非参数曲线提取方法研究
|
摘要
曲线提取与曲线识别是图像识别、图像理解、机器视觉等领域中非常重要的基本识别技术,在经济、国防、工业、安全等诸多方面有着广泛应用。在进行图像识别时,要首先对图像进行预处理、分割运算,然后提取曲线特征,最后进行识别。而图像的复杂性和多样性以及预处理、分割算法的局限性使得分割后的二值图像中存在大量的噪声,同时曲线中也存在断点,为曲线的特征提取带来了困难。Hough变换能够有效的从充斥噪声的二值图像中提取曲线,是曲线识别中的主要工具。但利用Hough变换进行曲线识别,需要预知曲线方程或形状,而实际图像中的曲线在许多情况下是无法在识别前预知其方程或形状的,也就无法使用Hough变换来提取曲线。论文将这类曲线称之为非参数曲线,而对它的提取问题归结为离散的组合优化问题,并在对遗传算法、蚁群优化算法进行深入研究的基础上,提出了基于蚁群算法的非参数曲线提取方法。论文的主要研究内容和所取得的成果包括如下几个方面:
(1)论文介绍了用Hough变换识别参数曲线的理论方法,以及参数曲线与非参数曲线的概念。阐明了基于组合优化理论的非参数曲线识别的基本思想,制定了基于优化算法的非参数曲线提取方案,并在研究前人基于小生境遗传优化的非参数曲线特征提取算法的基础上,采用蚁群优化来对非参数曲线进行提取,取得了较好的效果。
(2)论文对遗传算法、蚁群优化算法展开了深入的研究。针对算法中的缺陷与不足,提出了三种改进算法:具有局部搜索能力的小生境遗传算法、蚁群遗传混合算法、求解旅行商问题的智能蚁群优化算法。论文阐述了改进算法的思想、算法流程、和算子的设计,并通过多峰值函数、旅行商问题的仿真实验,验证了改进算法的合理性和有效性。
(3)针对非参数曲线识别问题,论文在基于蚁群优化的非参数曲线提取算法中设计了搜索终止概率函数,用于动态的判断蚂蚁是否继续添加解成分,解决了非参数曲线提取问题中解不定长的问题;路径翻转算子与搜索终止函数的共同作用解决了非参数曲线提取问题中曲线起点像素、终点像素不合一的问题,使得蚂蚁可以随机选择初始非零像素;论文同时对蚁群优化中的启发式信息给出了合理定义,并设计了相应的状态转移规则和信息素更新规则;局部搜索算子的引入一定程度上对蚁群优化的粗搜索进行了弥补,进一步优化了蚂蚁所构造的曲线;通过对含有各种长度、各种角度、各种纹理、存在各种噪声的二值图像的实验,结果表明算法是有效的。
(4)为了在同一幅二值图像当中同时提取两条甚至多条非参数曲线,论文对两曲线之间的相似度进行了定义,并在此基础上讨论了基于蚁群优化的多曲线提取算法,也取得了良好的效果。
Curve extraction and recognition is an important and basic recognition technique in image recognition and computer vision field. It has extensive application in economic, national defense, industry, security and so on. In image recognition algorithm, image preprocessing and image segmentation are firstly used before curve feature extraction and recognition. There are always large noise pixels in the binary images segmented from original images and break points on the curve for the complexity and variety of the images and the limitation of the segmentation algorithm, which brings difficulty for curve feature extraction. Hough transform (HT) can identify curves with break points on them in binary images with large noise, while curve function or shape is must given before recognition when using HT. But in actual images, the curve function or shape is not a priori knowledge before recognition in most cases and the curve can not be recognized by HT. This kind of curve is called nonparametric curve and its extraction is considered as a kind of permutation-based optimization problem in this paper. Basing on the deep research of genetic algorithm (GA) and ant colony optimization (ACO), this dissertation proposes a new nonparametric curve extraction algorithm by using ant colony system. The main research contexts and contributions of this dissertation are as follows:
1. The definition of nonparametric curve and academic parametric curve extraction approaches using HT are introduced in this dissertation. The basic idea and frame of nonparametric curve extraction based on permutation-based optimization theory is expressed. This dissertation successfully uses ant colony optimization to extract the nonparametric curves at the basic of the previous research using niche genetic algorithm proposed by other scholars.
2. This dissertation does a lot research of GA and ACO and introduces their shortcomings. In order to improve the performance of them, this dissertation proposes three improved algorithms: a novel niche genetic algorithm with local search ability, a new hybrid algorithm of ant colony system and genetic algorithm, a new intelligent ACO for traveling salesman problem (TSP). The flows and design methods of the algorithms’operators are given in the dissertation. Compared with the original algorithms, the simulation results show the superiority of the improved algorithms by using multi-modal function optimization and TSP correspondingly.
3. In the design of ACO nonparametric curve extraction, a variety of techniques are proposed. The searching termination probability function dynamically judges whether the ant adds new solution component to the current path, which solves the unfixed-length problem in solution coding of nonparametric curve extraction. The combination of path reversal operator and searching termination function makes the ants find reasonable solutions at any random starting pixel. This dissertation defines the heuristic information in ACO properly and designs the corresponding ACO’s state transition rule and pheromone updating rule. The introduced local search operator compensates ACO’s rough searching in some degree. Lots of binary images with different curves and noise are used to test the algorithm and the results show its effectiveness.
4. In order to identify two curves or even more than two curves from a binary image simultaneously, this dissertation defines the similarity between two curves and discusses the method of multi-curve extraction based on ACO. The experiments show the effectiveness of the method.
(1)论文介绍了用Hough变换识别参数曲线的理论方法,以及参数曲线与非参数曲线的概念。阐明了基于组合优化理论的非参数曲线识别的基本思想,制定了基于优化算法的非参数曲线提取方案,并在研究前人基于小生境遗传优化的非参数曲线特征提取算法的基础上,采用蚁群优化来对非参数曲线进行提取,取得了较好的效果。
(2)论文对遗传算法、蚁群优化算法展开了深入的研究。针对算法中的缺陷与不足,提出了三种改进算法:具有局部搜索能力的小生境遗传算法、蚁群遗传混合算法、求解旅行商问题的智能蚁群优化算法。论文阐述了改进算法的思想、算法流程、和算子的设计,并通过多峰值函数、旅行商问题的仿真实验,验证了改进算法的合理性和有效性。
(3)针对非参数曲线识别问题,论文在基于蚁群优化的非参数曲线提取算法中设计了搜索终止概率函数,用于动态的判断蚂蚁是否继续添加解成分,解决了非参数曲线提取问题中解不定长的问题;路径翻转算子与搜索终止函数的共同作用解决了非参数曲线提取问题中曲线起点像素、终点像素不合一的问题,使得蚂蚁可以随机选择初始非零像素;论文同时对蚁群优化中的启发式信息给出了合理定义,并设计了相应的状态转移规则和信息素更新规则;局部搜索算子的引入一定程度上对蚁群优化的粗搜索进行了弥补,进一步优化了蚂蚁所构造的曲线;通过对含有各种长度、各种角度、各种纹理、存在各种噪声的二值图像的实验,结果表明算法是有效的。
(4)为了在同一幅二值图像当中同时提取两条甚至多条非参数曲线,论文对两曲线之间的相似度进行了定义,并在此基础上讨论了基于蚁群优化的多曲线提取算法,也取得了良好的效果。
Curve extraction and recognition is an important and basic recognition technique in image recognition and computer vision field. It has extensive application in economic, national defense, industry, security and so on. In image recognition algorithm, image preprocessing and image segmentation are firstly used before curve feature extraction and recognition. There are always large noise pixels in the binary images segmented from original images and break points on the curve for the complexity and variety of the images and the limitation of the segmentation algorithm, which brings difficulty for curve feature extraction. Hough transform (HT) can identify curves with break points on them in binary images with large noise, while curve function or shape is must given before recognition when using HT. But in actual images, the curve function or shape is not a priori knowledge before recognition in most cases and the curve can not be recognized by HT. This kind of curve is called nonparametric curve and its extraction is considered as a kind of permutation-based optimization problem in this paper. Basing on the deep research of genetic algorithm (GA) and ant colony optimization (ACO), this dissertation proposes a new nonparametric curve extraction algorithm by using ant colony system. The main research contexts and contributions of this dissertation are as follows:
1. The definition of nonparametric curve and academic parametric curve extraction approaches using HT are introduced in this dissertation. The basic idea and frame of nonparametric curve extraction based on permutation-based optimization theory is expressed. This dissertation successfully uses ant colony optimization to extract the nonparametric curves at the basic of the previous research using niche genetic algorithm proposed by other scholars.
2. This dissertation does a lot research of GA and ACO and introduces their shortcomings. In order to improve the performance of them, this dissertation proposes three improved algorithms: a novel niche genetic algorithm with local search ability, a new hybrid algorithm of ant colony system and genetic algorithm, a new intelligent ACO for traveling salesman problem (TSP). The flows and design methods of the algorithms’operators are given in the dissertation. Compared with the original algorithms, the simulation results show the superiority of the improved algorithms by using multi-modal function optimization and TSP correspondingly.
3. In the design of ACO nonparametric curve extraction, a variety of techniques are proposed. The searching termination probability function dynamically judges whether the ant adds new solution component to the current path, which solves the unfixed-length problem in solution coding of nonparametric curve extraction. The combination of path reversal operator and searching termination function makes the ants find reasonable solutions at any random starting pixel. This dissertation defines the heuristic information in ACO properly and designs the corresponding ACO’s state transition rule and pheromone updating rule. The introduced local search operator compensates ACO’s rough searching in some degree. Lots of binary images with different curves and noise are used to test the algorithm and the results show its effectiveness.
4. In order to identify two curves or even more than two curves from a binary image simultaneously, this dissertation defines the similarity between two curves and discusses the method of multi-curve extraction based on ACO. The experiments show the effectiveness of the method.
引文
[1] P L Palmer,J Kittler,M Petrou. An Optimizing Line Finder Using a Hough Transform Algorithm[J]. Computer Vision and Image Understanding, 1999,73(3):329-345
[2] J M Nash,J N Carter,R I Damper. Robust Evidence-based Object Tracking[J]. Pattern Recognition Letters, 2002,23:253-260
[3] D Walsh,A E Raftery. Accurate and Efficient Curve Detection in Images:the Importance Sampling Hough Transform[J]. Pattern Recognition, 2002,35:1421-1431
[4] P V C Hough. Methods and Means for Recognizing Complex Patterns. U.S.Patent.3069654
[5] R O Duda,P E Hart. Use of the Hough Transform to Detect Lines and Curves in Pictures[J]. Communi. ACM1972,15:11-15
[6] C M Brown. Inherent Bias and Noise in the Hough Transform[J]. IEEE Trans. Pattern Anal. Mach. Intell,1983,5(5):493-505
[7] D Casasent,R Krishnapuram. Curved Object Location by Hough Transformations and Inversions[J]. Pattern Recognition, 1987,20(2):181-188
[8] J Sklansky. On the Hough Technique for Curve Detection[J]. IEEE Trans. Compute, 1978,27(10):923-926
[9] S Tsuji,F Matsumoto. Detection of Ellipses by a modified Hough Transform[J]. IEEE Trans. Computer 1987,C-27(8):777-781
[10] D H Ballard. Generalizing the Hough Transform to Detect Arbitrary Shapes[J]. Pattern Recognition, 1981,13(2):111-122
[11] 王凌. 智能优化算法及其应用[M]. 北京:清华大学出版社&施普林格出版社,2001
[12] Wei Wei,Qi Wang,Hua Wang,et al. The feature extraction of nonparametric curves based on niche genetic algorithms and multi-population competition[J]. Pattern Recognition Letters, 2005,26:1483-1497
[13] M Dorigo,V Maniezzo,A Colorni. Ant System:Optimization by a colony of cooperating agents[J]. IEEE Transactions on Systems,Man,and Cybernetics-Part B,1996,26(1):29-41
[14] M Dorigo,L M Gambardella. Ant Colony System:A cooperative learning approach to the traveling salesman problem[J]. IEEE Trans on Evolutionary Computation,1997,1:53-66
[15] Stützle T,H Hoos. The MAX-MIN Ant System and Local Search for the Traveling Salesman Problem[C]. In Proceedings of ICEC'97-1997 IEEE 4th International Conference on Evolutionary Computation. IEEE Press.1997,308-313
[16] B Bullnheimer,R F Hartl,C Strauss. A new rank-based version of the ant system:a computational study[J]. Central European Journal of Operations Research,1999,7 (1):25–38
[17] Christian Blum,Joaquin Batista,Jordi Pereira.Beam-ACO applied to assembly line balancing[C].5t h international workshop,ANTS2006,Brussels,Belgium,2006
[18] 胡小兵,黄席樾. 蚁群优化算法及其应用[J]. 计算机仿真,2004,24(5):81-85
[19] M Dorigo,T Stützle. Ant Colony Optimization[M]. America:The MIT Press,2004
[20] Joseph M Pasia,Richard F Hartl,Karl F Doerner.Solving a bi-objective flowshop scheduling problem by pareto-ant colony optimization. 5t h international workshop,ANTS2006,Brussels,Belgium,2006
[21] M Dorigo,G Di Carol,L M Gambardella. Ant Algorithm for discrete optimization[J]. Artificial life, 1999,5(2):137-172
[22] 贺秋伟. 基于计算机视觉的微小尺寸精密检测理论与技术研究:[博士论文]. 吉林:吉林大学, 2007 年
[23] 王化楠. Hough 变换在视觉检测系统中的应用研究:[硕士论文]. 辽宁:大连理工大学,2006 年
[24] 魏玮. 基于遗传优化的非参数曲线识别算法研究:[博士论文]. 黑龙江:哈尔滨工业大学,2005 年
[25] 张文修,梁怡. 遗传算法的数学基础[M]. 西安:西安交通大学出版社,2000,10-96
[26] 董云影. 基于遗传算法的模糊聚类技术的研究:[硕士论文]. 大连:大连海事大学,2005
[27] 王小平,曹立明. 遗传算法:理论、应用及软件实现[M]. 西安:西安交通大学出版社,2002
[28] 邹林,夏巨谌,胡国安. 基于实数编码的多种群并行遗传算法研究[J]. 小型微型计算机系 统,2004,25(6):982-986
[29] 魏平,熊伟清. 一种改进的实数编码遗传算法[J]. 计算机应用研究,2004(9):87-89
[30] 陈国良,王煦法,庄镇. 遗传算法及其应用[M]. 北京:人民邮电出版社,1996
[31] 周明,孙树栋. 遗传算法原理及应用[M]. 北京:国防工业出版社,1999
[32] D J Cavicchio. Adaptive Search Using Simulated Evolution:[Doctoral Dissertation]. University of Michigan,Ann,Arbor,1970
[33] De Jong K A. An analysis of the behavior of a class of genetic adaptive systems:[Dissertation]. Ann Arbor:University of Michigan,1975
[34] D E Goldberg,J Richardson. Genetic Algorithms with Sharing for Multi-model Function Optimization[C]. In Proceedings of the Second International Conference on Genetic Algorithms (ICGA2),NJ:Lawrence Erlbaum Associates,1987:41-49
[35] D Beasley,D R Bull,R R Martin. A Sequential Niche Technique for Multi-modal Function Optimization[J]. Evolutionary Computation,1993,1(2):101-125
[36] Shreni B,Klahenbuhl L. Fitness Sharing and Niching Methods Revisited[J]. IEEE Trans. on Evolutionary Computation,1988,2 (3):97-106
[37] Antonio Della Cioppa,Claudio De Stefano,Angelo Marcelli. On the Role of Population Size and Niche Radius in Fitness Sharing[J]. IEEE Transactions on Evolutionary Computation, 2004,12, vol.8(6):580-592
[38] Thierens D. Scalability problems of simple genetic algorithms[J]. Evolutionary Computation,1999,7 (4):331-352
[39] 袁丽华,黎明,李军华. 进化优化小生境遗传算法控制参数的研究[J]. 计算机工程,2006,vol.32 (17):206-208
[40] 陈娟,许立鸿. 动态小生境遗传算法在多模函数优化中的应用[J]. 同济大学学报(自然科学 版),2006,vol.34 (5):684-688
[41] 敖磊. 求解 TSP 问题的改进蚁群算法: [硕士论文]. 西安:西安电子科技大学,2005
[42] J L Deneubourg,S Aron,S Goss,et al. The self-organizing exploratory Patten of the argentine ant[J]. Journal of Insect Behavio,1990,5:159-168
[43] 李士勇等. 蚁群算法及其应用[M]. 哈尔滨:哈尔滨工业大学出版社,2004.29-40
[44] M Dorigo,L M Gambardella. Ant Colonies for the Traveling Salesman Problem[J]. BioSystems,1997,43:73-81
[45] Cordon,I Fernandez de Viana,F Herrera,et al. A new ACO model integrating evolutionary computation concepts:the best-worst ant system[C]. In Proceedings ofANTS2000 from ant colonies to artificial ants,Universitè Libre de Bruxelles,2000
[46] T White,B Pagurek,F Oppacher. ASGA:Improving the Ant System by Integrating with Genetic Algorithms[C]. In Proceedings of the 3rd Conference on Genetic Programming,1998
[47] 吴庆洪,张继会,徐心和. 具有变异特征的蚁群算法[J]. 计算机研究与发展,1999,36(10)
[48] 陈烨. 带杂交算子的蚁群算法[J]. 计算机工程,2001,12:27-30
[49] 丁建立,陈增强,袁著祉. 遗传算法与蚂蚁算法的融合[J]. 计算机研究与发展, 2003, 40(9):1351-1356
[50] 曹浪财,罗键,李天成. 智能蚂蚁算法——蚁群算法的改进[J]. 计算机应用研究,2003,10:62-64
[51] 夏国成,赵佳宝. 智能蚂蚁算法求解多目标 TSP 问题的改进研究[J]. 计算机工程与应用, 2006,09:56-59
[52] 蔡利剑. 智能蚂蚁系统研究[硕士论文]. 天津:河北工业大学,2001,1
[53] TSPLIB:http://www.iwr.uni-heidelberg.de/groups/comopt/software/TSPLIB95/
[2] J M Nash,J N Carter,R I Damper. Robust Evidence-based Object Tracking[J]. Pattern Recognition Letters, 2002,23:253-260
[3] D Walsh,A E Raftery. Accurate and Efficient Curve Detection in Images:the Importance Sampling Hough Transform[J]. Pattern Recognition, 2002,35:1421-1431
[4] P V C Hough. Methods and Means for Recognizing Complex Patterns. U.S.Patent.3069654
[5] R O Duda,P E Hart. Use of the Hough Transform to Detect Lines and Curves in Pictures[J]. Communi. ACM1972,15:11-15
[6] C M Brown. Inherent Bias and Noise in the Hough Transform[J]. IEEE Trans. Pattern Anal. Mach. Intell,1983,5(5):493-505
[7] D Casasent,R Krishnapuram. Curved Object Location by Hough Transformations and Inversions[J]. Pattern Recognition, 1987,20(2):181-188
[8] J Sklansky. On the Hough Technique for Curve Detection[J]. IEEE Trans. Compute, 1978,27(10):923-926
[9] S Tsuji,F Matsumoto. Detection of Ellipses by a modified Hough Transform[J]. IEEE Trans. Computer 1987,C-27(8):777-781
[10] D H Ballard. Generalizing the Hough Transform to Detect Arbitrary Shapes[J]. Pattern Recognition, 1981,13(2):111-122
[11] 王凌. 智能优化算法及其应用[M]. 北京:清华大学出版社&施普林格出版社,2001
[12] Wei Wei,Qi Wang,Hua Wang,et al. The feature extraction of nonparametric curves based on niche genetic algorithms and multi-population competition[J]. Pattern Recognition Letters, 2005,26:1483-1497
[13] M Dorigo,V Maniezzo,A Colorni. Ant System:Optimization by a colony of cooperating agents[J]. IEEE Transactions on Systems,Man,and Cybernetics-Part B,1996,26(1):29-41
[14] M Dorigo,L M Gambardella. Ant Colony System:A cooperative learning approach to the traveling salesman problem[J]. IEEE Trans on Evolutionary Computation,1997,1:53-66
[15] Stützle T,H Hoos. The MAX-MIN Ant System and Local Search for the Traveling Salesman Problem[C]. In Proceedings of ICEC'97-1997 IEEE 4th International Conference on Evolutionary Computation. IEEE Press.1997,308-313
[16] B Bullnheimer,R F Hartl,C Strauss. A new rank-based version of the ant system:a computational study[J]. Central European Journal of Operations Research,1999,7 (1):25–38
[17] Christian Blum,Joaquin Batista,Jordi Pereira.Beam-ACO applied to assembly line balancing[C].5t h international workshop,ANTS2006,Brussels,Belgium,2006
[18] 胡小兵,黄席樾. 蚁群优化算法及其应用[J]. 计算机仿真,2004,24(5):81-85
[19] M Dorigo,T Stützle. Ant Colony Optimization[M]. America:The MIT Press,2004
[20] Joseph M Pasia,Richard F Hartl,Karl F Doerner.Solving a bi-objective flowshop scheduling problem by pareto-ant colony optimization. 5t h international workshop,ANTS2006,Brussels,Belgium,2006
[21] M Dorigo,G Di Carol,L M Gambardella. Ant Algorithm for discrete optimization[J]. Artificial life, 1999,5(2):137-172
[22] 贺秋伟. 基于计算机视觉的微小尺寸精密检测理论与技术研究:[博士论文]. 吉林:吉林大学, 2007 年
[23] 王化楠. Hough 变换在视觉检测系统中的应用研究:[硕士论文]. 辽宁:大连理工大学,2006 年
[24] 魏玮. 基于遗传优化的非参数曲线识别算法研究:[博士论文]. 黑龙江:哈尔滨工业大学,2005 年
[25] 张文修,梁怡. 遗传算法的数学基础[M]. 西安:西安交通大学出版社,2000,10-96
[26] 董云影. 基于遗传算法的模糊聚类技术的研究:[硕士论文]. 大连:大连海事大学,2005
[27] 王小平,曹立明. 遗传算法:理论、应用及软件实现[M]. 西安:西安交通大学出版社,2002
[28] 邹林,夏巨谌,胡国安. 基于实数编码的多种群并行遗传算法研究[J]. 小型微型计算机系 统,2004,25(6):982-986
[29] 魏平,熊伟清. 一种改进的实数编码遗传算法[J]. 计算机应用研究,2004(9):87-89
[30] 陈国良,王煦法,庄镇. 遗传算法及其应用[M]. 北京:人民邮电出版社,1996
[31] 周明,孙树栋. 遗传算法原理及应用[M]. 北京:国防工业出版社,1999
[32] D J Cavicchio. Adaptive Search Using Simulated Evolution:[Doctoral Dissertation]. University of Michigan,Ann,Arbor,1970
[33] De Jong K A. An analysis of the behavior of a class of genetic adaptive systems:[Dissertation]. Ann Arbor:University of Michigan,1975
[34] D E Goldberg,J Richardson. Genetic Algorithms with Sharing for Multi-model Function Optimization[C]. In Proceedings of the Second International Conference on Genetic Algorithms (ICGA2),NJ:Lawrence Erlbaum Associates,1987:41-49
[35] D Beasley,D R Bull,R R Martin. A Sequential Niche Technique for Multi-modal Function Optimization[J]. Evolutionary Computation,1993,1(2):101-125
[36] Shreni B,Klahenbuhl L. Fitness Sharing and Niching Methods Revisited[J]. IEEE Trans. on Evolutionary Computation,1988,2 (3):97-106
[37] Antonio Della Cioppa,Claudio De Stefano,Angelo Marcelli. On the Role of Population Size and Niche Radius in Fitness Sharing[J]. IEEE Transactions on Evolutionary Computation, 2004,12, vol.8(6):580-592
[38] Thierens D. Scalability problems of simple genetic algorithms[J]. Evolutionary Computation,1999,7 (4):331-352
[39] 袁丽华,黎明,李军华. 进化优化小生境遗传算法控制参数的研究[J]. 计算机工程,2006,vol.32 (17):206-208
[40] 陈娟,许立鸿. 动态小生境遗传算法在多模函数优化中的应用[J]. 同济大学学报(自然科学 版),2006,vol.34 (5):684-688
[41] 敖磊. 求解 TSP 问题的改进蚁群算法: [硕士论文]. 西安:西安电子科技大学,2005
[42] J L Deneubourg,S Aron,S Goss,et al. The self-organizing exploratory Patten of the argentine ant[J]. Journal of Insect Behavio,1990,5:159-168
[43] 李士勇等. 蚁群算法及其应用[M]. 哈尔滨:哈尔滨工业大学出版社,2004.29-40
[44] M Dorigo,L M Gambardella. Ant Colonies for the Traveling Salesman Problem[J]. BioSystems,1997,43:73-81
[45] Cordon,I Fernandez de Viana,F Herrera,et al. A new ACO model integrating evolutionary computation concepts:the best-worst ant system[C]. In Proceedings ofANTS2000 from ant colonies to artificial ants,Universitè Libre de Bruxelles,2000
[46] T White,B Pagurek,F Oppacher. ASGA:Improving the Ant System by Integrating with Genetic Algorithms[C]. In Proceedings of the 3rd Conference on Genetic Programming,1998
[47] 吴庆洪,张继会,徐心和. 具有变异特征的蚁群算法[J]. 计算机研究与发展,1999,36(10)
[48] 陈烨. 带杂交算子的蚁群算法[J]. 计算机工程,2001,12:27-30
[49] 丁建立,陈增强,袁著祉. 遗传算法与蚂蚁算法的融合[J]. 计算机研究与发展, 2003, 40(9):1351-1356
[50] 曹浪财,罗键,李天成. 智能蚂蚁算法——蚁群算法的改进[J]. 计算机应用研究,2003,10:62-64
[51] 夏国成,赵佳宝. 智能蚂蚁算法求解多目标 TSP 问题的改进研究[J]. 计算机工程与应用, 2006,09:56-59
[52] 蔡利剑. 智能蚂蚁系统研究[硕士论文]. 天津:河北工业大学,2001,1
[53] TSPLIB:http://www.iwr.uni-heidelberg.de/groups/comopt/software/TSPLIB95/