地球物理资料非线性反演方法讲座(九)——蚁群算法
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摘要
蚁群算法是一种仿生类非线性优化算法,具有并行性、正反馈性和全局极小搜索能力强等特点。蚁群算法的机理是:生物界中的蚂蚁在搜寻食物源时,能在其走过的路径上释放一种蚂蚁特有的分泌物-信息素,使得一定范围内的其他蚂蚁能够觉察并影响其行为。当某些路径上走过的蚂蚁越来越多时,留下的这种信息素轨迹也越多,以至信息素强度增大,使后来蚂蚁选择该路径的概率也越高,从而更增加了该路径的信息素强度。为了将起源于离散网络路径优化的原始蚁群算法思想用于连续函数优化的地球物理反演问题,必须对有关实施细节进行改造和修正,本文基于网格划分策略的连续域蚁群算法实现了连续域大地电磁蚁群算法。通过选择蚂蚁数、信息素挥发系数等参数,利用三层K型模型和四层HA型模型进行数值试验,结果表明,蚁群算法可以稳定收敛,反演结果接近理论模型。
Ant colony optimization is a kind of bionics non-linear optimization algorithm.The principle of ant colony optimization is: when one ant finds a good path from the colony to a food source,a kind of pheromone trail starts to evaporate,and then the other ants are more likely to follow that path.The more time it takes for an ant to travel down the path and back again,the more time the pheromones have to evaporate.A short path,by comparison,gets marched over faster,and thus the pheromone density remains high as it is laid on the path as fast as it can evaporate.Based on continuous domain ant colony algorithm with network division strategy,magnetotelluric ant colony inversion in continuous domain has been carried out in this paper.By taking characteristics of geophysics inversion into account,this paper successfully actualized magnetotelluric ant colony inversion in continuous domain.By choosing suitable inversion parameters such as a number of ants and pheromone volatilization coefficient,the numerical tests were done through taking use of 3-layer K models and 4-layer HA models.The results show that ant colony optimization can be stably converged,and the results of inversion are close to the theoretical models.
Ant colony optimization is a kind of bionics non-linear optimization algorithm.The principle of ant colony optimization is: when one ant finds a good path from the colony to a food source,a kind of pheromone trail starts to evaporate,and then the other ants are more likely to follow that path.The more time it takes for an ant to travel down the path and back again,the more time the pheromones have to evaporate.A short path,by comparison,gets marched over faster,and thus the pheromone density remains high as it is laid on the path as fast as it can evaporate.Based on continuous domain ant colony algorithm with network division strategy,magnetotelluric ant colony inversion in continuous domain has been carried out in this paper.By taking characteristics of geophysics inversion into account,this paper successfully actualized magnetotelluric ant colony inversion in continuous domain.By choosing suitable inversion parameters such as a number of ants and pheromone volatilization coefficient,the numerical tests were done through taking use of 3-layer K models and 4-layer HA models.The results show that ant colony optimization can be stably converged,and the results of inversion are close to the theoretical models.
引文
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[23]王家映.地球物理反演理论[M].北京:高等教育出版社,2002.
[24]杨文采.地震道的非线性混沌反演理论和数值试验[J].地球物理学报,1993,36(3):376~387.
[25]陈乐寿,王光锷,陈久平,等.一种大地电磁成像技术[J].地球物理学报,1993,36(3):337~346.
[26]杨文采.神经网络算法在地球物理反演中的应用[J].石油物探,1995,34(2):116~120.
[27]徐义贤,王家映.大地电磁多尺度反演[J].地球物理学报,1998,41(5):704~711.
[28]姚姚.蒙特卡洛非线性反演方法极其应用[M].北京:冶金工业出版社,1997.
[29]师学明,王家映,张胜业,等.多尺度逐次逼近遗传算法反演大地电磁资料[J].地球物理学报,2000,43(1):122~130.
[30]朱培民,王家映.随机共轭梯度反演法[J].石油地球物理勘探,2000,35(2):208~213.
[31]张纪中,徐心和.一种新的进化算法-蚁寻群算法[J].系统工程理论与实践,1999,19(3):84~87.
[32]张纪会,高齐圣,徐心和.具有变异特征的蚁群算法[J].控制理论与应用,2000,17(1):123.
[33]陈双全,王尚旭,季敏,等.地震波阻抗反演的蚁群算法实现[J].石油物探,2005,44(6):551~553.
[34]Bilehev G,Parmee I C.The ant colony metaphorfor searching continuous design spaces[C].LectureNotes in Computer Science,1995,993:25~39.
[35]杨勇,宋晓峰.蚁群算法求解连续空间优化问题[J].控制与决策,2003,18(5):573~576.
[36]Jayaraman V K,Kulkarni B D,Karale S,et al.Ant colony framework for optimal design and sched-uling of batch plants[J].Computers&ChemicalEngineering,2000,24(8):1901~1912.
[37]Wang Lei,Wu Qidi.Linear system parameters i-dentification based on ant system algorithm[A].Proceedings of the 2001 IEEE International Confer-ence on Control App1ications[C].Mexico City:Mexico,2001:401~406.
[38]Wang Lei,Wu Qidi.Ant system algorithm for opti-mization in continuous space.Proceedings of the2001 IEEE International Conference on Control Ap-plications[C],Mexico City:Mexico,2001.
[39]Jun L Y,Jun W T.An adaptive ant colony systemalgorithm for continuous space optimization prob-lems[J].Journal of Zhejiang University Science.2003,4(1):40~46.
[40]Ling C,Jie S.A method for solving optimizationproblems in continuous space using ant colony algo-rithm[J].Lecture Notes in Computer Science.2002,2463:288~289.
[41]陈峻,沈洁,秦玲.蚁群算法求解连续空间优化问题的一种方法[J].软件学报,2002,13(12):2317~2323.
[42]汪镭,吴启迪.蚁群算法在系统辨识中的应用[J].自动化学报,2003,29(1):102~109.
[43]汪镭,吴启迪.蚁群算法在连续空间寻优问题求解中的应用[J].控制与决策,2003,18(1):45~48.
[44]李艳君,吴铁军.求解混杂生产调度问题的嵌套混合蚁群算法[J].自动化学报,2003,29(1):95~101.
[45]李艳君,吴铁军.连续空间优化问题的自适应蚁群系统算法[J].模式识别增人工智能,2001,14(4):423~427.
[46]J Dreo,P Siarry.Continuous interacting ant colonyalgorithm based on dense hierarchy[J].Future Gen-eration Computer Systems,2004,20:841~856.
[2]Smith J T,Booker J R.Magnetotelluric inversion forminimum structure[J].Geophysics,1988,53:1565~1576.
[3]Rothman D H.Non-linear inversion,statistical me-chanics,and residual statics estimation[J].Geo-physics,1985,50:2784~2796.
[4]Rothman D H.Automatic estimation of large residu-al statics correction[J].Geophysics,1986,51:332~346.
[5]Sen M K,Bhattacharya B B,Stoffa P L.Non-line-ar inversion of resistivity sounding data[J].Geo-physics,1993,58:496~507.
[6]Sen M K,Stoffa P L.Non-linear one-dimensionseismic waveform inversion using simulate-ed an-nealing[J].Geophysics,1991,56:1624~1638.
[7]Sen M K,Stoffa P L.Rapid sampling of modelspace using genetic algorithm:Examples from seis-mic waveform inversion[J].Geophys.J.Int.,1992,108:281~292.
[8]Stoffa P L,Sen M K.Non-linear multiparameteroptimization using genetic algorithms:Inversion ofplane-wave seismograms[J]Geophysics,1991,56:1794~1810.
[9]Press F.Earth models obtained by Monte-Carlo in-version[J].J.Geophys.Res.,1968,73:5223~5234.
[10]Levy S,Oldenburg D,Wang J.Subsurface imagingusing magnetotelluricdata[J].Geophysics,1988,53:104~117.
[11]Whittall K P,Oldenburg D W.Inversion of magne-totelluric data for a one-dimensional conductivity[A].Society of Exploration Geophysicists,1992.
[12]Hopfield J J,Tank D W.Neural computation of de-cisions in optimization problems[J].Biological cy-bernetics,1985,52:141~152.
[13]Rodi W,Mackie R L.Non-linear conjugate gradi-ents algorithm for 2-D magnetotelluric inversion[J].Geophysics,2001,66:174~186.
[14]Pederson L B,Gharibi.Automatic 1-D inversionof MT data:finding the simplest possible modelthat fit the data[J].Geophysics,2000,65:773~782.
[15]Siripunvaporn W,Egbert G.An efficient data sub-space inversion method for 2-D MT data[J].Geo-physics,2000,65:773~782.
[16]Kirkpatrck S,Gelatt C,D Jr,Vecchi M P.Op-timazationby simulated annealing[J].Science,1983,220:671~680.
[17]Zhang Y,Paulson K V.Magnetotelluric inversionusing regularized Hopfield neural networks[J].Ge-ophysical prospecting,1977,725~743.
[18]Rodi W,Mackie R L.Non-linear conjugate gradi-ents algorithm for 2-D magneto-telluric inversion[J].Geophysics,2001,66:174~186.
[19]Dorigo M,Bonabeau E,Theraulaz G.Ant algo-rithms and stigmergy[J].Future GenerationCom-puter systems,2000,16(8):851~871.
[20]Colorni A.Ant system for job-shop scheduling[J].Jorbel,1994,34(1):39~53.
[21]Colorni A,Dorigo M,Maniezzo V.Distributed op-timization by ant colonies[A].Proc.of the FirstEuropean Conference on artificial Life[C].Paris,France:Elsevier Publishing,1991:134~142.
[22]Colorni A,Dorigo M,Maniezzo V.An investiga-tion of some properties of an ant aigorithm[A].Proc.of the Parallel Problem Solving from NatureConference(PPSN'92)[C].Brussels,Blegium:Elsevier Publishing,1992:509~520.
[23]王家映.地球物理反演理论[M].北京:高等教育出版社,2002.
[24]杨文采.地震道的非线性混沌反演理论和数值试验[J].地球物理学报,1993,36(3):376~387.
[25]陈乐寿,王光锷,陈久平,等.一种大地电磁成像技术[J].地球物理学报,1993,36(3):337~346.
[26]杨文采.神经网络算法在地球物理反演中的应用[J].石油物探,1995,34(2):116~120.
[27]徐义贤,王家映.大地电磁多尺度反演[J].地球物理学报,1998,41(5):704~711.
[28]姚姚.蒙特卡洛非线性反演方法极其应用[M].北京:冶金工业出版社,1997.
[29]师学明,王家映,张胜业,等.多尺度逐次逼近遗传算法反演大地电磁资料[J].地球物理学报,2000,43(1):122~130.
[30]朱培民,王家映.随机共轭梯度反演法[J].石油地球物理勘探,2000,35(2):208~213.
[31]张纪中,徐心和.一种新的进化算法-蚁寻群算法[J].系统工程理论与实践,1999,19(3):84~87.
[32]张纪会,高齐圣,徐心和.具有变异特征的蚁群算法[J].控制理论与应用,2000,17(1):123.
[33]陈双全,王尚旭,季敏,等.地震波阻抗反演的蚁群算法实现[J].石油物探,2005,44(6):551~553.
[34]Bilehev G,Parmee I C.The ant colony metaphorfor searching continuous design spaces[C].LectureNotes in Computer Science,1995,993:25~39.
[35]杨勇,宋晓峰.蚁群算法求解连续空间优化问题[J].控制与决策,2003,18(5):573~576.
[36]Jayaraman V K,Kulkarni B D,Karale S,et al.Ant colony framework for optimal design and sched-uling of batch plants[J].Computers&ChemicalEngineering,2000,24(8):1901~1912.
[37]Wang Lei,Wu Qidi.Linear system parameters i-dentification based on ant system algorithm[A].Proceedings of the 2001 IEEE International Confer-ence on Control App1ications[C].Mexico City:Mexico,2001:401~406.
[38]Wang Lei,Wu Qidi.Ant system algorithm for opti-mization in continuous space.Proceedings of the2001 IEEE International Conference on Control Ap-plications[C],Mexico City:Mexico,2001.
[39]Jun L Y,Jun W T.An adaptive ant colony systemalgorithm for continuous space optimization prob-lems[J].Journal of Zhejiang University Science.2003,4(1):40~46.
[40]Ling C,Jie S.A method for solving optimizationproblems in continuous space using ant colony algo-rithm[J].Lecture Notes in Computer Science.2002,2463:288~289.
[41]陈峻,沈洁,秦玲.蚁群算法求解连续空间优化问题的一种方法[J].软件学报,2002,13(12):2317~2323.
[42]汪镭,吴启迪.蚁群算法在系统辨识中的应用[J].自动化学报,2003,29(1):102~109.
[43]汪镭,吴启迪.蚁群算法在连续空间寻优问题求解中的应用[J].控制与决策,2003,18(1):45~48.
[44]李艳君,吴铁军.求解混杂生产调度问题的嵌套混合蚁群算法[J].自动化学报,2003,29(1):95~101.
[45]李艳君,吴铁军.连续空间优化问题的自适应蚁群系统算法[J].模式识别增人工智能,2001,14(4):423~427.
[46]J Dreo,P Siarry.Continuous interacting ant colonyalgorithm based on dense hierarchy[J].Future Gen-eration Computer Systems,2004,20:841~856.
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