粒子群算法及其在图像分割中的应用与研究
|
摘要
粒子群优化算法源于鸟群和鱼群群体运动行为的研究,是一种新的群体智能优化算法,是演化计算领域中的一个新的分支。它的主要特点是原理简单、参数少、收敛速度快,所需领域知识少。该算法的出现引起了学者们极大的关注,已在函数优化、神经网络训练、组合优化、机器人路径规划等领域获得了广泛应用,并取得了较好的效果。尽管粒子群优化算法发展近十年,但无论是理论分析还是实践应用都尚未成熟,有大量的问题值得研究。
本文从算法机理、算法改进和算法应用等方面对其进行了系统性的研究。此外,图像分割是图像分析和模式识别的首要问题,也是图像处理的经典难题之一。本文将微粒群算法和图像分割法相结合,提出了基于改进PSO算法的分割算法,在取得良好的分割效果的同时,运用算法的并行搜索机制显著的提高了分割速度。论文具体内容如下:
(1)对粒子群算法及其理论基础(优化方法和进化计算)进行了详细的综述。首先本文概述了优化方法的产生和发展,着重介绍了优化方法的基本思想、研究领域、应用发展情况;阐述了进化计算的产生、定义以及研究内容,并介绍了几种典型的进化计算方法,包括遗传算法、进化策略、微分进化等;最后介绍了粒子群优化算法,阐述了粒子群优化算法的起源,介绍了粒子群优化算法的初始版本和标准版本,从理论研究和应用研究的角度综述了粒子群优化研究的现状,总结了标准粒子群优化算法存在的问题。同时本文使用了蒙特卡罗方法对粒子的行为进行了研究,结果显示PSO算法在迭代后期具有搜索能力较弱的缺点,同时也给出了如何提高PSO算法收敛性的方法。此外,九个标准测试函数用来测试PSO算法和其他几种流行的进化计算方法的性能,结果验证了PSO有着其他进化算法无法比拟的快速收敛等特性。
(2)尽管PSO算法比其他算法对复杂函数有着较强的寻优能力以及收敛速度快等特点,但是它依然无法保证在搜索空间中找到全局最优点。因此在本文中引入了具有着更强全局搜索能力的QPSO算法来进行研究改进。但是由于QPSO同PSO算法一样的是,它也把粒子作为一个整体来进行更新,因此QPSO算法同样具有维数限制的缺点。通过把一个具有复杂高维的粒子分解为多个一维的子个体进行优化,使用协作方法的QPSO算法能够很好的克服这一缺点。八个测试函数以及应用于图像分割领域的最大类间方差法(OTSU方法)在本文中用来测试改进以后的QPSO算法的成绩。仿真结果表明,与其他算法比较来看,协作方法帮助QPSO算法获得更精确的解。它同样也克服了OTSU方法受维数束缚的缺陷。
(3)在分析了粒子群全局收敛能力的基础之上,针对粒子群算法局部收敛和搜索精度低的问题,提出了一种全局的基于Gaussian变异的粒子群算法(GGPSO).该算法结合了局部和全局变异因子使算法在全局和局部搜索能力中找到了一个很好的平衡,并证明了它能以概率1收敛到全局最优解。典型函数优化的仿真结果表明,该算法不仅可有效的避免标准PSO算法的早熟收敛,而且具有寻优能力强、搜索精度高、稳定性好等优点。同时针对图像信息处理中的图象分割这一难点问题,以Kapur算法为优化目标,验证了该算法克服了图象分割中寻优速度慢的缺点,与其他群体算法比较获得了更大的适应度函数值。因此,该算法更适合于图像分割以及相关的函数优化问题。
(4)在分析了粒子群收敛性的基础之上,针对粒子群(PSO)算法后期搜索能力下降的问题,提出了一种基于适度随机搜索策略的粒子群算法(IRPSO).该方法在提高粒子群算法收敛速度的前提下,有效的提高了粒子的全局搜索能力。另外,由于该方法只有一个控制参数和迭代公式,因此更为简单易实现。典型函数优化的仿真结果表明,该算法相对于比较算法来说获得了更好的性能。同时针对图像分割这一难点问题,以互信息熵差为优化目标,验证了该算法在比较算法中获得了更好的分割效果。
论文最后对所做工作进行了总结,并提出了进一步研究的方向。
Particle swarm optimization (PSO) is an evolutionary computation technique developed by Dr. Eberhart and Dr. Kennedy in 1995, inspired by social behavior of bird flocking or fish schooling. Recently, PSO algorithm has been gradually attracted more attention over another intelligent algorithm. PSO is simple in concept, few in parameters, and easy in implementation. It was proved to be an efficient method to solve optimization problems, and has successfully been applied in the area of function optimization, neural network training and fuzzy control systems, etc. However, both theory and application of PSO are still far from mature.
The paper gives a comprehensive study on PSO from the aspect of algorithm mechanism, algorithm modification and its application. Furthermore, image segmentation is the first and foremost problem in image analyzing and mode recognition, and is also a typical stumbling block in image processing. In order to raise its speed, we combined the method of PSO and image segmentation algorithm on valves and therefore proposed several segmentation algorithms based on improved PSO. As we achieve an effective segmentation, we also raised the speed of the parallel searching system. The main content is as follows:
(1) The paper surveys PSO algorithm and its basic theories (Optimization method and Evolutionary Computation, EC). First we summarize the generation and development of Optimization method in detail, and emphasize the basic idea, research field and applications. And then we expatiate the emergence, definition and research field, and some typical EC methods, e.g. Genetic Algorithm, Evolutionary Strategy, Differential Algorithm are introduced. At last we introduce PSO algorithm, including its original edition and standard edition, summarize its theoretical and applied research. Monte Carlo method is presented to investigate the ability of particles. The results reveal why the PSO has relative poor global searching ability in the last stage of iteration, it also gives the way how to improve the convergence rate of PSO. Furthermore, nine benchmark functions are used to test the performance of PSO and other popular EC algorithms. The results show that the merits of PSO in terms of the fast convergence rate.
(2) In spite of PSO has comparable or even superior search performance for many hard optimization problems with faster and more stable convergence rates, but it can’t guarantee to find the global optima in the search space. So the Quantum-behaved PSO (QPSO) algorithm which has power global searching ability than PSO is introduced for improving in this paper. But for QPSO updating the position of particle as whole-item which likes PSO, it also has the problem of the curse of dimensionality. Hence two new hybrid QPSO algorithms with cooperative method (CQPSO and ICQPO) is proposed in this paper for solving this problem. The cooperative method is specifically employed to conquer the“curse of dimensionality”, by splitting a particle with composite high-dimensional into several one-dimensional sub-parts. Nine benchmark functions and Maximization of the measure of separability on the basis of between-class variance method (often called OTSU method), a popular thresholding technique, is employed to evaluate the performance of the proposed method. The experiment results show that, compared with the exiting EC methods, the cooperative method helps the new PSO algorithm to get more effective and efficient results. It also conquers the curse of dimension of traditional OTSU method.
(3) Based on analysis of the global searching ability of PSO, a new global Gaussian PSO (GGPSO) is proposed to overcome the problem of the premature and low precision of the standard PSO. In this algorithm, combining with global and local mutating method finds an excellent balance between global searching and local searching, which is also guaranteed to converge to the global optimization solution with probability one. Experiment simulations show that the proposed algorithm can not only avoid premature effectively but also has powerful optimizing ability, good stability and higher optimizing precision. For solving image segmentation which is the great importance in the field of image processing, we use Kapur function as the optimization object, and the experiments show that the GGPSO algorithm outperforms the compared algorithms especially in maximum the fitness value, so it can applied in image segmentation and optimization problems well.
(4) Based on analysis of the convergence of particle swarm optimization (PSO), a new PSO based on improved Moderate Random Searching ability (IRPSO) is proposed to overcome the problem of bad searching ability in the last stage of the standard PSO. It helps the particles have more exploration ability and fast convergence rate. Furthermore, for the improved algorithm only having one parameter and iteration formula, it is simpler than PSO. Experiments show that the proposed algorithm performs much better than the other algorithms in terms of the quality of solution. For solving the problem in image segmentation, we use the difference of mutual information (DMI) as the optimization function, and the experiments show that the IRPSO algorithm gets the better performance of image segmentation among the compared algorithms.
Finally, the work of this dissertation is summarized and the prospective of future research is discussed.
本文从算法机理、算法改进和算法应用等方面对其进行了系统性的研究。此外,图像分割是图像分析和模式识别的首要问题,也是图像处理的经典难题之一。本文将微粒群算法和图像分割法相结合,提出了基于改进PSO算法的分割算法,在取得良好的分割效果的同时,运用算法的并行搜索机制显著的提高了分割速度。论文具体内容如下:
(1)对粒子群算法及其理论基础(优化方法和进化计算)进行了详细的综述。首先本文概述了优化方法的产生和发展,着重介绍了优化方法的基本思想、研究领域、应用发展情况;阐述了进化计算的产生、定义以及研究内容,并介绍了几种典型的进化计算方法,包括遗传算法、进化策略、微分进化等;最后介绍了粒子群优化算法,阐述了粒子群优化算法的起源,介绍了粒子群优化算法的初始版本和标准版本,从理论研究和应用研究的角度综述了粒子群优化研究的现状,总结了标准粒子群优化算法存在的问题。同时本文使用了蒙特卡罗方法对粒子的行为进行了研究,结果显示PSO算法在迭代后期具有搜索能力较弱的缺点,同时也给出了如何提高PSO算法收敛性的方法。此外,九个标准测试函数用来测试PSO算法和其他几种流行的进化计算方法的性能,结果验证了PSO有着其他进化算法无法比拟的快速收敛等特性。
(2)尽管PSO算法比其他算法对复杂函数有着较强的寻优能力以及收敛速度快等特点,但是它依然无法保证在搜索空间中找到全局最优点。因此在本文中引入了具有着更强全局搜索能力的QPSO算法来进行研究改进。但是由于QPSO同PSO算法一样的是,它也把粒子作为一个整体来进行更新,因此QPSO算法同样具有维数限制的缺点。通过把一个具有复杂高维的粒子分解为多个一维的子个体进行优化,使用协作方法的QPSO算法能够很好的克服这一缺点。八个测试函数以及应用于图像分割领域的最大类间方差法(OTSU方法)在本文中用来测试改进以后的QPSO算法的成绩。仿真结果表明,与其他算法比较来看,协作方法帮助QPSO算法获得更精确的解。它同样也克服了OTSU方法受维数束缚的缺陷。
(3)在分析了粒子群全局收敛能力的基础之上,针对粒子群算法局部收敛和搜索精度低的问题,提出了一种全局的基于Gaussian变异的粒子群算法(GGPSO).该算法结合了局部和全局变异因子使算法在全局和局部搜索能力中找到了一个很好的平衡,并证明了它能以概率1收敛到全局最优解。典型函数优化的仿真结果表明,该算法不仅可有效的避免标准PSO算法的早熟收敛,而且具有寻优能力强、搜索精度高、稳定性好等优点。同时针对图像信息处理中的图象分割这一难点问题,以Kapur算法为优化目标,验证了该算法克服了图象分割中寻优速度慢的缺点,与其他群体算法比较获得了更大的适应度函数值。因此,该算法更适合于图像分割以及相关的函数优化问题。
(4)在分析了粒子群收敛性的基础之上,针对粒子群(PSO)算法后期搜索能力下降的问题,提出了一种基于适度随机搜索策略的粒子群算法(IRPSO).该方法在提高粒子群算法收敛速度的前提下,有效的提高了粒子的全局搜索能力。另外,由于该方法只有一个控制参数和迭代公式,因此更为简单易实现。典型函数优化的仿真结果表明,该算法相对于比较算法来说获得了更好的性能。同时针对图像分割这一难点问题,以互信息熵差为优化目标,验证了该算法在比较算法中获得了更好的分割效果。
论文最后对所做工作进行了总结,并提出了进一步研究的方向。
Particle swarm optimization (PSO) is an evolutionary computation technique developed by Dr. Eberhart and Dr. Kennedy in 1995, inspired by social behavior of bird flocking or fish schooling. Recently, PSO algorithm has been gradually attracted more attention over another intelligent algorithm. PSO is simple in concept, few in parameters, and easy in implementation. It was proved to be an efficient method to solve optimization problems, and has successfully been applied in the area of function optimization, neural network training and fuzzy control systems, etc. However, both theory and application of PSO are still far from mature.
The paper gives a comprehensive study on PSO from the aspect of algorithm mechanism, algorithm modification and its application. Furthermore, image segmentation is the first and foremost problem in image analyzing and mode recognition, and is also a typical stumbling block in image processing. In order to raise its speed, we combined the method of PSO and image segmentation algorithm on valves and therefore proposed several segmentation algorithms based on improved PSO. As we achieve an effective segmentation, we also raised the speed of the parallel searching system. The main content is as follows:
(1) The paper surveys PSO algorithm and its basic theories (Optimization method and Evolutionary Computation, EC). First we summarize the generation and development of Optimization method in detail, and emphasize the basic idea, research field and applications. And then we expatiate the emergence, definition and research field, and some typical EC methods, e.g. Genetic Algorithm, Evolutionary Strategy, Differential Algorithm are introduced. At last we introduce PSO algorithm, including its original edition and standard edition, summarize its theoretical and applied research. Monte Carlo method is presented to investigate the ability of particles. The results reveal why the PSO has relative poor global searching ability in the last stage of iteration, it also gives the way how to improve the convergence rate of PSO. Furthermore, nine benchmark functions are used to test the performance of PSO and other popular EC algorithms. The results show that the merits of PSO in terms of the fast convergence rate.
(2) In spite of PSO has comparable or even superior search performance for many hard optimization problems with faster and more stable convergence rates, but it can’t guarantee to find the global optima in the search space. So the Quantum-behaved PSO (QPSO) algorithm which has power global searching ability than PSO is introduced for improving in this paper. But for QPSO updating the position of particle as whole-item which likes PSO, it also has the problem of the curse of dimensionality. Hence two new hybrid QPSO algorithms with cooperative method (CQPSO and ICQPO) is proposed in this paper for solving this problem. The cooperative method is specifically employed to conquer the“curse of dimensionality”, by splitting a particle with composite high-dimensional into several one-dimensional sub-parts. Nine benchmark functions and Maximization of the measure of separability on the basis of between-class variance method (often called OTSU method), a popular thresholding technique, is employed to evaluate the performance of the proposed method. The experiment results show that, compared with the exiting EC methods, the cooperative method helps the new PSO algorithm to get more effective and efficient results. It also conquers the curse of dimension of traditional OTSU method.
(3) Based on analysis of the global searching ability of PSO, a new global Gaussian PSO (GGPSO) is proposed to overcome the problem of the premature and low precision of the standard PSO. In this algorithm, combining with global and local mutating method finds an excellent balance between global searching and local searching, which is also guaranteed to converge to the global optimization solution with probability one. Experiment simulations show that the proposed algorithm can not only avoid premature effectively but also has powerful optimizing ability, good stability and higher optimizing precision. For solving image segmentation which is the great importance in the field of image processing, we use Kapur function as the optimization object, and the experiments show that the GGPSO algorithm outperforms the compared algorithms especially in maximum the fitness value, so it can applied in image segmentation and optimization problems well.
(4) Based on analysis of the convergence of particle swarm optimization (PSO), a new PSO based on improved Moderate Random Searching ability (IRPSO) is proposed to overcome the problem of bad searching ability in the last stage of the standard PSO. It helps the particles have more exploration ability and fast convergence rate. Furthermore, for the improved algorithm only having one parameter and iteration formula, it is simpler than PSO. Experiments show that the proposed algorithm performs much better than the other algorithms in terms of the quality of solution. For solving the problem in image segmentation, we use the difference of mutual information (DMI) as the optimization function, and the experiments show that the IRPSO algorithm gets the better performance of image segmentation among the compared algorithms.
Finally, the work of this dissertation is summarized and the prospective of future research is discussed.
引文
1.陈宝林.最优化理论与算法(第二版)[M].清华大学出版社,北京, 2005,10
2. www.wiki.cn/wiki,2007,最优化方法[M]
3.李国勇等。最优化控制理论及参数优化[M]。国防工业出版社,北京,2006,1
4.章敬东。复杂优化问题中智能算法的分析与集成[D]:[博士学位论文].华南理工大学工学博士学位论文, 2003
5. Holland J H. Adaptation in Nature and Artificial Systems [M]. University of Michigan, Ann Arbor, 1975
6.汪定伟,唐加福,黄敏。遗传算法与工程设计[M]。北京:科学出版社,2000
7. Dorigo M, Maniezzo V, Colorni A. The ant system: optimization by a colony of cooperating agents. IEEE Trans. on Systems, Man and Cybernetics Part B, 1996, 26(1): 29-41
8. Kennedy J, Eberhart R C. Particle Swarm Optimization [C], Proc. IEEE International Conference on Neural Networks. Piscataway NJ: IEEE Service Center, 1995, 1942-1948
9. Eberhart R C, Kennedy J. A new optimizer using particle swarm theory [C], Proc. On 6th International Symposium on Micromachine and Human Science. Piscataway NJ: IEEE Service Center, 1995, 39-43
10. Storn R, Price K. Differential Evolution-a Simple and Efficient Adaptive Scheme for Global Optimization over Continuous Space. Technical report, International Computer Science Institute, Berkley, 1995
11. Storn R, Price K. Differential Evolution-a Simple and Efficient Heuristic for Global Optimization over Continuous Space. Journal of Global Optimization, 1997, 11(4): 341-359
12. Ozcan, E. and Mohan, C. K. Particle swarm optimization: surfing the waves. Procedings of the IEEE Congress on Evolutionary Computation (CEC) [C]. Picataway, NJ, 1999, 1939-1944
13. Van den Bergh F. An Analysis of Particle Swarm Optimizers. [D]: PhD Thesis. University of Pretoria, Nov 2001
14. Kennedy, J. Bare bones particle swarms. Proceddings of the IEEE Swarm Intelligence Symposium (SIS 2003). Indianapolis, Indiana, 2003, 80-87
15. Shi, Y and Eberhart, R.C. Empirical study of particle swarm optimization. Proceedings of the World Multiconference on Systemics, Cybernetics and Informatics [C]. Orlando, FL, 2000, 1945-1950
16. Rui Mendes. Population Topologies and Their Influence in Particle Swarm Performance [D]: PhD. Thesis. University of do Minho, April, 2004
17. Wolpert, D. H. and Macready, W. G. No free lunch theorems for search. Technical Report SFI-TR-95-02-010, Santa Fe Inst., Sante Fe, New Mexico, 1994. [online]: Available: citeseer.nj.nec.com/wolPert95no.html.
18. Wolpert, D. H. and Macready, W. G. No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation, 1997, 1(1): 67-82
19. Christensen, S. and Oppacher, F. What can we learn from No Free Lunch? A first attempt to characterize the concept of a searchable function [C]. Proceeding of GECCO. Morgan Kaufmann, 2001, 1219-1226
20. Holland, J. H. Adaptation in Nature and Artificial System [M]. The University of Michigan Press, 1975
21. Rechenberg I. Cybernetic solution path of an experimental problem [M]. Liberary Translation, 1965: 1122
22.李宏,唐焕文,郭崇慧。一类进化策略的收敛性分析[J].运筹学学报, 1999,vol. 3(4): 79-83
23. Fogel, D. B. An introduction to simulated evolutionary optimization. IEEE Transaction on Neural Networks, 1994, 5(1): 3-14
24. Fogel, D.B. Applying evolution programming to selected traveling salesman problems. Cybernetics and Systems, 1993, 24: 27-36
25. Fogel, D. B. Asymptotic convergence properties of genetic algorithms and evolutionary programming and analysis and experiments. Cybernetic and Systems, 1994, 25: 389-407
26. Colorni, A., Dorigo, M., and Maniezzo, V., An investigation of some Properties of an ant algorithm. Proceedings of the Parallel Problem Solving from Nature Conference (PPSN
92). Brussels, Beigium, Manner, R. and Manderich, B.(Eds.), Elsevier Publishing, 1992, 509-520
27. Dorigo, M., Maniezzo, V., and Colorni, A. Ant system: optimization by a colony of cooperation agents. IEEE Transaction on Systems, Man and Cybernetics-Part B. 1996, 26(1): 1-26
28. Storn R, Price K. Differential Evolution - a Simple and Efficient Adaptive Scheme for Global Optimization over Continuous Space. Technical report, International Computer Science Institute, Berkley, 1995
29. Storn R, Price K. Differential Evolution-a Simple and Efficient Heuristic for Global Optimization over Continuous Spaces. Journal of Global Optimization, 1997, 11(4): 341–359
30. Kennedy, J. and Mendes, R. Neighborhood topolgies in fully-informed and best-of-neighborhood particles swarms[C]. Proceedings of the 2003 IEEE International Workshop on Soft Computing in Industrial Applications 2003(SMCia/03), 2003, 45-50
31. Lotfi K. Gaafar, Sherif A. Masoud, Ashraf O. Nassef. A particle swarm-based genetic algorithm for scheduling in an agile environment, Com. & Indu. Engineering, 2008, vol. 55(3), pp. 707-720
32. X. H. Shi, Y. C. Liang, C. Lu, L. M. Wang. An improved GA and a novel PSO-GA-based hybrid algorithm. Inform Process Lett, 2005, 255-261
33.周殊,潘讳,罗斌等。一种基于粒子群优化方法的改进量子遗传算法及应用[J]。电子学报,2006, vol. 34 (5), 897-901
34. Rui Xu, Ganesh K. Venayagamoorthy, Donald C. Wunsch II, Modeling of gene regulatory networks with hybrid differential evolutionary and particle swarm optimization, Neural Networks, 2007, vol. 266 (1-3), pp. 917-927
35.窦全胜,周春光,张忠波等。基于微分演化的PSO参数选择策略[J]。计算机科学,2007, vol. 34 (4), 228-230
36. M. G. H. Omran, A. P. Engelbrecht, A. Salman, Differential Evolution Based Particle Swarm Optimization [C], in Pro. of IEEE Swarm Intelligence Symposium (SIS), 2007, 112-119
37.赫然,王永吉,王清。一种改进的自适应逃逸微粒群算法及试验分析[J]。软件学报,2005,16(12):2036-2044
38. A. Ratnaweera, S. K. Halgamuge, and H. C. Watson. Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients. IEEE Transactions on Evolutionary Computation, 2004, 8(3): 240-255
39. N. Higashi and H. Iba, Particle swarm optimization with Gaussian mutation [C]. Proceedings of IEEE Swarm Intelligence Symposium (SIS), 2003: 71-79
40. J. Kennedy. In Search of the Essential Particle Swarm [C]. IEEE Congress on Evolutionary Computation, Canada: IEEE Press, 2006, 1(1): 1694-1701
41. Stacey. A, Jancic. M, Grundy. I, Particle swarm optimization with mutation [C]. Proceedings of IEEE International Conference on Evolutionary Computation, 2003, vol. 2, 1425-1430
42. H. Wang and Y. Liu. A Hybrid Particle Swarm Algorithm with Cauchy Mutation [C], in Proc IEEE Int. Conf. Swarm Intelligence Symposium (SIS), 2007, pp: 356-360
43. H. Wang, Y. Liu. An improved particle swarm optimization with adaptive jumps [C]. In Proceedings of IEEE International Conference on Evolutionary Computation, 2008, 392-397
44. S. H. Ling, H. H. C. Iu, K. Y. Chan, et al. Hybrid particle swarm optimization with wavelet mutation and its industrial applications, IEEE Trans, Systems, Man, and Cybernetics, 2008, vol. 38, no. 3, pp. 743-763
45. Shi. Y and Eberthart R. C. Empirical study of particle swarm optimization, Proceedings of the World Multiconference on Systemics, Cybernetics and Informatics, Orlando, FL, 2000, 1945-1950
46. M. Clerc and J. Kennedy. The particle swarm-Explosion, stability, and convergence in a multi-dimensional complex space. IEEE Trans. Evoltionary Computation, 2002, vol. 6, pp. 58-73
47. R. C. Eberhart and Y. Shi. Particle swarm optimization: Developments, applications and resources. IEEE Int. Conf. Evolutionay Computaion, 2001, vol. 1, pp. 81-86
48. F. Van den Bergh. An analysis of Particle Swarm optimizers [D]: South Africa: University of Pretoria, Nov. 2001
49. P. P. Boyle. Options: A Monte Carlo approach. Journal of Financial Economics, 1977. 4(3): 323-338
50. X. Yao, Y. Liu, G. M. Lin, Evolutionary programming made faster. IEEE Transactions on Evolutionary Computation, 1999, 3(2): 82-10
51. M. Senthil Arumugam, M. V. C. Rao, Alan W. C. Tan. A novel and effective particle swarm optimization like algorithm with extrapolation technique. Applied Soft Computing, 2009, vol. 9 (1), pp. 308-320
52. Erwie Zahara, Yi-Tung Kao. Hybrid Nelder-Mead Simplex search and particle swarm optimization for constrained engineering design problems. Expert Systems with Applications, 2009, Vol. 36 (2), pp. 3880-3886
53. Krohling, R.A., dos Santos Coelho, L.. Coevolutionary Particle Swarm Optimization Using Gaussian Distribution for Solving Constrained Optimization Problems. IEEE Trans. on Systems, Man, and Cybernetics, 2006, vol. 36 (6), pp. 1407-1416
54. M. A. Abido. Multiobjective particle swarm optimization for environmental/economic dispatch problem. Electric Power Systems Research, 2009, vol. 79 (7), pp. 1105-1113
55. Junjie Yang, Jianzhong Zhou, Li Liu, Yinghai Li. A novel strategy of pareto-optimal solution searching in multi-objective particle swarm optimization. Com. & Math. With Applications, 2008, (in press).
56. Jehad I. Ababneh, Mohammad H. Bataineh. Linear phase FIR filter design using particle swarm optimization and genetic algorithms [C]. Digital Signal Processing, 2008, vol. 18 (4), pp. 657-668
57. Luitel, B., Venayagamoorthy, G. K.. Differential evolution particle swarm optimization for digital filter design [C]. CEC 2008, pp. 3954-3961
58. Boo, Junyou, Stock Price forecasting using PSO-trained neural networks [C]. IEEE Congress on Evolutionary Computation, 2007, 2879-2885.
59. Cheng-Jian Lin, Yong-Cheng Liu, Image backlight compensation using neuron-fuzzy networks with immune particle swarm optimization. Expert Systems with Applications, 2009, vol. 36 (3), pp. 5212-5220
60. Chao-Ming Huang, Fu-Lu Wang, An RBF Network with OLS and EPSO Algorithms for Real-Time Power Dispatch. IEEE Trans. on Power Systems, 2006, vol. 22 (1), pp. 96-104
61. Jun Ying Chen, Zheng Qin, Ji Jia, A PSO-based subtractive clustering technique for designing RBF neural networks [C]. IEEE world Congress on Computational Intelligence, 2008, pp. 2047-2052.
62.赫万君,强文义,柴庆宣等。基于粒子群优化的一类模糊控制器设计[J]。控制与决策,2007,vol. 22 (5), pp. 585-588.
63. Yiming Li, Shao-Ming Yu, Yih-Lang Li. Electronic design automation using a unified optimization framework. Mathematics and Computers in Simulation, 2008, vol. 79 (4), pp. 1137-1152
64. Araujo. E,; dos Santos Coelho, L.. Fuzzy Model and Particle Swarm Optimization for Nonlinear Identification of a Chua’s Oscillator [C]. IEEE International Fuzzy Systems Con., 2007, pp. 1-6
65.雷开友。粒子群算法及其应用研究[D]:[博士学位论文].西南大学博士论文.2006.
66. Saska, M., Macas, M., Preucil, L., Lhotska, L.. Robot Path Planning using particle swarm optimization of Ferguson Splines [C]. IEEE Con. Emerging Tech. and Factory Auto., 2006, vol. 20 (22), pp. 833-839.
67. Hwan II Kang, Byunghee Lee, Kabil Kom, Path Planning algorithm using the Particle Swarm Optimization and the Improved Dijistra Algorithm [C]. IEEE Con. Computational Intelligence and Industrial Application, 2008, vol. 2, pp. 1002-1004.
68.王俊伟。粒子群优化算法的改进及应用[D]:[博士学位论文].东北大学博士学位论文.2006.
69. N. Otsu. A threshold selection method from gray-level histograms. IEEE Transactions on Systems, Man, Cybernetics, SMC-9, pp. 62-66, 1979
70. J. Sun, W.B. Xu. A Global Search Strategy of Quantum-behaved Particle Swarm Optimization [C]. IEEE Int. Conf. on Cybernetics and Intelligent Systems, vol. 1, pp. 111-116, 2004
71. SUN J, XU WB. Particle Swarm Optimization with Particle Having Quantum Behavior [C]. IEEE Congress .Evolutionary Computation. 2004, pp. 325-331
72. J. Kennedy. Some Issues and Practices for Particle Swarms[C]. IEEE Swarm Intelligence Symposium, 2007, pp. 162-169
73. J. Liu, J. Sun, Wenbo Xu. Quantum-Behaved Particle Swarm Optimization for Integer Programming [C]. Neural Information Processing, 2006
74. J. Sun, Wenbo Xu, J Liu. Training RBF Neural Network via Quantum-Behaved Particle Swarm Optimization [C]. Nerual Information Processing, 2006
75. S. Y. Li, R. G. Wang, W. W. Hu, J. Q. Sun. A new QPSO based BP neural network for face detection. Advances in Soft Computing, vol. 40, pp. 355-363, 2007
76. L. dos S. Coelho, V. C. Mariani. Particle swarm approach based on quantum mechanics and harmonic oscillator potential well for economic load dispatch with valve-point effects. Energy Conversion and Management, 2008, vol. 49, no. 11, pp. 3080-3085
77. F. van. Den Bergh and A. P. Engelbrecht. A cooperative approach to particle swarm optimization. IEEE Transactions on Evolutionary Computation, 2004, vol. 8, no. 3, pp. 225-238
78. Rivals, I. and L. Personnaz, No free lunch with the sandwich [sandwich estimator]. Neural Networks. IEEE Transactions on, 2003. 14(6): pp. 1553-1559
79. Goldberg DE. Genetic Algorithm in search, optimization and Machine Learning [M], Addison-wesley Publising Company, Inc. 1989
80.章毓晋。图像分割[M]。北京:科学出版社,2001
81.石岩,张天序,樊荣,江浩洋。基于两阶段搜索自适应正交投影分解的图像分割方法[J]。中国图像图形学报,2005,10(9):1089-1095
82. Wells WM, Grimson EL, Kikinis K, and Jolesz FA. Adaptive segmentation of MRI data. IEEE Trans. Med. Imag., 1996, vol. 15, pp. 429-442
83. Yang F, Jiang T. Pixon. Based image segmentation with Markov random fields. IEEE Trans. Image Process., 2003, 12(12): 1552-1559
84. W. B. Tao, H. Jin, L. M. Liu. Object segmentation using ant colony optimization algorithm and fuzzy entropy. Pattern Recognition Letters, 2008, vol. 28, no. 7, pp. 788-796
85. P. Y. Yin, L. H. Chen. A fast iterative scheme for multilevel thresholding methods. Signal Process, 1997, vol. 60, no. 3, pp. 305-313
86. L. Cao, P. Bao, Z. K. Shi. The strongest schema learning GA and its application to multilevel thresholding. Image and Vision Computing, 2008, vol. 26, no. 5, pp. 716-724
87. P. P. Yin. Multilevel minimum cross entropy threshold selection based on particle swarm optimization. Applied Mathematics and Computation, 2007, vol. 184, no. 2, pp. 503-513
88. E. Zahara, S. K. S. Fan, D. M. Tsai. Optimal multi-thresholding using a hybrid optimization approach. Pattern Recognition Letters, 2005, vol. 26, no. 8, pp. 1082-1095
89. M. Maitra, A. Chatterjee. A hybrid cooperative-comprehensive learning based PSO algorithm for image segmentation using multilevel thresholding. Expert Systems with Applications, 2008, vol. 34, no. 2, pp. 1341-1350
90. http://www.eecs.berkeley.edu/Research/Projects/CS/vision/bsds/
91. AP Engelbrecht, BS Masiye, G Pampara. Niching Ability of Basic Particle Swarm Optimization Algorithms [C]. Proceedings of IEEE Swarm Intelligence Symposium (SIS), Pasadena, California, USA. 2005: 397-400.
92. Paul S. Andrews. An Investigation into Mutation Operators for Particle Swarm Optimization. IEEE Congress on Evolutionary Computation, Vancouver, BC, Canada. 2006, 16(21), 1044-1051.
93. HU XH, Eberhart RC. Adaptive particle swarm optimization: Detection and response to dynamic system [C]. In Proc. Of the IEEE Conf on Evolutionary Computation. Honolulu USA. 2002: 1666-1670.
94.郭崇慧,唐焕文。演化策略的全局收敛性[J]。计算数学,2001,23(1):105-110.
95. Kapur J. N., SAHOO P. K., WONG A. K. C. A new method for gray-level picture thresholding using the entropy of the histogram. Computer vision, graphics, and image processing, 1985, vol. 29 (3), pp. 273-285.
96. Y. Shi, R. C. Eberhart. A modified particle swarm optimizer. IEEE Int. Conf. of Evolutionary Computation, Piscataway: IEEE Press, 1998. 69-73.
97.方伟,群体智能算法机器在数字滤波器优化设计中的研究[D]:[博士学位论文].江南大学博士学位论文,2008.
98.胡旺,李志蜀。一种更简化而高效的粒子群优化算法[J]。软件学报,2007,18(4):861-868。
99. T. O. Ting, M. V. C. Rao, and C. K. Loo. A novel approach for unit commitment problem via an effective hybrid particle swarm optimization. IEEE Trans, Power Syst., vol. 21, no. 1, pp. 411-418, Feb. (2006).
100.Y. Song, Z. Chen, and Z. Yuan. New chaotic PSO-based neural network predictive control for nonlinear process. IEEE Trans. Neural Netw., 2007, vol. 18, no. 2, pp. 595-601
101.唐贤伦。混沌粒子群优化算法理论及应用研究[D]:[博士学位论文].重庆大学博士学位论文。2007.
102.H. M. Feng. Particle swarm optimization learning fuzzy systems design [C]. Proceedings of the ICITA 2005 3rd International Conference on Information Technology and Applications, 2005, vol. 1. July 4-7, pp. 363-366
103.张利彪。基于粒子群和微分进化的优化算法研究[D]:[博士学位论文].吉林大学博士论文。2007.
104.Maes F, Collignon A. Multimodality image registration by maximization of mutual information. IEEE Trans. Med. Imag., 1997, 16(2): 187-198.
105.Studholme C, Hill DLG, Hawkes DJ. Incorporating connected region labeling into automated image registration using mutual information[C]. In: Proc. Of MMBIA’96 (San Francisco), Piscataway: IEEE Press, 1996, 3-31.
106.Rigau J, Feixas M, Sbert M, et al. Medical image segmentation based on mutual information maximization [C]. In: Proc. Of MICCAI 2004 (Saint-Malo), Belin: Springer, 2004, 135-142
107.Kim J, Fisher III JW, Yezzi A, et al. A nonparametric statistical method for image segmentation using information theory and curve evolution. IEEE Trans. Image Process, 2005, 14(10):1486-1502
108.吕庆文,陈武凡。基于互信息量的图像分割.计算机学报,2006,29(2):296-301.
2. www.wiki.cn/wiki,2007,最优化方法[M]
3.李国勇等。最优化控制理论及参数优化[M]。国防工业出版社,北京,2006,1
4.章敬东。复杂优化问题中智能算法的分析与集成[D]:[博士学位论文].华南理工大学工学博士学位论文, 2003
5. Holland J H. Adaptation in Nature and Artificial Systems [M]. University of Michigan, Ann Arbor, 1975
6.汪定伟,唐加福,黄敏。遗传算法与工程设计[M]。北京:科学出版社,2000
7. Dorigo M, Maniezzo V, Colorni A. The ant system: optimization by a colony of cooperating agents. IEEE Trans. on Systems, Man and Cybernetics Part B, 1996, 26(1): 29-41
8. Kennedy J, Eberhart R C. Particle Swarm Optimization [C], Proc. IEEE International Conference on Neural Networks. Piscataway NJ: IEEE Service Center, 1995, 1942-1948
9. Eberhart R C, Kennedy J. A new optimizer using particle swarm theory [C], Proc. On 6th International Symposium on Micromachine and Human Science. Piscataway NJ: IEEE Service Center, 1995, 39-43
10. Storn R, Price K. Differential Evolution-a Simple and Efficient Adaptive Scheme for Global Optimization over Continuous Space. Technical report, International Computer Science Institute, Berkley, 1995
11. Storn R, Price K. Differential Evolution-a Simple and Efficient Heuristic for Global Optimization over Continuous Space. Journal of Global Optimization, 1997, 11(4): 341-359
12. Ozcan, E. and Mohan, C. K. Particle swarm optimization: surfing the waves. Procedings of the IEEE Congress on Evolutionary Computation (CEC) [C]. Picataway, NJ, 1999, 1939-1944
13. Van den Bergh F. An Analysis of Particle Swarm Optimizers. [D]: PhD Thesis. University of Pretoria, Nov 2001
14. Kennedy, J. Bare bones particle swarms. Proceddings of the IEEE Swarm Intelligence Symposium (SIS 2003). Indianapolis, Indiana, 2003, 80-87
15. Shi, Y and Eberhart, R.C. Empirical study of particle swarm optimization. Proceedings of the World Multiconference on Systemics, Cybernetics and Informatics [C]. Orlando, FL, 2000, 1945-1950
16. Rui Mendes. Population Topologies and Their Influence in Particle Swarm Performance [D]: PhD. Thesis. University of do Minho, April, 2004
17. Wolpert, D. H. and Macready, W. G. No free lunch theorems for search. Technical Report SFI-TR-95-02-010, Santa Fe Inst., Sante Fe, New Mexico, 1994. [online]: Available: citeseer.nj.nec.com/wolPert95no.html.
18. Wolpert, D. H. and Macready, W. G. No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation, 1997, 1(1): 67-82
19. Christensen, S. and Oppacher, F. What can we learn from No Free Lunch? A first attempt to characterize the concept of a searchable function [C]. Proceeding of GECCO. Morgan Kaufmann, 2001, 1219-1226
20. Holland, J. H. Adaptation in Nature and Artificial System [M]. The University of Michigan Press, 1975
21. Rechenberg I. Cybernetic solution path of an experimental problem [M]. Liberary Translation, 1965: 1122
22.李宏,唐焕文,郭崇慧。一类进化策略的收敛性分析[J].运筹学学报, 1999,vol. 3(4): 79-83
23. Fogel, D. B. An introduction to simulated evolutionary optimization. IEEE Transaction on Neural Networks, 1994, 5(1): 3-14
24. Fogel, D.B. Applying evolution programming to selected traveling salesman problems. Cybernetics and Systems, 1993, 24: 27-36
25. Fogel, D. B. Asymptotic convergence properties of genetic algorithms and evolutionary programming and analysis and experiments. Cybernetic and Systems, 1994, 25: 389-407
26. Colorni, A., Dorigo, M., and Maniezzo, V., An investigation of some Properties of an ant algorithm. Proceedings of the Parallel Problem Solving from Nature Conference (PPSN
92). Brussels, Beigium, Manner, R. and Manderich, B.(Eds.), Elsevier Publishing, 1992, 509-520
27. Dorigo, M., Maniezzo, V., and Colorni, A. Ant system: optimization by a colony of cooperation agents. IEEE Transaction on Systems, Man and Cybernetics-Part B. 1996, 26(1): 1-26
28. Storn R, Price K. Differential Evolution - a Simple and Efficient Adaptive Scheme for Global Optimization over Continuous Space. Technical report, International Computer Science Institute, Berkley, 1995
29. Storn R, Price K. Differential Evolution-a Simple and Efficient Heuristic for Global Optimization over Continuous Spaces. Journal of Global Optimization, 1997, 11(4): 341–359
30. Kennedy, J. and Mendes, R. Neighborhood topolgies in fully-informed and best-of-neighborhood particles swarms[C]. Proceedings of the 2003 IEEE International Workshop on Soft Computing in Industrial Applications 2003(SMCia/03), 2003, 45-50
31. Lotfi K. Gaafar, Sherif A. Masoud, Ashraf O. Nassef. A particle swarm-based genetic algorithm for scheduling in an agile environment, Com. & Indu. Engineering, 2008, vol. 55(3), pp. 707-720
32. X. H. Shi, Y. C. Liang, C. Lu, L. M. Wang. An improved GA and a novel PSO-GA-based hybrid algorithm. Inform Process Lett, 2005, 255-261
33.周殊,潘讳,罗斌等。一种基于粒子群优化方法的改进量子遗传算法及应用[J]。电子学报,2006, vol. 34 (5), 897-901
34. Rui Xu, Ganesh K. Venayagamoorthy, Donald C. Wunsch II, Modeling of gene regulatory networks with hybrid differential evolutionary and particle swarm optimization, Neural Networks, 2007, vol. 266 (1-3), pp. 917-927
35.窦全胜,周春光,张忠波等。基于微分演化的PSO参数选择策略[J]。计算机科学,2007, vol. 34 (4), 228-230
36. M. G. H. Omran, A. P. Engelbrecht, A. Salman, Differential Evolution Based Particle Swarm Optimization [C], in Pro. of IEEE Swarm Intelligence Symposium (SIS), 2007, 112-119
37.赫然,王永吉,王清。一种改进的自适应逃逸微粒群算法及试验分析[J]。软件学报,2005,16(12):2036-2044
38. A. Ratnaweera, S. K. Halgamuge, and H. C. Watson. Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients. IEEE Transactions on Evolutionary Computation, 2004, 8(3): 240-255
39. N. Higashi and H. Iba, Particle swarm optimization with Gaussian mutation [C]. Proceedings of IEEE Swarm Intelligence Symposium (SIS), 2003: 71-79
40. J. Kennedy. In Search of the Essential Particle Swarm [C]. IEEE Congress on Evolutionary Computation, Canada: IEEE Press, 2006, 1(1): 1694-1701
41. Stacey. A, Jancic. M, Grundy. I, Particle swarm optimization with mutation [C]. Proceedings of IEEE International Conference on Evolutionary Computation, 2003, vol. 2, 1425-1430
42. H. Wang and Y. Liu. A Hybrid Particle Swarm Algorithm with Cauchy Mutation [C], in Proc IEEE Int. Conf. Swarm Intelligence Symposium (SIS), 2007, pp: 356-360
43. H. Wang, Y. Liu. An improved particle swarm optimization with adaptive jumps [C]. In Proceedings of IEEE International Conference on Evolutionary Computation, 2008, 392-397
44. S. H. Ling, H. H. C. Iu, K. Y. Chan, et al. Hybrid particle swarm optimization with wavelet mutation and its industrial applications, IEEE Trans, Systems, Man, and Cybernetics, 2008, vol. 38, no. 3, pp. 743-763
45. Shi. Y and Eberthart R. C. Empirical study of particle swarm optimization, Proceedings of the World Multiconference on Systemics, Cybernetics and Informatics, Orlando, FL, 2000, 1945-1950
46. M. Clerc and J. Kennedy. The particle swarm-Explosion, stability, and convergence in a multi-dimensional complex space. IEEE Trans. Evoltionary Computation, 2002, vol. 6, pp. 58-73
47. R. C. Eberhart and Y. Shi. Particle swarm optimization: Developments, applications and resources. IEEE Int. Conf. Evolutionay Computaion, 2001, vol. 1, pp. 81-86
48. F. Van den Bergh. An analysis of Particle Swarm optimizers [D]: South Africa: University of Pretoria, Nov. 2001
49. P. P. Boyle. Options: A Monte Carlo approach. Journal of Financial Economics, 1977. 4(3): 323-338
50. X. Yao, Y. Liu, G. M. Lin, Evolutionary programming made faster. IEEE Transactions on Evolutionary Computation, 1999, 3(2): 82-10
51. M. Senthil Arumugam, M. V. C. Rao, Alan W. C. Tan. A novel and effective particle swarm optimization like algorithm with extrapolation technique. Applied Soft Computing, 2009, vol. 9 (1), pp. 308-320
52. Erwie Zahara, Yi-Tung Kao. Hybrid Nelder-Mead Simplex search and particle swarm optimization for constrained engineering design problems. Expert Systems with Applications, 2009, Vol. 36 (2), pp. 3880-3886
53. Krohling, R.A., dos Santos Coelho, L.. Coevolutionary Particle Swarm Optimization Using Gaussian Distribution for Solving Constrained Optimization Problems. IEEE Trans. on Systems, Man, and Cybernetics, 2006, vol. 36 (6), pp. 1407-1416
54. M. A. Abido. Multiobjective particle swarm optimization for environmental/economic dispatch problem. Electric Power Systems Research, 2009, vol. 79 (7), pp. 1105-1113
55. Junjie Yang, Jianzhong Zhou, Li Liu, Yinghai Li. A novel strategy of pareto-optimal solution searching in multi-objective particle swarm optimization. Com. & Math. With Applications, 2008, (in press).
56. Jehad I. Ababneh, Mohammad H. Bataineh. Linear phase FIR filter design using particle swarm optimization and genetic algorithms [C]. Digital Signal Processing, 2008, vol. 18 (4), pp. 657-668
57. Luitel, B., Venayagamoorthy, G. K.. Differential evolution particle swarm optimization for digital filter design [C]. CEC 2008, pp. 3954-3961
58. Boo, Junyou, Stock Price forecasting using PSO-trained neural networks [C]. IEEE Congress on Evolutionary Computation, 2007, 2879-2885.
59. Cheng-Jian Lin, Yong-Cheng Liu, Image backlight compensation using neuron-fuzzy networks with immune particle swarm optimization. Expert Systems with Applications, 2009, vol. 36 (3), pp. 5212-5220
60. Chao-Ming Huang, Fu-Lu Wang, An RBF Network with OLS and EPSO Algorithms for Real-Time Power Dispatch. IEEE Trans. on Power Systems, 2006, vol. 22 (1), pp. 96-104
61. Jun Ying Chen, Zheng Qin, Ji Jia, A PSO-based subtractive clustering technique for designing RBF neural networks [C]. IEEE world Congress on Computational Intelligence, 2008, pp. 2047-2052.
62.赫万君,强文义,柴庆宣等。基于粒子群优化的一类模糊控制器设计[J]。控制与决策,2007,vol. 22 (5), pp. 585-588.
63. Yiming Li, Shao-Ming Yu, Yih-Lang Li. Electronic design automation using a unified optimization framework. Mathematics and Computers in Simulation, 2008, vol. 79 (4), pp. 1137-1152
64. Araujo. E,; dos Santos Coelho, L.. Fuzzy Model and Particle Swarm Optimization for Nonlinear Identification of a Chua’s Oscillator [C]. IEEE International Fuzzy Systems Con., 2007, pp. 1-6
65.雷开友。粒子群算法及其应用研究[D]:[博士学位论文].西南大学博士论文.2006.
66. Saska, M., Macas, M., Preucil, L., Lhotska, L.. Robot Path Planning using particle swarm optimization of Ferguson Splines [C]. IEEE Con. Emerging Tech. and Factory Auto., 2006, vol. 20 (22), pp. 833-839.
67. Hwan II Kang, Byunghee Lee, Kabil Kom, Path Planning algorithm using the Particle Swarm Optimization and the Improved Dijistra Algorithm [C]. IEEE Con. Computational Intelligence and Industrial Application, 2008, vol. 2, pp. 1002-1004.
68.王俊伟。粒子群优化算法的改进及应用[D]:[博士学位论文].东北大学博士学位论文.2006.
69. N. Otsu. A threshold selection method from gray-level histograms. IEEE Transactions on Systems, Man, Cybernetics, SMC-9, pp. 62-66, 1979
70. J. Sun, W.B. Xu. A Global Search Strategy of Quantum-behaved Particle Swarm Optimization [C]. IEEE Int. Conf. on Cybernetics and Intelligent Systems, vol. 1, pp. 111-116, 2004
71. SUN J, XU WB. Particle Swarm Optimization with Particle Having Quantum Behavior [C]. IEEE Congress .Evolutionary Computation. 2004, pp. 325-331
72. J. Kennedy. Some Issues and Practices for Particle Swarms[C]. IEEE Swarm Intelligence Symposium, 2007, pp. 162-169
73. J. Liu, J. Sun, Wenbo Xu. Quantum-Behaved Particle Swarm Optimization for Integer Programming [C]. Neural Information Processing, 2006
74. J. Sun, Wenbo Xu, J Liu. Training RBF Neural Network via Quantum-Behaved Particle Swarm Optimization [C]. Nerual Information Processing, 2006
75. S. Y. Li, R. G. Wang, W. W. Hu, J. Q. Sun. A new QPSO based BP neural network for face detection. Advances in Soft Computing, vol. 40, pp. 355-363, 2007
76. L. dos S. Coelho, V. C. Mariani. Particle swarm approach based on quantum mechanics and harmonic oscillator potential well for economic load dispatch with valve-point effects. Energy Conversion and Management, 2008, vol. 49, no. 11, pp. 3080-3085
77. F. van. Den Bergh and A. P. Engelbrecht. A cooperative approach to particle swarm optimization. IEEE Transactions on Evolutionary Computation, 2004, vol. 8, no. 3, pp. 225-238
78. Rivals, I. and L. Personnaz, No free lunch with the sandwich [sandwich estimator]. Neural Networks. IEEE Transactions on, 2003. 14(6): pp. 1553-1559
79. Goldberg DE. Genetic Algorithm in search, optimization and Machine Learning [M], Addison-wesley Publising Company, Inc. 1989
80.章毓晋。图像分割[M]。北京:科学出版社,2001
81.石岩,张天序,樊荣,江浩洋。基于两阶段搜索自适应正交投影分解的图像分割方法[J]。中国图像图形学报,2005,10(9):1089-1095
82. Wells WM, Grimson EL, Kikinis K, and Jolesz FA. Adaptive segmentation of MRI data. IEEE Trans. Med. Imag., 1996, vol. 15, pp. 429-442
83. Yang F, Jiang T. Pixon. Based image segmentation with Markov random fields. IEEE Trans. Image Process., 2003, 12(12): 1552-1559
84. W. B. Tao, H. Jin, L. M. Liu. Object segmentation using ant colony optimization algorithm and fuzzy entropy. Pattern Recognition Letters, 2008, vol. 28, no. 7, pp. 788-796
85. P. Y. Yin, L. H. Chen. A fast iterative scheme for multilevel thresholding methods. Signal Process, 1997, vol. 60, no. 3, pp. 305-313
86. L. Cao, P. Bao, Z. K. Shi. The strongest schema learning GA and its application to multilevel thresholding. Image and Vision Computing, 2008, vol. 26, no. 5, pp. 716-724
87. P. P. Yin. Multilevel minimum cross entropy threshold selection based on particle swarm optimization. Applied Mathematics and Computation, 2007, vol. 184, no. 2, pp. 503-513
88. E. Zahara, S. K. S. Fan, D. M. Tsai. Optimal multi-thresholding using a hybrid optimization approach. Pattern Recognition Letters, 2005, vol. 26, no. 8, pp. 1082-1095
89. M. Maitra, A. Chatterjee. A hybrid cooperative-comprehensive learning based PSO algorithm for image segmentation using multilevel thresholding. Expert Systems with Applications, 2008, vol. 34, no. 2, pp. 1341-1350
90. http://www.eecs.berkeley.edu/Research/Projects/CS/vision/bsds/
91. AP Engelbrecht, BS Masiye, G Pampara. Niching Ability of Basic Particle Swarm Optimization Algorithms [C]. Proceedings of IEEE Swarm Intelligence Symposium (SIS), Pasadena, California, USA. 2005: 397-400.
92. Paul S. Andrews. An Investigation into Mutation Operators for Particle Swarm Optimization. IEEE Congress on Evolutionary Computation, Vancouver, BC, Canada. 2006, 16(21), 1044-1051.
93. HU XH, Eberhart RC. Adaptive particle swarm optimization: Detection and response to dynamic system [C]. In Proc. Of the IEEE Conf on Evolutionary Computation. Honolulu USA. 2002: 1666-1670.
94.郭崇慧,唐焕文。演化策略的全局收敛性[J]。计算数学,2001,23(1):105-110.
95. Kapur J. N., SAHOO P. K., WONG A. K. C. A new method for gray-level picture thresholding using the entropy of the histogram. Computer vision, graphics, and image processing, 1985, vol. 29 (3), pp. 273-285.
96. Y. Shi, R. C. Eberhart. A modified particle swarm optimizer. IEEE Int. Conf. of Evolutionary Computation, Piscataway: IEEE Press, 1998. 69-73.
97.方伟,群体智能算法机器在数字滤波器优化设计中的研究[D]:[博士学位论文].江南大学博士学位论文,2008.
98.胡旺,李志蜀。一种更简化而高效的粒子群优化算法[J]。软件学报,2007,18(4):861-868。
99. T. O. Ting, M. V. C. Rao, and C. K. Loo. A novel approach for unit commitment problem via an effective hybrid particle swarm optimization. IEEE Trans, Power Syst., vol. 21, no. 1, pp. 411-418, Feb. (2006).
100.Y. Song, Z. Chen, and Z. Yuan. New chaotic PSO-based neural network predictive control for nonlinear process. IEEE Trans. Neural Netw., 2007, vol. 18, no. 2, pp. 595-601
101.唐贤伦。混沌粒子群优化算法理论及应用研究[D]:[博士学位论文].重庆大学博士学位论文。2007.
102.H. M. Feng. Particle swarm optimization learning fuzzy systems design [C]. Proceedings of the ICITA 2005 3rd International Conference on Information Technology and Applications, 2005, vol. 1. July 4-7, pp. 363-366
103.张利彪。基于粒子群和微分进化的优化算法研究[D]:[博士学位论文].吉林大学博士论文。2007.
104.Maes F, Collignon A. Multimodality image registration by maximization of mutual information. IEEE Trans. Med. Imag., 1997, 16(2): 187-198.
105.Studholme C, Hill DLG, Hawkes DJ. Incorporating connected region labeling into automated image registration using mutual information[C]. In: Proc. Of MMBIA’96 (San Francisco), Piscataway: IEEE Press, 1996, 3-31.
106.Rigau J, Feixas M, Sbert M, et al. Medical image segmentation based on mutual information maximization [C]. In: Proc. Of MICCAI 2004 (Saint-Malo), Belin: Springer, 2004, 135-142
107.Kim J, Fisher III JW, Yezzi A, et al. A nonparametric statistical method for image segmentation using information theory and curve evolution. IEEE Trans. Image Process, 2005, 14(10):1486-1502
108.吕庆文,陈武凡。基于互信息量的图像分割.计算机学报,2006,29(2):296-301.
© 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 |