自适应光学仿真系统关键技术研究
详细信息    本馆镜像全文|  推荐本文 |  |   获取CNKI官网全文
摘要
激光大气传输由于受到大气湍流和热晕的影响,导致光学系统的成像质量下降。为了提高光学系统成像质量,需要使用自适应光学系统对畸变波前进行校正。无波前传感器的自适应光学是自适应光学技术的研究热点之一。基于优化算法的无波前传感器自适应光学能避免传统的波前测量所带来的一系列问题,具有结构简单紧凑的特点。优化算法的效率是影响无波前传感器自适应光学系统性能的关键技术之一。要提高无波前传感器自适应光学系统的性能,需要寻找适合的优化算法。本文在对自适应光学技术进行深入分析研究的基础上,建立了自适应光学系统模型,并对模式波前复原算法进行了详尽的讨论和研究,从而提高了自适应光学系统的波前校正性能。
     论文完成的主要工作内容如下:
     1.研究了自适应光学系统入射波前像差,根据光束的线性传输特性,设计了自适应光学仿真系统的控制结构;在此基础上,对波前探测、波前复原及波前校正三个主要过程进行了系统分析和仿真建模。通过对激光大气湍流和热晕的理论分析,数值模拟了激光大气的湍流效应和热晕效应。建立了基于点扩散函数和斯特列尔比的成像质量评价模型。
     2.建立了一套无波前传感器的自适应光学系统模型,提出了一种基于粒子群算法的模式波前复原算法。该算法用来控制变形镜补偿波前像差。算法首先以一组随机解作为初始种群,以针孔内的光强作为系统性能评价函数,并按照粒子群的进化规则在搜索空间内寻找最优解。结果表明,这种算法能够找到补偿像差所需的变形镜的最优面形。
     3.为了提高优化算法控制的自适应光学系统的收敛性能,提出一种基于改进粒子群算法的模式波前复原算法。在分析标准粒子群算法的基础上,将变异策略引入到粒子群算法中。算法通过变异策略来保持粒子群的多样性,并且能够加快粒子搜索空间的速度。仿真实验表明改进的粒子群算法可以有效地提高随机像差波前复原的精度。
     4.提出了基于并行变异粒子群算法的模式波前复原算法。该算法将粒子群算法的内在并行性与并行模型相结合。本文设计了基于主从模型的多核并行模型。实验结果表明,当迭代步数选取合适时,并行变异粒子群算法具有较好的收敛性能。计算机多核仿真实验表明该算法可以减少波前复原过程中寻找最优电压的时间。
     5.提出了一种基于互信息的模式波前复原算法,并利用该算法建立了一套快速模式波前复原的自适应光学系统。通过研究模式基的波前复原能力和减少波前复原模式基的维数,大幅度地提高了复原速度。实验结果表明,该算法具有较好的校正效果。
     6.建立了一套基于面向对象技术的61单元自适应光学仿真实验平台。研究了变形镜驱动器的布局和传感器子孔径布局,并且计算了波前复原矩阵;利用模拟大气湍流扰动在激光传输中引入畸变波前像差。最终通过实验测试,分析了自适应光学仿真系统的校正性能,并给出了实验的结果。
Adaptive optics systems have been playing an important role in improving imagequality obtained by large telescopes. Image quality can be reduced by the influence ofatmospheric turbulence and thermal blooming. Wavefront sensor-less adaptive optics isone of the most important research focuses in adaptive optics technology. Wavefrontsensor-less adaptive optics systems based on the optimization algorithm can avoid aseries of problems caused by conventional wavefront measurement. The structure issimple and compact. The efficiency of an optimization algorithm has influenced theperformance of wavefront sensor-less adaptive optics systems. In order to improve thecorrection capability of the system, the suitable optimization algorithm of wavefrontreconstruction is studied. In the paper, based on analysis and research on the adaptiveoptics technology, adaptive optics system models are established. Modal wavefrontreconstruction algorithms are discussed for improving the correction capability of theadaptive optics system.
     The main contents can be summarized as follows:
     1. This paper studies the principle of wavefront aberration and the propagation oflight beam. The system control structure is described. Further, the working process ofthe system is introduced in details such as wavefront detection, wavefrontreconstruction and wavefront aberration correction. The research on numericalsimulation of light propagation in the atmosphere is carried out. Light beam qualityevaluating methods are discussed.
     2. A wavefront sensor-less adaptive optics system is set up, and a modal wavefrontreconstruction algorithm based on particle swarm optimization (PSO) algorithm whichis applied to controlling a deformable mirror (DM) is proposed. It is initialized with apopulation of random solutions. The system takes the laser power through the pinhole asthe system performance metric. According to evolution rules of PSO algorithm, thesolution space is searched for the global optimization. The simulation results show thatthis algorithm can find the optimum DM shape which is applied to correcting phaseaberration.
     3. To improve the convergence performance of the adaptive optics systemcontrolled by the optimization algorithm, an improved particle swarm optimization(IPSO) algorithm using mutation strategies is proposed. In this proposed algorithm,mutation strategies are used to keep the diversity of the particle swarm and makeparticles explore the space more efficiently. The experimental results show that thealgorithm can improve the precision of wavefront reconstruction.
     4. A modal wavefront reconstruction algorithm based on the parallel mutationparticle swarm optimization (PMPSO) is proposed by combining the inherentparallelism of PSO algorithm with parallel models. The PMPSO is designed based onmaster-slave model. The results show that the PMPSO has good convergenceperformance when the communication time step is appropriate. The experimental resultsshow that the optimization scheme can provide better efficiency for finding the optimalcombination of actuator voltages.
     5. A fast modal wavefront reconstruction approach based on mutual information isproposed. An adaptive optics system based the fast modal wavefront reconstructionalgorithm is established. By studying the capability of wavefront reconstruction of themodal basis and reducing the basis dimension of wavefront reconstruction, thereconstruction speed can be improved. The simulation results show that the proposedalgorithm can achieve good correction result.
     6. An object-oriented simulation platform of a61-element adaptive optics system isestablished. This paper solves the layout of actuators and subapertures on the adaptiveoptics simulation platform. The reconstruction matrix is calculated. The Gauss randomnumber is used to simulate influence of atmosphere turbulence on transmission of lightbeam. Finally, the performance of the adaptive optics system is analyzed and theexperimental results are presented.
引文
[1] R. K. Tyson. Principles of Adaptive Optics[M]. New York: Academic,1991.
    [2]周仁忠,阎吉祥.自适应光学理论[M].北京:北京理工大学出版社,1996.
    [3] H. W. Babcock. The possibility of compensating astronomical seeing[J]. Publ. Astron. Soc.Pac.,1953,65(386):229-236.
    [4] B. L. Zeldovich, N. F. Pilipetski, V. V. Shkunov. Principles of phase conjugation[M]. Berlin:Springer,1985,230-247.
    [5] S. S. Olivier. Advanced adaptive optics technology development[C]. Proceedings of SPIE-The International Society for Optical Engineering,2002,4494:1-10.
    [6] J. M. Beckers. Adaptive optics for astronomy: principles, performance, and applications[J].Annu. Rev. Astron. Astrophys,1993,31(9):13-62.
    [7] J. W. Hardy. Adaptive Optics for Astronomical Telescopes[M]. Oxford:Oxford UniversityPress,1998.
    [8] C. S. Goadner. Design and Performance Analysis of Adaptive Optics telescope using laseguide stars[J]. IEEE Proc.,1990,78(11):172-1743.
    [9] L. Serfert, J. Liesener, H. J. Tiziani. The adaptive Shack-Hartmann sensor[J]. OpticsCommunications,2003,216:313-319.
    [10] F. Roddier. Curvature sensing and compensation: a new concept in adaptive optics[J]. ApplOptics,1980,27:1223.
    [11] W. H. Jiang, H. G. Li. Hartmann-Shack wavefront Sensing and wavefront controlalgorithm[C].Proc,SPIE,1990,1271:998-1006.
    [12] J. A. Fleck, J. R. Morris, M. D. Feit. Time-dependent propagation of high energy laserbeams through the atmosphere[J]. Appl.Phys.,1976,10(2):129-160.
    [13]严海星,张德良,李树山.自适应光学系统的数值模拟:直接斜率控制法[J].光学学报,1997,17:758-765.
    [14]严海星,陈涉,张德良,等.自适应光学系统的模式法数值模拟[J].光学学报,1998,18:103-108.
    [15] H. X. Yan, S. S. Li, D. L. Zhang, et al. Numerical simulation of an adaptive optics systemwith laser propagation in the atmosphere[J].Appl. Opt,2000,39:3023-3031.
    [16] H. X. Yan, S. Chen, S. S. Li. Numerical simulation investigations of the effects of noise anddetection error in an adaptive optics system[C]. Proc. SPIE,2002,4494:144-155.
    [17] H. X. Yan, S. S. Li, S. Chen. Numerical simulation investigations of the dynamic controlprocess and frequency response characteristics in an adaptive optics system[C]. Proc. SPIE,2002,4494:156-166.
    [18]陈栋泉,李有宽,徐锡申,等.激光大气传输中热晕的数值模拟[J].强激光与粒子束,1993,5:243-252.
    [19]张天树,雷广玉,谢利娟,等.计及风和湍流的热晕及其相位补偿的数值模拟[J].强激光与粒子束,1994,6:16-22.
    [20]邵力,鲜浩.变形镜参数变化对湍流像差校正效果的影响[J].光电工程,2004,31(5):7-10.
    [21]赵洪志,赵达尊,沙定国.分块式变形镜的计算机模拟[J].光学技术,1993,1:36-41.
    [22]周昶宁,阎吉祥,俞信,等.自适应光学系统中大气湍流的模型分析与计算机仿真[J].光学技术,2005,31(2):249-251.
    [23] R. K. Tyson.Adaptive optics and ground-to-space laser communications[J]. AppliedOptics,1996,35(19):3640-3646.
    [24] J. W. Hardy, J. E. Lefebvre, C. L. Koliopoulos. Real-time atmospheric compensation[J].J.Opt.Soc.Am.1977,67(3):360-369.
    [25] R. Angel, B. Fugate. Astronomy-Adaptive optics[J]. Science,2000,288(5465):455-456.
    [26] J. M. Beckers, T. E. Andersen, M. Owner-Petersen. Very high-resolution spectroscopy forextremely large telescopes using pupil slicing and adaptive optics[J]. Optics Express,2007,15(5):1983-1994.
    [27] G. B.Scharmer, P. Dettori, M. G. Lofdahl, et al. Adaptive optics system for the new Swedishsolar telescope[C]. Institute for Solar Physics of the Royal Swedish Academy of SciencesSystems Research Center. SPIE,2002,1-11.
    [28]季虎,夏胜平,郁文贤.快速傅立叶变换算法概述[J].现代电子技术,2001,76(8):5-8.
    [29] V. E. Zuev, V. P. Lukin. Dynamic characteristics of optical adaptive systems[J]. AppliedOptics,1987,26(1):139-144.
    [30]姜文汉.光电技术研究所的自适应光学技术[J].光电工程,1995,22(1):1-13.
    [31]姜文汉.中科院光电技术研究所自适应光学技术专辑(上、下)[J].光电工程,1995,22:1-2.
    [32]姜文汉,王春红,凌宁,等.61单元自适应光学系统[J].量子电子学报,1998,15(2):193-199.
    [33] W. H. Jiang, M. Q. Li, G. M. Tang, et al. Adaptive Optical Image CompensationExperiments on Stellar Objects[J]. Optica1Engineering,1990,34(1):7-14.
    [34] W. H. Jiang, G. M. Tang, M. Q. Li, et al.61-element adaptive optics system at YunnanObservatory[C]. Proc. SPIE,1999,3762:142-147.
    [35] K. Murphy, D. Burke, N. Devaney, et al. Experimental detection of optical vortices with aShack-Hartmann wavefront sensor[J]. Optics Express,2010,18(15):15448-15460.
    [36] M. A. van Dam, R. G. Lane. Effect of aperture subdivision on wavefront sensing[C].Proc.SPIE2000,4125:53-64.
    [37] J. Prinmot, G. Rousset, J. C. Fontanella. Deconvolution from wavefront sensing: a newtechnique for compensation turbulence-degraded images[J]. J.Opt.Soc.Am,1990,7(9):1598-1608.
    [38] R. A. Muller, A. Buffington. Real-time correction of atmospherically degraded telescopeimages through image sharpening[J]. J. Opt. Soc. Am,1974,64(9):1200-1210.
    [39]姜文汉,黄树辅,吴旭斌.爬山法自适应光学波前校正系统[J].中国激光,1988,15(1):19-22.
    [40]王开云.由波前斜率信息进行波前重建[J].强激光与粒子束,1990,2(1):93-100.
    [41] R. H. Hudgin. Wave-front reconstruction for compensated imaging[J]. JOSA,1977,67(3):375-378.
    [42]李新阳,姜文汉.自适应光学系统的最优斜率复原算法[J].光学学报,2003,23(6):53-56.
    [43] X. Y. Li, C. H. Wang, H. Xian, et al. Zernike modal compensation analysis for an adaptiveoptics system using direct-gradient wavefront reconstruction algorithm[C]. Proc.SPIE,1999,3762:116-124.
    [44]李新阳,王春鸿,鲜浩,等.自适应光学系统的实时模式复原算法[J].强激光和粒子束,2002,14(1):53-56.
    [45] R. Cubolchini. Modal wavefront estimation from phase derivative measurement[J].J.Opt.Sco.Am1979,69(7):972-977.
    [46] J. Herrmann. Least-squares wavefront errors of minimum norm[J]. J.Opt.Soc.Am.A,1980,70(1):28-35374.
    [47]向东,王青玲,张光勇,等.可变形反射镜的研究进展及应用[J].半导体光电,2006,27(6):659-666.
    [48]饶学军,凌宁,姜文汉.用数字干涉仪测量变形镜影响函数的实验研究[J].光学学报,1995,15(10):1446-1450.
    [49]杨连臣.大气湍流效应的模拟[D].成都:中国科学院光电技术研究所,2001.
    [50]邢建斌,许国良,张旭苹,等.大气湍流对激光通信系统的影响[J].光子学报,2005,34(12):1850-1852.
    [51]张文涛,朱保华.大气湍流对激光信号传输影响的研究[J].电子科技大学学报,2007,36(4):784-787.
    [52]杨迪.大气湍流闪烁效应对激光通信系统影响及补偿研究[D],长春:长春理工大学,2009.
    [53]武琳,应家驹,耿彪.大气湍流对激光传输的影响[J].激光与红外,2008,38(10):974-977.
    [54]于继平,齐文宗,郭春风,等.激光大气传输特性的数值模拟[J].激光与红外,2008,38:523-527.
    [55]钱仙妹,朱文越,黄印博,等.激光湍流大气传输数值模拟中计算参量的选取[J].光子学报,2008,37(10):1986-1991.
    [56]徐光勇.大气湍流中的激光传输数值模拟及其影响分析[D],成都:电子科技大学,2008.
    [57]严海星,李树山,孙原隆.大气湍流中激光传输的理论模拟计算[J].中国激光,1992,19(12):936.
    [58]王立瑾,李强,魏宏刚,等.大气湍流随机相位屏的数值模拟和验证[J].光电工程,2007,34(3):1-9.
    [59]张兆顺,崔桂香,许春晓.湍流理论与模拟[M].北京:北京大学出版社,2005.
    [60]吴晗玲,严海星,李新阳,等.基于畸变相位波前分形特征产生矩形湍流相屏[J].光学学报,2009,29(1):114-119.
    [61]张慧敏,李新阳.大气湍流畸变相位屏的数值模拟方法研究[J].光电工程,2006,33(1):14-19.
    [62] P. Zhang, P. Wei, H. Y. Yu, et al. A Novel Search Algorithm Based on Particle SwarmOptimization and Simplex Method for Block Motion Estimation[J]. JDCTA,2011,5(1):76-86.
    [63] P. Yang, Y. M. Qian. A Particle Swarm Optimization to Vehicle Routing Problem with FuzzyDemands[J]. JCIT,2010,5(6):112-119.
    [64] S. Benedict, V. Vasudevan. Scheduling of scientific workflows using Discrete PSOAlgorithm for Grids[J]. JCIT,2007,2(4):29-35.
    [65] D. Fried. Least-square fitting a wave-front distortion estimate to an array ofphase-difference measurements[J]. J.Opt.Soc.Am,1977,67(3):370-375.
    [66] W. H. Southwell. Wave-front estimation from wavefront slope measurements[J].J.Opt.Soc.Am,1980,70(8):998-1006.
    [67] J. Y. Wang, D. E. Silva. Wave-front interpretation with Zernike polynomials[J]. AppliedOptics,1980,19(9):1510-1518.
    [68]朱孔风,姜维,王瑞芳,等.一种新的图像清晰度评价函数[J].红外与激光工程,2005,34(4):464-468.
    [69]王鸿南,钟文,汪静,等.图像清晰度评价方法研究[J].中国图象图形学报,2004,9(7):828-831.
    [70] J. Kennedy, R. Eberhart. Particle swarm optimization[C]. In Proceedings of IEEE Int. Conf.on Neural Networks,1995,1942-1948.
    [71] R. Eberhart, J. Kennedy. A new optimizer using particle swarm theory[C]. In Proceedings ofthe6th Int’1Symposium on Micro Machine and Human Science,1995,39-43.
    [72] A. Ratnaweera, S. K. Halgamuge, H. C. Watson. Self-organizing hierarchical particle swarmoptimizer with time-varying acceleration coefficients[J]. IEEE Transactions on EvolutionaryComputation,2004,8(3):240-255.
    [73]吕振肃,侯志荣.自适应变异的粒子群优化算法[J].电子学报,2004,32(3):416-420.
    [74] M. A. Vorontsov, G. W. Carhart, D. V. Pruidze, et al. Image quality criteria for an adaptiveimaging system based on statistical analysis of the speckle field[J]. J. Opt. Soc. Am,1996,13(7):1456-1466.
    [75] J. R. Fienup, J. J. Miller. Aberration correction by maximizing generalized sharpnessmetrics[J]. J. Opt. Soc. Am,2003,20(4):609-620.
    [76] M. Booth. Wave front sensor-less adaptive optics: a model-based approach using spherepackings[J]. Optics Express,2006,14(4):1339-1352.
    [77] Y. Chen, Y. Feng, Z. Y. Tan, et al. A Novel Modal Wavefront Reconstruction Algorithmbased on PSO Algorithm[J]. JDCTA,2011,5(4):131-137.
    [78] F. Han, T. Y. Gu, S. G. Ju. An Improved Hybrid Algorithm Based on PSO and BP forFeedforward Neural Networks[J]. JDCTA,2011,5(2):106-115.
    [79] Z. Y. Li, R. Ngambusabongsopa, E. Mohammed, et al. A Novel Diversity Guided ParticleSwarm Multi-objective Optimization Algorithm[J]. JDCTA,2011,5(1):269-278.
    [80] Y. Shi, R. Eberhart. A Modified Particle Swarm Optimizer[C]. In Proceedings of IEEEInt.Conf. on Evolutionary Computation,1998,69-73.
    [81] M. Clerc, J. Kennedy. The particle swarm-explosion, stability, and convergence in amultidimensional complex space[J]. IEEE Transactions on Evolutionary Computation,2002,6(1):58-73.
    [82] Y. Shi, R. C. Eberhart. Empirical study of particle swarm optimization[C]. Proc. IEEE Int.Congr. Evolutionary Computation,1999,3:101-106.
    [83] R. C. Eberhart, Y. Shi. Tracking and optimizing dynamic systems with particle swarms[C].Proc. IEEE Congr. Evolutionary Computation2001, Seoul, Korea,2001,94-97.
    [84]屈玉贵,梁晓雯.并行处理系统结构[J].合肥:中国科学技术大学出版社,1999.
    [85]计永昶,丁卫群,陈国良,等.一种实用的并行计算模型[J].计算机学报,2001,24(4):437-441.
    [86] K. Y. Tu, Z. C. Liang. Parallel computation models of particle swarm optimizationimplemented by multiple threads[J]. Expert Systems with Applications,2011,38(5):5858-5866.
    [87] G. Venter, J. Sobieszczanski-Sobieski. Parallel particle swarm optimization algorithmaccelerated by asynchronous evaluations[J].Journal of Aerospace Computing, Informationand Communication,2006,3(3):123-137.
    [88] A. W. McNabb, C. K. Monson, K. D. Seppi. Parallel PSO using MapReduce[C]. IEEECongress on Evolutionary Computation, CEC2007,2007,7-14.
    [89] O. Kiyarazm, M. Moeinzadeh, S. Sharifian-R. A new method for scheduling load balancingin multi-processor systems based on PSO[C]. Proceedings-20112nd InternationalConference on Intelligent Systems, Modelling and Simulation, ISMS2011,2011,71-76.
    [90] N. C. Chauhan, D. Aggarwal, R. Banga, et al. Parallelization of particle swarm optimizationand its implementation on scalable multi-core architecture[C].2009IEEE InternationalAdvance Computing Conference, IACC2009,2009,392-397.
    [91] M. Stangalini, D. D. Moro, F. Berrilli, et al. Zernike basis optimization for solar adaptiveoptics by using information theory[J]. Applied Optics,2010,49(11):2090-2094.
    [92] T. M. Cover, J. A. Thomas. Elements of Information Theory[M]. New York:John Willy,1991.
    [93] R. M. Gray. Entropy and Information Theory[M]. New York:Springer-Verlag,1990.
    [94] N. Doble, G. Yoon, L. Chen, et al. Use of a micro-electromechanical mirror for adaptiveoptics in the human eye[J]. Optics Letters,2002,27(17):1537-1539.
    [95] J. E. Pearson, S. A. Kokorowski, M. E. Pedinoff. Effects of speckle in adaptive opticalsystems[J]. J. Opt.Soc,1976,66(11):1261-1267.
    [96]王英俭,吴毅,龚知本.自适应光学系统的数值模型[J].强激光与粒子束,1994,6(1):59-64.
    [97]冯惠军,冯允成.面向对象的仿真综述[J].系统仿真学报,1995,7(3):58-64.
    [98]刘瑞叶,任洪林,李志民.计算机仿真技术基础[M].北京:电子工业出版社,2004.
    [99] P. Wolfgan. Design patterns for object-oriented software development[M]. New York:ACMPress/Addison-Wesley Publishing Co.,1995.
    [100]巴拉赫,兰宝. UML面向对象建模与设计(车皓阳,杨眉)[M].北京:人民邮电出版社,2006.
    [101] S. Akhter, J. Roberts.多核程序设计—通过软件多线程提升性能(李宝峰,富弘毅,李韬)
    [M].北京:电子工业出版社,2007.
    [102]多核系列教材编写组.多核程序设计[M].北京:清华大学出版社,2007.
    [103] A. Basden, T. Butterley, R. Myers, et al. Durham extremely large telescope adaptive opticssimulation platform[J]. Applied Optics,2007,46(7):1089-1098.
    [104] C. Baranec, M. Lloyd-Hart, N. M. Milton, et al. Astronomical imaging using ground-layeradaptive optics[C]. Proceedings of SPIE-The International Society for Optical Engineering,2007,6691.
    [105] C. C. Wilcox, T. Martinez, F. Santiago, et al. Atmospheric simulator for testing adaptiveoptics systems[C]. Proceedings of SPIE-The International Society for Optical Engineering,2008,7015.
    [106] S. Monirabbasi, S. Gibson. Adaptive control in an adaptive optics experiment withsimulated turbulence-induced optical wavefronts[C]. Proceedings of SPIE-TheInternational Society for Optical Engineering,2009,7466.
    [107] F. Y. Kanev, V. V. Lukin, N. A. Makenova. Numerical simulation in adaptive optics[C].Proceedings of SPIE-The International Society for Optical Engineering,2005,6018.
    [108] D. J. Link. Simulation of laser guidestar adaptive optics systems[C]. Proceedings of SPIE-The International Society for Optical Engineering,1995,2375:30-40.
    [109] Y. Chen, Y. Feng, Z. Y. Tan, et al. Object-oriented simulation software for an adaptive opticssystem[C]. Communication Software and Networks (ICCSN),2011,297-299.
    [110] X. Y. Shi, Y. Chen, Z. Y. Tan, et al. Numerical simulation of adaptive optics correctionsystem[C]. Communication Software and Networks (ICCSN),2011,293-296.
    [111] Y. Chen, Y. Feng, Z. Y. Tan, et al. A Particle Swarm Optimization with DifferentialEvolution[C]. Communications in Computer and Information Science,2011,158:384-389.
    [112] Y. Chen, Y. Feng, Z. Y. Tan, et al. A Study of an Improved PSO Algorithm Used in anAdaptive Optics System[J]. International Journal of Digital Content Technology and itsApplications,2011,5(7):135-141.
    [113] Z. Michalewicz, J. B. Krawczyk, M. Kazemi, et al. Genetic Algorithms and OptimalControl Problems[C]. In: Proc. Of29th IEEE Conf. on Decision and Control,1990,1664-1666.
    [114] D. E. Goldberg. Genetic Algorithms in Search, Optimization and Machine Learning[M].USA: Addison-Wesley,1989.
    [115] S. Kirkpatrick, C. Gelatt, M. Vecchi. Optimization by simulated Annealing[J]. Science1983,220:671-680.

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700