群智能算法研究及应用
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摘要
实际工程问题的复杂性、约束性、非线性和建模困难等特点,对优化和计算技术提出了更高的要求,寻找新型的智能优化方法逐渐成为一个新的研究热点。群体智能,作为一种新兴的智能计算技术正受到越来越多研究者的关注。
本文主要研究了群智能领域中两个具有代表性的算法:粒子群优化算法和蚁群优化算法。通过对已有理论的研究对比,进一步加深对两种算法的认识。并在研究已有基本粒子群优化算法及其改进形式的基础上,基于基本粒子群优化算法搜索后期,众多微粒都拥挤在历史最优位置周围进行重复性无效搜索这一现象,提出一种自适应搜索区域的粒子群优化算法。其优化性能比基本粒子群优化算法有明显提高,并有效地避免了粒子群优化算法早熟收敛的问题。其次,在分析K-均值聚类算法原有缺陷的基础上,将传统的K-均值聚类算法思想融入到粒子群优化算法中,提出了基于粒子群优化算法的聚类算法,通过粒子群优化算法基于种群的全局寻优能力更好地弥补了聚类算法的不足。从而提高收敛速度并改善分类效果。
最后,将基于粒子群优化算法的聚类算法与蚁群算法相结合应用于旅行商问题(Traveling Salesman Problem,简称TSP)的求解中,从问题本身着手,利用基于粒子群优化算法的聚类算法将大规模旅行商问题划分为多个小规模旅行商问题,然后进行并行处理,从而克服了蚁群算法收敛速度过慢的缺点。并在旅行商问题的求解中取得了较好的结果。
The characteristics of the practical engineering problems, such as complexity, constraint, nonlinearity and difficulty of modeling etc, ask for the higher effectiveness of optimization and computation technology, Therefore, it is important to find a new type of intelligent optimization method. Swarm intelligence, as a kind of intelligence computation, which is attractive for more and more researchers.
This dissertation focuses on two algorithms of Swarm Intelligence: Particle Swarm Optimization algorithm (PSO) and Ant Colony Optimization algorithm (ACO), on the basis of systematical research of PSO algorithm and its modification, based on the phenomena that a lot of particles crowded around the best position and many particles repeated an ineffective search in search later period,Proposes an improved algorithm mode, which is called Particle Swarm Optimization algorithm based on Self-adaptive Search Area (SSAPSO), it has better optimization performance than PSO and avoids effectively the precocious convergence problem. Secondly, after analyzing the disadvantages of the classical K-means clustering algorithm, combines the core idea of k-means clustering method with PSO algorithm and proposes a clustering algorithm based on PSO algorithm, it used the global optimization of PSO algorithm to make up the shortage of clustering method and enhances convergent rate.
Finally, combines the clustering algorithm based on PSO algorithm with Ant Colony Optimization algorithm and apply it to Traveling Salesman Problem (TSP). Divides the large-scale TSP into much small scale TSP, and then carries on the parallel processing.Solved the problem of slowly convergent rate of Ant Colony Optimization algorithm. The application effect is comparative ideal.
本文主要研究了群智能领域中两个具有代表性的算法:粒子群优化算法和蚁群优化算法。通过对已有理论的研究对比,进一步加深对两种算法的认识。并在研究已有基本粒子群优化算法及其改进形式的基础上,基于基本粒子群优化算法搜索后期,众多微粒都拥挤在历史最优位置周围进行重复性无效搜索这一现象,提出一种自适应搜索区域的粒子群优化算法。其优化性能比基本粒子群优化算法有明显提高,并有效地避免了粒子群优化算法早熟收敛的问题。其次,在分析K-均值聚类算法原有缺陷的基础上,将传统的K-均值聚类算法思想融入到粒子群优化算法中,提出了基于粒子群优化算法的聚类算法,通过粒子群优化算法基于种群的全局寻优能力更好地弥补了聚类算法的不足。从而提高收敛速度并改善分类效果。
最后,将基于粒子群优化算法的聚类算法与蚁群算法相结合应用于旅行商问题(Traveling Salesman Problem,简称TSP)的求解中,从问题本身着手,利用基于粒子群优化算法的聚类算法将大规模旅行商问题划分为多个小规模旅行商问题,然后进行并行处理,从而克服了蚁群算法收敛速度过慢的缺点。并在旅行商问题的求解中取得了较好的结果。
The characteristics of the practical engineering problems, such as complexity, constraint, nonlinearity and difficulty of modeling etc, ask for the higher effectiveness of optimization and computation technology, Therefore, it is important to find a new type of intelligent optimization method. Swarm intelligence, as a kind of intelligence computation, which is attractive for more and more researchers.
This dissertation focuses on two algorithms of Swarm Intelligence: Particle Swarm Optimization algorithm (PSO) and Ant Colony Optimization algorithm (ACO), on the basis of systematical research of PSO algorithm and its modification, based on the phenomena that a lot of particles crowded around the best position and many particles repeated an ineffective search in search later period,Proposes an improved algorithm mode, which is called Particle Swarm Optimization algorithm based on Self-adaptive Search Area (SSAPSO), it has better optimization performance than PSO and avoids effectively the precocious convergence problem. Secondly, after analyzing the disadvantages of the classical K-means clustering algorithm, combines the core idea of k-means clustering method with PSO algorithm and proposes a clustering algorithm based on PSO algorithm, it used the global optimization of PSO algorithm to make up the shortage of clustering method and enhances convergent rate.
Finally, combines the clustering algorithm based on PSO algorithm with Ant Colony Optimization algorithm and apply it to Traveling Salesman Problem (TSP). Divides the large-scale TSP into much small scale TSP, and then carries on the parallel processing.Solved the problem of slowly convergent rate of Ant Colony Optimization algorithm. The application effect is comparative ideal.
引文
[1]康琦.微粒群优化算法的研究与应用[D].上海:同济大学,2005
[2]姜长元.蚁群算法的理论及其应用[J].计算机时代,2004,(6):1-3
[3]彭宇.群智能优化算法及理论研究[D].哈尔滨:哈尔滨工业大学,2004
[4] Kennedy J.,Eberhart R.C..Particle swarm optimization[A].Proceeding IEEE International Conference on Neural Networks[C].1995:1942-1948
[5]康琦,张燕,汪镭,等.智能微粒群算法[J].冶金自动化,2005,(4):5-9
[6]张燕,汪镭,康琦,等.微粒群优化算法及其改进形式综述[J].计算机工程与应用,2005,1-3
[7]徐志烽.粒子群优化算法的改进研究[D].广州:中山大学,2005
[8]李博.粒子群优化算法及其在神经网络中的应用[D].大连:大连理工大学,2005.
[9] Shi Y.,Eberhart R.C..A modified particle swarm optimizer[A].IEEE World Congress on Computational Intelligence[C].Anchorage:IEEE,1998:69-73
[10] Eberhart R.C., Kennedy J..A new optimizer using particle swarm theory[A].Proceedings of the Sixth International Symposium on Micro Machine and Human Science[C].NJ:IEEE Service Center, 1995:39-43
[11] Shi Y.,Eberhart R.C..Fuzzy adaptive particle swarm optimization [A].Proceedings of the IEEE Conference on Evolutionary Computation [C].Soul:IEEE,2001:101-106
[12]张丽平,俞欢军,陈德钊,等.粒子群优化算法的分析与改进[J].信息与控制,2004,33(5):513-517.
[13] Fan H.Y..A modification to particle swarm optimization algorithm [J].Engineering Computations,2002,19(8):970-989.
[14] Eberhart R.C.,Shi Y..Comparing inertia weights and constriction factors in particle swarm optimization[A].Proceedings of the IEEE Conference on Evolutionary Computation [C].California:IEEE,2000:84-88.
[15] Kennedy J.,Eberhart R.C..A discrete binary version of the particle swarm algorithm [A].Proceedings of the 1997 International Conference on Systems,Man,and Cybernetics[C]. USA:IEEE,1997:4104-4109
[16]杨淑媛.量子进化算法的研究及其应用[D].西安:西安电子科技大学,2003
[17] Clere M..Discrete particle optimization illustrated by the traveling salesman problem [EB/OL],http://www.mauriceclerc.net,2000
[18] Suganthan P.N..Particle swarm optimizer with neighbourhood operator[A].Proceedings of the 1999 Congress on Evolutionary Computation[C].NJ:IEEE Service Center, 1999:1958-1962
[19] Lovbjerg M.,Rasmussen T.K.,Krink T..Hybrid particle swarm optimizer with breeding and subpopulations[A].Proceedings of the Genetic and Evolutionary Computation Conference[C]. SanFransisco:Morgan Kaufmann Publishers Inc, 2001:469-476
[20] Ratnaweera A.,Halgamuge S.K.,Watson H.C..Self-organizingHierarchical Particle Swarm Optimizer With Time-varying Acceleration Coefficients [J]. IEEE Transactions on Evolutionary Computation, 2004, 8(3): 240-255.
[21] Eberhart R.C., Hu Xiaohui..Human Tremor Analysis Using Particle Swarm Optimization [A].Proc.Congress on Evolutionary Computation[C].1999:1927-1930
[22]高海兵,高亮,周驰,等.基于粒子群优化的神经网络训练算法研究[J].电子学报,2004,32(9):1572-1574
[23]刘飞,孙明,李宁,等.粒子群算法及其在布局优化中的应用[J].计算机工程与应用,2004,71-73
[24]周驰,高亮,高海兵.基于粒子群优化算法的约束布局优化[J].控制与决策,2005,20(1):36-40
[25] Nara K,Mishima Y.Particle Swarm Optimization for Fault State Power Supply Reliability Enhancement.[A]Proc.of IEEE International Conference on Intelligent Systems Applications to Power Systems[C].2001
[26] El-Gallad A,El-Hawary M.Particle swam optimizer for constrained economic dispatch with prohibited operating zones[A].Canadian Conference on Electrical and Computer Enginering[C].2002:78-81.
[27] Naka S,Genji T,Yura T,et al. Practical distribution state estimation using hybrid particle swarm optimization[A].In:Proc of IEEE Power engineering society winter meeting[C]. Columbus,ohio,USA:2001
[28]刘钊,陈建勋.基于粒子群算法的足球机器人动作选择研究[J].武汉科技大学学报(自然科学版),2006,29(1):83-85
[29]秦元庆,孙德宝,李宁,等.基于粒子群算法的移动机器人路径规划[J].机器人,2004,26(3):222-225
[30]李宁,邹彤,孙德宝.车辆路径问题的粒子群算法研究[J].系统工程学报,2004,19(6):596-600
[31]李宁,邹彤,孙德宝.带时间窗车辆路径问题的粒子群算法[J].系统工程理论与实践,2004,(4):130-135
[32] ZhangY.Y.,Ji C.L.,YuanPing.Particle swarm optimization for base station placement in mobile communication.[A].2004 IEEE International Conference on Networking,Sensing and Control[C].Taipei, Taiwan, 2004:428-432
[33]原萍,王光兴,张洋洋.求解通信优化问题的一种微粒群优化方法[J].东北大学学报(自然科学版),2004,25(10):934-937
[34]刘靖明,韩丽川,侯立文.一种新的聚类算法——粒子群聚类算法[J].计算机工程与应用,2005,183-185
[35]高尚,杨静宇.求解聚类问题的混合粒子群优化算法[J].科学技术与工程,2005,5(23):1792-1795
[36] Bonabeau E.,Dorigo M.,Theraulaz G.Inspiration for optimization from social insect behaviour[J].Nature,2000,406(6):39-42
[37] Katja V.,Ann N..Colonies of learning automata[J].IEEE Trans on Systems,Man,and Cybernetics-Part B.2002,32(6):772-780
[38] Dorigo M.,Maniezzo V.,Colorni A.Ant system:Optimization by a colony of cooperating Agents[J].IEEE Trans on Systems,Man,and Cybernetics-Part B,1996,26(1):29-41
[39] Dorigo M., Carp G.D., Gambardella L.M..Ant algorithms for discrete optimization [J]. Artificial Life,1999,5(2):137-172
[40] James M.,Marcus R..Anti-pheromone as a tool for better exploration of search space[A].Proc of 3rd Int Workshop on Ant Algorithms [C].Brussels,2002:100-110
[41] Colorni A.,Dorigo M.,Maniezzo V.,et a1.Distributed optimization by ant colonies[A].Proc of European conf on Artificial Life [C].Paris, 1991:134-142
[42]詹士昌,徐婕,吴俊.蚁群算法中有关算法参数的最优选择[J].科技通报,2003,19(5):381-386
[43]段海滨.蚁群算法原理及其应用[M].北京:科学出版社,2005:33-37
[44]李炳宇.群体智能模型算法的研究与应用[D].上海:同济大学,2004
[45] Dorigo M.,Gambardella L.M..A study of some properties of Ant-Q[A].Proceedings of PPSN IV-Fourth International Conference on Parallet Problem Solving From Nature[C]. Berlin:Springer-Verlag, 1996:656-665
[46] STUTZLE T.,HOOS H.H..MAX-MIN ant system[J].Future Generation Computer Systems Journal, 2000, 16 (8) : 889-914.
[47]吴庆洪,张纪会,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):1240-1245
[48] Bilchev G., Parmee I.C.. Adaptive search strategies for heavily constrained design spaces [A].Proceedings of 22nd International Conference on Computer Aided Design’95 yelta[C].Ukraine,l995:230-235
[49]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
[50]段海滨,马冠军,王道波,等.一种求解连续空间优化问题的改进蚁群算法[J].系统仿真学报,2007,19(5):974-977
[51]陈崚,沉洁,秦玲.蚁群算法进行连续参数优化的新途径[J].系统工程理论与实践,2003,(3):48-53
[52]杨勇,宋晓峰,王建飞,等.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
[53]张勇德,黄莎白.多目标优化问题的蚁群算法研究[J].控制与决策,2005,20(2):170-173
[54] ISAACS J.C.,WATKINS R.K.,FOO S.Y..Evolving ant colony systems in hardware for random number generation[A].Proceedings of the 2002 Congress on Evolutionary Computation[C].2002:1450-1455
[55] SCHEUERMANN B.,SO K.,GUNTSCH M.,et al.FPGA implementation of population -based ant colony optimization [J]. Applied Soft Computing,2004,4(4):303-322.
[56]熊志辉,李思昆,陈吉华.遗传算法与蚂蚁算法动态融合的软硬件划分[J].软件学报,2005,16(4):503-511
[57]马良,项培军.蚂蚁算法在组合优化中的应用[J].管理科学学报,2001,4(2):32-36
[58]李士勇.蚁群优化算法及其应用研究进展.[J]计算机测量与控制,2003,11(12):911-913
[59]秦玲.蚁群算法的改进与应用[D].扬州:扬州大学,2004
[60] Colorni A.,Dorigo M..Ant system for job-shop scheduling[J].Belgian Journal of Operations Research Statistics and Computer Science,1994,34(1):39-53.
[61] White T..Connection management using adaptive mobile agents[A].In Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications[C].CSTEA Press,1998:802-809
[62] Bonabeau E..Routing in telecommunication networks with”Smart”ant-like agents telecommunication applications [A].In Proceedings of IATA’98 Second Int.Work Shop on Intelligent Agents for Telecommnication Applications[C].Lectures Notes in AI vol.Springer Verlag,1998:1437
[63] Dicaro G.,Dorigo M..Extending AntNet for best-effort Quality-of-Service routing [A].Proc.ANTS’98 First International Workshop on Ant Colony Optimization[C]. Brussels,Belgium,1998:15-16
[64]张素兵,吕国英,刘泽民,等.基于蚂蚁算法的QoS路由调度方法[J].电路与系统学报,2000,5(1):1-5
[65]张素兵,刘泽民.基于蚂蚁算法的分级QoS路由调度方法[J].北京邮电大学学报,2000,23(4):11-15
[66]杨燕,靳蕃,Kamel M.微粒群优化算法研究现状及其进展[J].计算机工程,2004,30(21):3-4
[67] Parsopoulos K E,Vrahatis M N.Recent approaches to global optimization problems through particle swarm optimization[J].Natural Computing,2002,1(2~3):235 -306
[68] Ioan C T.The particle swarm optimization algorithm:Convergence analysis and parameter selection [J].Information Processing Letters,2003,85(1):317-325
[69]谢晓锋,张文俊,杨之廉.微粒群算法综述[J].控制与决策,2003,18(2):129-134
[70] Ratnaweera A.,Halgamuge S.K., Watson H.C..Self-Organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients[J].IEEE Trans.on Evolutionary Computation, 2004,8(3):240-255
[71] MacQueen J..Some methods for classification and analysis of multivariate observations [A].In:proceedings of the 5th Berkeley Symposium on mathematics Statistic Problem[C]. 1967:281-297
[2]姜长元.蚁群算法的理论及其应用[J].计算机时代,2004,(6):1-3
[3]彭宇.群智能优化算法及理论研究[D].哈尔滨:哈尔滨工业大学,2004
[4] Kennedy J.,Eberhart R.C..Particle swarm optimization[A].Proceeding IEEE International Conference on Neural Networks[C].1995:1942-1948
[5]康琦,张燕,汪镭,等.智能微粒群算法[J].冶金自动化,2005,(4):5-9
[6]张燕,汪镭,康琦,等.微粒群优化算法及其改进形式综述[J].计算机工程与应用,2005,1-3
[7]徐志烽.粒子群优化算法的改进研究[D].广州:中山大学,2005
[8]李博.粒子群优化算法及其在神经网络中的应用[D].大连:大连理工大学,2005.
[9] Shi Y.,Eberhart R.C..A modified particle swarm optimizer[A].IEEE World Congress on Computational Intelligence[C].Anchorage:IEEE,1998:69-73
[10] Eberhart R.C., Kennedy J..A new optimizer using particle swarm theory[A].Proceedings of the Sixth International Symposium on Micro Machine and Human Science[C].NJ:IEEE Service Center, 1995:39-43
[11] Shi Y.,Eberhart R.C..Fuzzy adaptive particle swarm optimization [A].Proceedings of the IEEE Conference on Evolutionary Computation [C].Soul:IEEE,2001:101-106
[12]张丽平,俞欢军,陈德钊,等.粒子群优化算法的分析与改进[J].信息与控制,2004,33(5):513-517.
[13] Fan H.Y..A modification to particle swarm optimization algorithm [J].Engineering Computations,2002,19(8):970-989.
[14] Eberhart R.C.,Shi Y..Comparing inertia weights and constriction factors in particle swarm optimization[A].Proceedings of the IEEE Conference on Evolutionary Computation [C].California:IEEE,2000:84-88.
[15] Kennedy J.,Eberhart R.C..A discrete binary version of the particle swarm algorithm [A].Proceedings of the 1997 International Conference on Systems,Man,and Cybernetics[C]. USA:IEEE,1997:4104-4109
[16]杨淑媛.量子进化算法的研究及其应用[D].西安:西安电子科技大学,2003
[17] Clere M..Discrete particle optimization illustrated by the traveling salesman problem [EB/OL],http://www.mauriceclerc.net,2000
[18] Suganthan P.N..Particle swarm optimizer with neighbourhood operator[A].Proceedings of the 1999 Congress on Evolutionary Computation[C].NJ:IEEE Service Center, 1999:1958-1962
[19] Lovbjerg M.,Rasmussen T.K.,Krink T..Hybrid particle swarm optimizer with breeding and subpopulations[A].Proceedings of the Genetic and Evolutionary Computation Conference[C]. SanFransisco:Morgan Kaufmann Publishers Inc, 2001:469-476
[20] Ratnaweera A.,Halgamuge S.K.,Watson H.C..Self-organizingHierarchical Particle Swarm Optimizer With Time-varying Acceleration Coefficients [J]. IEEE Transactions on Evolutionary Computation, 2004, 8(3): 240-255.
[21] Eberhart R.C., Hu Xiaohui..Human Tremor Analysis Using Particle Swarm Optimization [A].Proc.Congress on Evolutionary Computation[C].1999:1927-1930
[22]高海兵,高亮,周驰,等.基于粒子群优化的神经网络训练算法研究[J].电子学报,2004,32(9):1572-1574
[23]刘飞,孙明,李宁,等.粒子群算法及其在布局优化中的应用[J].计算机工程与应用,2004,71-73
[24]周驰,高亮,高海兵.基于粒子群优化算法的约束布局优化[J].控制与决策,2005,20(1):36-40
[25] Nara K,Mishima Y.Particle Swarm Optimization for Fault State Power Supply Reliability Enhancement.[A]Proc.of IEEE International Conference on Intelligent Systems Applications to Power Systems[C].2001
[26] El-Gallad A,El-Hawary M.Particle swam optimizer for constrained economic dispatch with prohibited operating zones[A].Canadian Conference on Electrical and Computer Enginering[C].2002:78-81.
[27] Naka S,Genji T,Yura T,et al. Practical distribution state estimation using hybrid particle swarm optimization[A].In:Proc of IEEE Power engineering society winter meeting[C]. Columbus,ohio,USA:2001
[28]刘钊,陈建勋.基于粒子群算法的足球机器人动作选择研究[J].武汉科技大学学报(自然科学版),2006,29(1):83-85
[29]秦元庆,孙德宝,李宁,等.基于粒子群算法的移动机器人路径规划[J].机器人,2004,26(3):222-225
[30]李宁,邹彤,孙德宝.车辆路径问题的粒子群算法研究[J].系统工程学报,2004,19(6):596-600
[31]李宁,邹彤,孙德宝.带时间窗车辆路径问题的粒子群算法[J].系统工程理论与实践,2004,(4):130-135
[32] ZhangY.Y.,Ji C.L.,YuanPing.Particle swarm optimization for base station placement in mobile communication.[A].2004 IEEE International Conference on Networking,Sensing and Control[C].Taipei, Taiwan, 2004:428-432
[33]原萍,王光兴,张洋洋.求解通信优化问题的一种微粒群优化方法[J].东北大学学报(自然科学版),2004,25(10):934-937
[34]刘靖明,韩丽川,侯立文.一种新的聚类算法——粒子群聚类算法[J].计算机工程与应用,2005,183-185
[35]高尚,杨静宇.求解聚类问题的混合粒子群优化算法[J].科学技术与工程,2005,5(23):1792-1795
[36] Bonabeau E.,Dorigo M.,Theraulaz G.Inspiration for optimization from social insect behaviour[J].Nature,2000,406(6):39-42
[37] Katja V.,Ann N..Colonies of learning automata[J].IEEE Trans on Systems,Man,and Cybernetics-Part B.2002,32(6):772-780
[38] Dorigo M.,Maniezzo V.,Colorni A.Ant system:Optimization by a colony of cooperating Agents[J].IEEE Trans on Systems,Man,and Cybernetics-Part B,1996,26(1):29-41
[39] Dorigo M., Carp G.D., Gambardella L.M..Ant algorithms for discrete optimization [J]. Artificial Life,1999,5(2):137-172
[40] James M.,Marcus R..Anti-pheromone as a tool for better exploration of search space[A].Proc of 3rd Int Workshop on Ant Algorithms [C].Brussels,2002:100-110
[41] Colorni A.,Dorigo M.,Maniezzo V.,et a1.Distributed optimization by ant colonies[A].Proc of European conf on Artificial Life [C].Paris, 1991:134-142
[42]詹士昌,徐婕,吴俊.蚁群算法中有关算法参数的最优选择[J].科技通报,2003,19(5):381-386
[43]段海滨.蚁群算法原理及其应用[M].北京:科学出版社,2005:33-37
[44]李炳宇.群体智能模型算法的研究与应用[D].上海:同济大学,2004
[45] Dorigo M.,Gambardella L.M..A study of some properties of Ant-Q[A].Proceedings of PPSN IV-Fourth International Conference on Parallet Problem Solving From Nature[C]. Berlin:Springer-Verlag, 1996:656-665
[46] STUTZLE T.,HOOS H.H..MAX-MIN ant system[J].Future Generation Computer Systems Journal, 2000, 16 (8) : 889-914.
[47]吴庆洪,张纪会,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):1240-1245
[48] Bilchev G., Parmee I.C.. Adaptive search strategies for heavily constrained design spaces [A].Proceedings of 22nd International Conference on Computer Aided Design’95 yelta[C].Ukraine,l995:230-235
[49]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
[50]段海滨,马冠军,王道波,等.一种求解连续空间优化问题的改进蚁群算法[J].系统仿真学报,2007,19(5):974-977
[51]陈崚,沉洁,秦玲.蚁群算法进行连续参数优化的新途径[J].系统工程理论与实践,2003,(3):48-53
[52]杨勇,宋晓峰,王建飞,等.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
[53]张勇德,黄莎白.多目标优化问题的蚁群算法研究[J].控制与决策,2005,20(2):170-173
[54] ISAACS J.C.,WATKINS R.K.,FOO S.Y..Evolving ant colony systems in hardware for random number generation[A].Proceedings of the 2002 Congress on Evolutionary Computation[C].2002:1450-1455
[55] SCHEUERMANN B.,SO K.,GUNTSCH M.,et al.FPGA implementation of population -based ant colony optimization [J]. Applied Soft Computing,2004,4(4):303-322.
[56]熊志辉,李思昆,陈吉华.遗传算法与蚂蚁算法动态融合的软硬件划分[J].软件学报,2005,16(4):503-511
[57]马良,项培军.蚂蚁算法在组合优化中的应用[J].管理科学学报,2001,4(2):32-36
[58]李士勇.蚁群优化算法及其应用研究进展.[J]计算机测量与控制,2003,11(12):911-913
[59]秦玲.蚁群算法的改进与应用[D].扬州:扬州大学,2004
[60] Colorni A.,Dorigo M..Ant system for job-shop scheduling[J].Belgian Journal of Operations Research Statistics and Computer Science,1994,34(1):39-53.
[61] White T..Connection management using adaptive mobile agents[A].In Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications[C].CSTEA Press,1998:802-809
[62] Bonabeau E..Routing in telecommunication networks with”Smart”ant-like agents telecommunication applications [A].In Proceedings of IATA’98 Second Int.Work Shop on Intelligent Agents for Telecommnication Applications[C].Lectures Notes in AI vol.Springer Verlag,1998:1437
[63] Dicaro G.,Dorigo M..Extending AntNet for best-effort Quality-of-Service routing [A].Proc.ANTS’98 First International Workshop on Ant Colony Optimization[C]. Brussels,Belgium,1998:15-16
[64]张素兵,吕国英,刘泽民,等.基于蚂蚁算法的QoS路由调度方法[J].电路与系统学报,2000,5(1):1-5
[65]张素兵,刘泽民.基于蚂蚁算法的分级QoS路由调度方法[J].北京邮电大学学报,2000,23(4):11-15
[66]杨燕,靳蕃,Kamel M.微粒群优化算法研究现状及其进展[J].计算机工程,2004,30(21):3-4
[67] Parsopoulos K E,Vrahatis M N.Recent approaches to global optimization problems through particle swarm optimization[J].Natural Computing,2002,1(2~3):235 -306
[68] Ioan C T.The particle swarm optimization algorithm:Convergence analysis and parameter selection [J].Information Processing Letters,2003,85(1):317-325
[69]谢晓锋,张文俊,杨之廉.微粒群算法综述[J].控制与决策,2003,18(2):129-134
[70] Ratnaweera A.,Halgamuge S.K., Watson H.C..Self-Organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients[J].IEEE Trans.on Evolutionary Computation, 2004,8(3):240-255
[71] MacQueen J..Some methods for classification and analysis of multivariate observations [A].In:proceedings of the 5th Berkeley Symposium on mathematics Statistic Problem[C]. 1967:281-297