The method presented in this paper can provide reference for finding the parameters of PSO algorithm in a specific application scenario.
The reasonable parameter settings in the particle swarm optimization algorithm can improve the optimization efficiency and avoid falling into the local optimum.However,common parameter settings are not universally applicable to specific optimization problems,such as the simulation of Xin′anjiang model.In this study,we conducted orthogonal tests to study the influence of 5 particle swarm parameters on the simulation results of Xin′anjiang model.Through the analysis of the test results,we revealed the influence of parameters on the performance of PSO algorithm and obtained the optimum parameters(pop=80,w=linear regression from 1.3 to 0.4,c1=1.85,c2=2.5,m=0.05).Through range analysis and variance analysis,we found that the parameters pop and w are highly significant to the simulation results,and the other three parameters are not significant to the simulation results.The different PSO parameter sets were applied to Xin′anjiang model simulation,and proved that the reasonable PSO algorithm parameter setting can effectively improve the simulation accuracy of Xin′anjiang model.Through the trend analysis of each factor,we obtained the relationship between the change trend of the factor value and the change trend of the model result.The method presented in this paper can provide reference for finding the parameters of PSO algorithm in a specific application scenario.
引文
[1]ZHAO R J.The Xinanjiang model applied in China[J].Journal of Hydrology,1992,135(1/4):371-381.DOI:10.1016/0022-1694(92)90096-E.
[2]栾承梅.流域水文模型参数优化问题研究[D].南京:河海大学,2005.(LUAN C M.Study on automatic optimization of hydrologic models′parameters[D].Nanjing:Hohai University,2005.(in Chinese))DOI:10.7666/d.y716959.
[3]杜非.伊洛河流域土地覆被变化水文效应的研究[D].河海大学,2007.(DU F.Hydrological effects of land cover change in Yiluo River Basin[D].Nanjing:Hohai University,2007.(in Chinese))DOI:10.7666/d.y1128418.
[4]ROSENBROCK H H.An automatic method for finding the greatest or least value of a function[J].1960,3(3):175-184.DOI:10.1093/comjnl/3.3.175.
[5]SPENDLEY W,HEXT G R,HIMSWORTH F R.Sequential application of simplex designs in optimisation and evolutionary operation[J].Technometrics,1962,4(4):441-461.DOI:10.1080/00401706.1962.10490033.
[6]WANG Q J.The genetic algorithm and its application to calibrating conceptual rainfall-runoff models[J].Water Resources Research,1991,27(9):2467-2471.DOI:10.1029/91WR01305.
[7]KENNEDY J,EBERHART R.Particle Swarm Optimization[C]//IEEE International Conference on Neural Networks,1995.Proceedings.IEEE,2002:1942-1948 vol.4.DOI:10.1109/ICNN.1995.488968.
[8]JAMIAN J J,ABDULLAH M N,MOKHLIS H,et al.Global particle swarm optimization for high dimension numerical functions analysis[J].Journal of Applied Mathematics,2014(2014),14.DOI:10.1155/2014/329193.
[9]丁根宏,曹文秀.改进粒子群算法在水库优化调度中的应用[J].南水北调与水利科技,2014(1):118-121.(DING G H,CAO W X.Application of improved particle swarm optimization algorithm in optimal operation of reservoir[J].South-to-North Water Transfers and Water Science&Technology,2014(1):118-121.(in Chinese))DOI:10.3724/SP.J.1201.2014.01118.
[10]宋健蛟,赵红莉,蒋云钟.粒子群算法在密云水库供水优化配置中的应用[J].南水北调与水利科技,2015(2):378-381.(SONG J J,ZHAO H L,JIANG Y Z.Application of particle swarm optimization in the optimal water allocation of Miyun Reservoir[J].South-to-North Water Transfers and Water Science&Technology,2015(2):378-381.(in Chinese))DOI:10.13476/j.cnki.nsbdqk.2015.02.041.
[11]关圣涛,楚纪正,邵帅.粒子群优化算法在非线性模型预测控制中的研究应用[J].北京化工大学学报(自然科学版),2007,34(6):653-656.(GUAN S T,CHU J Z,SHAO S.Application of nonlinear model predictive control based on particle swarm optimization[J].Journal of Beijing University of Chemical Technology(Natural Science Edition),2007,34(6):653-656.(in Chinese))DOI:10.3969/j.issn.1671-4628.2007.06.022.
[12]沈学利,张红岩,张纪锁.一种新的改进粒子群优化算法[J].计算机仿真,2011,28(3):246-249.(SHEN X L,ZHANG H Y,ZHANG J S.A new improved particle swarm optimization algorithm[J].Computer Simulation,2011,28(3):246-249.(in Chinese))DOI:10.3969/j.issn.1006-9348.2011.03.060.
[13]江燕,刘昌明,胡铁松,等.新安江模型参数优选的改进粒子群算法[J].水利学报,2007,38(10):1200-1206.(JIANG Y,LIU C M,HU T S,et al.Improved particle swarm optimization for parameter calibration of Xin′anjiang Model[J].Journal of Hydraulic Engineering,2007,38(10):1200-1206.(in Chinese))DOI:10.3321/j.issn:0559-9350.2007.10.008.
[14]张文明,董增川,朱成涛,等.基于粒子群算法的水文模型参数多目标优化研究[J].水利学报,2008,39(5):20-26.(ZHANG W M,DONG Z C,ZHU C T.Automatic Calibration of hydrologic model based on multi-objective particle swarm optimization method[J].Journal of Hydraulic Engineering,2008,39(5):20-26.(in Chinese))DOI:10.3321/j.issn:0559-9350.2008.05.003.
[15]王问宇,袁鹏,邵骏,等.改进粒子群算法在新安江模型参数优选中的应用[J].水力发电,2008,34(8):14-16.(WANG W Y,YUAN P,SHAO J,et al.Application of improved particle swarm algorithm to the parameter selection optimization of Xin′anjiang Model[J].Water Power,2008,34(8):14-16.(in Chinese))DOI:10.3969/j.issn.0559-9342.2008.08.005.
[16]REZAEE J A,JASNI J.Parameter selection in particle swarm optimization:A survey[J].Journal of Experimental&Theoretical Artificial Intelligence,2013,25(4):527-542.DOI:10.1080/0952813X.2013.782348.
[17]NOURMOHAMMADZADEH A,HARTMANN S,MA H.A Parallel Hybrid GA-PSO Approach with Dynamic Rule-based Parameter Setting[C]//Proceedings of the Genetic and Evolutionary Computation Conference Companion.ACM,2017:215-216.DOI:10.1145/3067695.3076051.
[18]SHI Y,EBERHART R C.Parameter selection in particle swarm optimization[C]//International Conference on Evolutionary Programming Vii.Springer-Verlag,1998:591-600.DOI:10.1007/BFb0040810.
[19]SHI Y,EBERHART R C.Empirical study of particle swarm optimization[J].Frontiers of Computer Science in China,1999,3(1):31-37.DOI:10.1109/CEC.1999.785511.
[20]TRELEA I C.The particle swarm optimization algorithm:convergence analysis and parameter selection[J].Information Processing Letters,2003,85(6):317-325.DOI:10.1016/S0020-0190(02)00447-7.
[21]王维博,林川,郑永康.粒子群算法中参数的实验与分析[J].西华大学学报(自然科学版),2008,27(1):76-79.(WANG W B,LIN C,ZHENG Y K.Experiment and analysis of parameters in particle swarm optimization[J].Journal of Xihua University(Natural Science),2008,27(1):76-79.(in Chinese))DOI:10.3969/j.issn.1673-159X.2008.01.026.
[22]ZHANG W,MA D,WEI J,et al.A parameter selection strategy for particle swarm optimization based on particle positions[J].Expert Systems with Applications,2014,41(7):3576-3584.DOI:10.1016/j.eswa.2013.10.061.
[23]刘苏宁,甘泓,魏国孝.粒子群算法在新安江模型参数率定中的应用[J].水利学报,2010,41(5):537-544.(LIU S N,GAN H,WEI G X.Application of PSO algorithm to calibrate the xin′anjiang hydrological model[J].Journal of Hydraulic Engineering,2010,41(5):537-544.(in Chinese))DOI:10.13243/j.cnki.slxb.2010.05.003.
[24]李爱国,覃征,鲍复民,等.粒子群优化算法[J].计算机工程与应用,2002,38(21):1-3.(LI A G,QIN Z,BAO F M,et al.Particle swarm optimization algorithms[J].Computer Engineering and Applications,2002,38(21):1-3.(in Chinese))DOI:10.3321/j.issn:1002-8331.2002.21.001.
[25]刘志煌,杨宜民.PSO的惯性权重与种群大小选择[J].计算机与现代化,2007,2007(6):1-3.(LIU Z H,YANG Y M.Inertia parameter and swarm size selection of PSO[J].Computer and Modemization,2007,2007(6):1-3.(in Chinese))DOI:10.3969/j.issn.1006-2475.2007.06.001.
[26]RATHORE A,SHARMA H.Review on inertia weight strategies for particle swarm optimization[C]//Proceedings of Sixth International Conference on Soft Computing for Problem Solving.Springer,Singapore,2017:76-86.DOI:10.1007/978-981-10-3322-3_8.
[27]NASH J E,SUTCLIFFE J V.River flow forecasting through conceptual models part I—A discussion of principles[J].Journal of Hydrology,1970,10(3):282-290.DOI:10.1016/0022-1694(70)90255-6.
[28]陈仲堂.应用数理统计[M].国防工业出版社,2011.(CHEN Z T.Applied Mathematical Statistics[M].National Defence Industry Press,2011.(in Chinese))
[2]栾承梅.流域水文模型参数优化问题研究[D].南京:河海大学,2005.(LUAN C M.Study on automatic optimization of hydrologic models′parameters[D].Nanjing:Hohai University,2005.(in Chinese))DOI:10.7666/d.y716959.
[3]杜非.伊洛河流域土地覆被变化水文效应的研究[D].河海大学,2007.(DU F.Hydrological effects of land cover change in Yiluo River Basin[D].Nanjing:Hohai University,2007.(in Chinese))DOI:10.7666/d.y1128418.
[4]ROSENBROCK H H.An automatic method for finding the greatest or least value of a function[J].1960,3(3):175-184.DOI:10.1093/comjnl/3.3.175.
[5]SPENDLEY W,HEXT G R,HIMSWORTH F R.Sequential application of simplex designs in optimisation and evolutionary operation[J].Technometrics,1962,4(4):441-461.DOI:10.1080/00401706.1962.10490033.
[6]WANG Q J.The genetic algorithm and its application to calibrating conceptual rainfall-runoff models[J].Water Resources Research,1991,27(9):2467-2471.DOI:10.1029/91WR01305.
[7]KENNEDY J,EBERHART R.Particle Swarm Optimization[C]//IEEE International Conference on Neural Networks,1995.Proceedings.IEEE,2002:1942-1948 vol.4.DOI:10.1109/ICNN.1995.488968.
[8]JAMIAN J J,ABDULLAH M N,MOKHLIS H,et al.Global particle swarm optimization for high dimension numerical functions analysis[J].Journal of Applied Mathematics,2014(2014),14.DOI:10.1155/2014/329193.
[9]丁根宏,曹文秀.改进粒子群算法在水库优化调度中的应用[J].南水北调与水利科技,2014(1):118-121.(DING G H,CAO W X.Application of improved particle swarm optimization algorithm in optimal operation of reservoir[J].South-to-North Water Transfers and Water Science&Technology,2014(1):118-121.(in Chinese))DOI:10.3724/SP.J.1201.2014.01118.
[10]宋健蛟,赵红莉,蒋云钟.粒子群算法在密云水库供水优化配置中的应用[J].南水北调与水利科技,2015(2):378-381.(SONG J J,ZHAO H L,JIANG Y Z.Application of particle swarm optimization in the optimal water allocation of Miyun Reservoir[J].South-to-North Water Transfers and Water Science&Technology,2015(2):378-381.(in Chinese))DOI:10.13476/j.cnki.nsbdqk.2015.02.041.
[11]关圣涛,楚纪正,邵帅.粒子群优化算法在非线性模型预测控制中的研究应用[J].北京化工大学学报(自然科学版),2007,34(6):653-656.(GUAN S T,CHU J Z,SHAO S.Application of nonlinear model predictive control based on particle swarm optimization[J].Journal of Beijing University of Chemical Technology(Natural Science Edition),2007,34(6):653-656.(in Chinese))DOI:10.3969/j.issn.1671-4628.2007.06.022.
[12]沈学利,张红岩,张纪锁.一种新的改进粒子群优化算法[J].计算机仿真,2011,28(3):246-249.(SHEN X L,ZHANG H Y,ZHANG J S.A new improved particle swarm optimization algorithm[J].Computer Simulation,2011,28(3):246-249.(in Chinese))DOI:10.3969/j.issn.1006-9348.2011.03.060.
[13]江燕,刘昌明,胡铁松,等.新安江模型参数优选的改进粒子群算法[J].水利学报,2007,38(10):1200-1206.(JIANG Y,LIU C M,HU T S,et al.Improved particle swarm optimization for parameter calibration of Xin′anjiang Model[J].Journal of Hydraulic Engineering,2007,38(10):1200-1206.(in Chinese))DOI:10.3321/j.issn:0559-9350.2007.10.008.
[14]张文明,董增川,朱成涛,等.基于粒子群算法的水文模型参数多目标优化研究[J].水利学报,2008,39(5):20-26.(ZHANG W M,DONG Z C,ZHU C T.Automatic Calibration of hydrologic model based on multi-objective particle swarm optimization method[J].Journal of Hydraulic Engineering,2008,39(5):20-26.(in Chinese))DOI:10.3321/j.issn:0559-9350.2008.05.003.
[15]王问宇,袁鹏,邵骏,等.改进粒子群算法在新安江模型参数优选中的应用[J].水力发电,2008,34(8):14-16.(WANG W Y,YUAN P,SHAO J,et al.Application of improved particle swarm algorithm to the parameter selection optimization of Xin′anjiang Model[J].Water Power,2008,34(8):14-16.(in Chinese))DOI:10.3969/j.issn.0559-9342.2008.08.005.
[16]REZAEE J A,JASNI J.Parameter selection in particle swarm optimization:A survey[J].Journal of Experimental&Theoretical Artificial Intelligence,2013,25(4):527-542.DOI:10.1080/0952813X.2013.782348.
[17]NOURMOHAMMADZADEH A,HARTMANN S,MA H.A Parallel Hybrid GA-PSO Approach with Dynamic Rule-based Parameter Setting[C]//Proceedings of the Genetic and Evolutionary Computation Conference Companion.ACM,2017:215-216.DOI:10.1145/3067695.3076051.
[18]SHI Y,EBERHART R C.Parameter selection in particle swarm optimization[C]//International Conference on Evolutionary Programming Vii.Springer-Verlag,1998:591-600.DOI:10.1007/BFb0040810.
[19]SHI Y,EBERHART R C.Empirical study of particle swarm optimization[J].Frontiers of Computer Science in China,1999,3(1):31-37.DOI:10.1109/CEC.1999.785511.
[20]TRELEA I C.The particle swarm optimization algorithm:convergence analysis and parameter selection[J].Information Processing Letters,2003,85(6):317-325.DOI:10.1016/S0020-0190(02)00447-7.
[21]王维博,林川,郑永康.粒子群算法中参数的实验与分析[J].西华大学学报(自然科学版),2008,27(1):76-79.(WANG W B,LIN C,ZHENG Y K.Experiment and analysis of parameters in particle swarm optimization[J].Journal of Xihua University(Natural Science),2008,27(1):76-79.(in Chinese))DOI:10.3969/j.issn.1673-159X.2008.01.026.
[22]ZHANG W,MA D,WEI J,et al.A parameter selection strategy for particle swarm optimization based on particle positions[J].Expert Systems with Applications,2014,41(7):3576-3584.DOI:10.1016/j.eswa.2013.10.061.
[23]刘苏宁,甘泓,魏国孝.粒子群算法在新安江模型参数率定中的应用[J].水利学报,2010,41(5):537-544.(LIU S N,GAN H,WEI G X.Application of PSO algorithm to calibrate the xin′anjiang hydrological model[J].Journal of Hydraulic Engineering,2010,41(5):537-544.(in Chinese))DOI:10.13243/j.cnki.slxb.2010.05.003.
[24]李爱国,覃征,鲍复民,等.粒子群优化算法[J].计算机工程与应用,2002,38(21):1-3.(LI A G,QIN Z,BAO F M,et al.Particle swarm optimization algorithms[J].Computer Engineering and Applications,2002,38(21):1-3.(in Chinese))DOI:10.3321/j.issn:1002-8331.2002.21.001.
[25]刘志煌,杨宜民.PSO的惯性权重与种群大小选择[J].计算机与现代化,2007,2007(6):1-3.(LIU Z H,YANG Y M.Inertia parameter and swarm size selection of PSO[J].Computer and Modemization,2007,2007(6):1-3.(in Chinese))DOI:10.3969/j.issn.1006-2475.2007.06.001.
[26]RATHORE A,SHARMA H.Review on inertia weight strategies for particle swarm optimization[C]//Proceedings of Sixth International Conference on Soft Computing for Problem Solving.Springer,Singapore,2017:76-86.DOI:10.1007/978-981-10-3322-3_8.
[27]NASH J E,SUTCLIFFE J V.River flow forecasting through conceptual models part I—A discussion of principles[J].Journal of Hydrology,1970,10(3):282-290.DOI:10.1016/0022-1694(70)90255-6.
[28]陈仲堂.应用数理统计[M].国防工业出版社,2011.(CHEN Z T.Applied Mathematical Statistics[M].National Defence Industry Press,2011.(in Chinese))