无线传感器网络分簇路由协议的研究与改进
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摘要
无线传感器网络因其广阔的应用前景和独特的技术挑战吸引了众多学者的研究兴趣,并逐渐成为了近几年来计算机网络领域中热门方向。路由协议作为无线传感器网络组网的基础和网络层的核心技术,成为无线传感器网络研究的重点。
本文首先对无线传感器网络的概念、体系结构、特点以及关键技术做了简要介绍,然后对现有的各种无线传感器网络的路由协议做了深入分析。针对分簇协议普遍存在能量消耗不均和负载不均衡的问题,设计了基于权值的聚簇路由协议(WCRP协议),通过局部拓扑信息的权值计算,增强簇头选举的合理性,通过基于消息驱动机制的簇划分,提高负载的均衡性。针对PEGASIS协议数据传输延时较大和能量消耗不均的问题,设计了双层链式路由协议(DCCR协议),根据地理位置实现集中式分簇,在簇内形成短小的数据传输融合链,在簇间形成簇头链,以减小通信时延;并引入能量和距离作为簇头选举因子,以均衡节点的能量消耗。针对PEGASIS协议因采用贪婪算法导致链路径较长的问题,设计了改进的PEGASIS协议(PPEG协议),使用简单高效的离散式PSO算法,构造全局近似最短链,并在簇头选举中引入能量因子,以减少全网能耗。
实验结果表明:WCRP协议具有良好的能量效率和负载平衡性,与采用MAXD成簇算法的协议相比,其网络生命周期延长约30%;DCCR协议具有良好的实时性,与PEGASIS协议相比,其传输延时降低约50%;PPEG协议能降低全网通信总距离,有效的减少了通信能耗。
Wireless sensor networks (WSN), due to its broad application prospects and technical challenges, is attracting a large number of scholars’interest, and has gradually become a popular direction in the area of computer network in recent years. As the basis of networking and core technology, routing protocol has become the focus of the study.
This paper firstly studied the concept and architecture of wireless sensor networks,, as well as the characteristics of a variety of key technologies, then analyzed the typical wireless sensor network routing protocol. In order to solve energy consumption and uneven load imbalance problem, this paper proposed a Weight-based Cluster Routing Protocol (WCRP), enhanced the election ability of cluster-head through calculating the local right of the topology information, improved the load balance based on message-driven mechanism. In order to solve the data transmission delay and greater energy consumption inequality problem, this paper proposed a Double Chain-cluster Routing Protocol (DCCR), achieved a short-chain of data transmission in the cluster and a chain of cluster-head during the clusters, to reduce the communication time delay, and involved the elements of energy and distance to balance the energy consumption of nodes. In order to solve the long chain path problem result from using greedy algorithm in the PEGASIS protocol, this paper proposed a Power-Efficient Gathering based PSO (PPEG), achieved a global short-chain by using the simple and efficient discrete-PSO algorithm, and involved the element of energy to reduce the whole energy consumption.
The result of the testing shows that WCRP has a good performance of energy efficiency and load balancing, compared with protocol based MAXD, the life cycle of network extends about 30%; DCCR has a good performance of real-time, compared with PEGASIS, the delay of transmission decreases about 50%; PPEG has a good performance of shorten the total communication distance, and reduces the energy consumption effectively.
本文首先对无线传感器网络的概念、体系结构、特点以及关键技术做了简要介绍,然后对现有的各种无线传感器网络的路由协议做了深入分析。针对分簇协议普遍存在能量消耗不均和负载不均衡的问题,设计了基于权值的聚簇路由协议(WCRP协议),通过局部拓扑信息的权值计算,增强簇头选举的合理性,通过基于消息驱动机制的簇划分,提高负载的均衡性。针对PEGASIS协议数据传输延时较大和能量消耗不均的问题,设计了双层链式路由协议(DCCR协议),根据地理位置实现集中式分簇,在簇内形成短小的数据传输融合链,在簇间形成簇头链,以减小通信时延;并引入能量和距离作为簇头选举因子,以均衡节点的能量消耗。针对PEGASIS协议因采用贪婪算法导致链路径较长的问题,设计了改进的PEGASIS协议(PPEG协议),使用简单高效的离散式PSO算法,构造全局近似最短链,并在簇头选举中引入能量因子,以减少全网能耗。
实验结果表明:WCRP协议具有良好的能量效率和负载平衡性,与采用MAXD成簇算法的协议相比,其网络生命周期延长约30%;DCCR协议具有良好的实时性,与PEGASIS协议相比,其传输延时降低约50%;PPEG协议能降低全网通信总距离,有效的减少了通信能耗。
Wireless sensor networks (WSN), due to its broad application prospects and technical challenges, is attracting a large number of scholars’interest, and has gradually become a popular direction in the area of computer network in recent years. As the basis of networking and core technology, routing protocol has become the focus of the study.
This paper firstly studied the concept and architecture of wireless sensor networks,, as well as the characteristics of a variety of key technologies, then analyzed the typical wireless sensor network routing protocol. In order to solve energy consumption and uneven load imbalance problem, this paper proposed a Weight-based Cluster Routing Protocol (WCRP), enhanced the election ability of cluster-head through calculating the local right of the topology information, improved the load balance based on message-driven mechanism. In order to solve the data transmission delay and greater energy consumption inequality problem, this paper proposed a Double Chain-cluster Routing Protocol (DCCR), achieved a short-chain of data transmission in the cluster and a chain of cluster-head during the clusters, to reduce the communication time delay, and involved the elements of energy and distance to balance the energy consumption of nodes. In order to solve the long chain path problem result from using greedy algorithm in the PEGASIS protocol, this paper proposed a Power-Efficient Gathering based PSO (PPEG), achieved a global short-chain by using the simple and efficient discrete-PSO algorithm, and involved the element of energy to reduce the whole energy consumption.
The result of the testing shows that WCRP has a good performance of energy efficiency and load balancing, compared with protocol based MAXD, the life cycle of network extends about 30%; DCCR has a good performance of real-time, compared with PEGASIS, the delay of transmission decreases about 50%; PPEG has a good performance of shorten the total communication distance, and reduces the energy consumption effectively.
引文
[1] Bultk Burstein,Chang D,Low power systems for wireless micro-sensors,International Symposium of Low Power Electronics and Design Monterey,CA,1996
[2]于海斌,曾鹏,等,智能无线传感器网络系统(第一版),科学出版社,2006,5~30
[3] Ten emerging technologies that will change the world.Technology Review,2003,106(l):22-49,http://www.techreview.com/articles/emerging0203.asp
[4] Akyildiz I F,Su W,Sankarasubramaniam Y,et al,A survey on sensor networks,IEEE Communication Magazine,2002,40(8):102~105
[5]孙利民,李建中,陈渝,等,无线传感器网络,清华大学出版社,2005:3~24
[6] S.Avnaeha,J.Undereoeff,A.JoshinadJ Pinkston,Securiy to frsnesor Newtokrs,Wierless Snesor Newtokrs (C.S.Raghvaendaretaleds·),ChPater12,Jnauayr2004:253~275
[7]郑少仁,王海涛,赵志峰,等,Ad hoc网络技术(第一版)[M],人民邮电出版社,2005:97~102,109~111
[8] Kemal Akkaya,A Survey on Routing Protocols for Wireless Sensor Networks, the Elsevier Ad Hoc NetworkJournal,August 2003
[9]任丰原,黄海宁,林闯,无线传感器网络,软件学报,2003,Vol.14 No.7
[10] Kawadia V,Kumar P R,Principles and Protocols for Power Control in Wireless Ad hoc Network[J],IEEE Journal on Selected Areas in Communications,2005,23(1):76~88
[11]李建中,李金宝,石胜飞,传感器网络及其数据管理的概念、问题与进展,软件学报,2003,Vol.12 No.2:110~116
[12] VieiraM AM,Coelho C N,Survey on wireless sensor network devices[J],Emerging Technologies and Factory Automation 2003:Proceedings ETFA 03 IEEE Conference,2003,16-19(1):537~544
[13] Deborah E,Wireless Sensor Networks Tutorial Part IV:Sensor Network Protocols[C], Atlanta,Georgia,USA,2002:23~28
[14] Shakkottai S,Rappaport T S,Karlsson P C,Cross layer design for wireless networks[J],IEEE Communications Magazine,2003,41(10):74~80
[15] J.QiangFeng and D.Manivannan,Routing Protocols for sensor networks,Presented at Consumer communications and Networking Conferenee,CCNC2004,First.IEEE,2004
[16] Akkaya K,Younis M,A survey of routing protocols in wireless sensor networks,Ad HocNetworks,2005,3(3):325~349
[17] Al-Karaki JN,Kamal AE,Routing techniques in wireless sensor networks,A survey,IEEE Wireless Communications,2004,11(6):6~28
[18] Hedetniem IS,Liestman A,A survey of gossip ing and broadcasting in communication networks [M],Networks,1988
[19] S.Hedetniemi,A.Liestman,A Survery of Gossiping and Broadcasting in Communication Networks,Sensors,2002(2):286-293
[20] Shedetniemi,Liestman A,A survey of gossiping and broadcasting in communication networks,Networks,1988,18(4):319~349
[21] Heinzelman W R,Kulik J,Balakrishnan H, Adaptive protocols for information disseminati on in wireless sensor networks,In:Proc.of the ACM MobiCom’99,ACM Press,1999:174~185
[22] Intanagonwiwat C,Govindan R,Estrin D,Directed diffusion:A scalable and robust communication paradigm for sensor networks,In:Proc.6th Annual Int’1 Conf. on Mobile Computing and Networks,Boston,MA,August 2000
[23] Sohrabi K, Gao J,Ailawadhi V,Protocols for self-organization of a wireless sensor network,IEEE Personal Communications,2000,7(5):16~27
[24] Yu Y,Govindan R,Estrin D,Geographical and energy aware routing: A recursive data dissemination protocol for wireless sensor networks,UCLA Computer Science Department Technical Report UCLA/CSD-TR-01-0023,May 2001
[25] Hedetniem IS,Liestman A,A survey of gossip ing and broadcasting in communication networks [M],Networks,1988
[26] S.Hedetniemi,A.Liestman,A Survery of Gossiping and Broadcasting in Communication Networks,Sensors,2002(2):286-293
[27] http://www.autocontrol.com.cn/article/image/wuxianchuanganqiwang-luoluyouxieyifenxi.pdf
[28] Hairong Qi,The Development of Localized Algorithms in Wireless Sensor Networks,Sensors,2002(2):236-243
[29] Intanagonwiwat C,Govindan R,Estrin D,Directed Diffusion:A Scalable and Robust Connnunieation Paradigm for Sensor Networks,In:Proc. of ACM Conference on Mobile Computing and Networking,Boston,MA,2000
[30] Heinzelman W R,Chandrakasan A,Balakrishnan H,An application-specific protocol architecture for wireless micro-sensor networks , IEEE Transactions on Wireless Communications,2002,1(4):660~670
[31] Heinzehnman W,Chandrakasan A,Balakrishnan H,Energy-efficient routing protocols for wireless micro-sensor networks[C],In:Proc.of 33rd Hawaii Int Conf System Sciences (HICSS),USA,Jan 2000
[32] Lindsey S,Raghavendra CS,PEGASIS:Power efficient gathering in sensor information systems,In:Proc. of the IEEE Aerospace Conf. San Francisco:IEEE Computer Society,2002:1-6
[33] Karp.B,Kung.H,“Greedy Perimeter stateless routing for wireless networks”in MOBICOM,Boston,USA,2000(8):243~254
[34] Man jeshwar A,Agrawal D,TEEN:A protocol for enhance deficiency in WSNs,In Proceedings of the 1st International Workshop on Parallel and Distributed Computing Issues in Wireless Networks and Mobile Computing,San Francisco,CA,USA,April 2001
[35] Younis O,Fahmy S,HEED:A Hybrid Energy-efficient Distributed Clustering Approach for Ad hoc Sensor Networks[C],IEEE Trans on Mobile Computing,2004,3(4):660~669
[36] Gupta I,Riordan D,Sampalli S,Cluster-Head election using fuzzy logic for wireless sensor networks,In:Proc. of the 3rd Annual Communication Networks and Services Research Conf. Halifax:IEEE Computer Society,2005:255~260
[37] Manjeshwar A , Agrawal DP , APTEEN : A hybrid protocol for efficient routing and comprehensive information retrieval in wireless sensor networks,In:Proc.of the 2nd Int’l Workshop on Parallel Distributed Computing Issues in Wireless Networks and Mobile Computing,IEEE Computer Society,2002:195~202
[38] Ye F,Luo H,Cheng J,Lu S,et al,A two-tier data dissemination model for large-scale wireless sensor networks,In:Proc.of the 8th Annual Int’l Conf. on Mobile Computing and Networking,Atlanta:ACM Press,2002:148~159
[39] Chan H,Perrig A,ACE:An emergent algorithm for highly uniform cluster formation,In: Proc.of the 1st European Workshop on Wireless Sensor Networks,LNCS 2920,Berlin,2004:154~171
[40] Soro S,Heinzelman WB,Prolonging the lifetime of wireless sensor networks via unequal clustering,In:Proc.of the 19th IEEE Int’1 on Parallel and Distributed Processing Symposium,San Francisco:IEEE Computer Society Press,2005:236~240
[41] Ye M,Li CF,Chen G,EECS:An energy eficient clustering scheme in wireless sensor networks,In:Proc. of the IEEE IPCCC 2005.New York:IEEE Press,2005:535-540
[42]沈波,张世永,钟亦平,无线传感器网络分簇路由协议,软件学报,2006,Vol.17 No.7:188~200
[43] Amis A D,Prakash R.Load- balancing clusters in wireless ad hoc networks//Proceedings of ASSET 2000,Richardson,Texas,March 2000
[44] Chatterjee M,Das S K,Turgut D,WCA:a weighted clustering algorithm for mobile ad hoc networks,Journal of Cluster Computing,Special Issue on Mobile Ad hoc Networking,2002(5):193~204.
[45] Muruganathan S D,Ma DCF,Bhasin PI,and et al,A centralized energy-efficient routing protocol for wireless sensor networks,IEEE Communications Magazine,2005,43(3):8~13
[46] Foss S G,Zuyev S A,On a voronoi aggregative process related to a bivariate poisson process,Advances in Applied Probability,1996,28(4):965~981
[47] Basagni S,Distributed clustering for ad hoc networks,In:Proc.of the’99 Int’l Symp. on Parallel Architectures,Algorithms,and Networks,IEEE Computer Society,1999:310~315
[48] Arisha K A,Youssef M A,Younis M F.Energy-aware TDMA-based MAC for sensor networks,In:Proc. IEEE Workshop on Integrated Management of Power Aware Communications,Computing and NeTworking (IMPACCT),New York,May 2002
[49]吴臻,金心宇,无线传感器网络的LEACH算法的改进.传感技术学报,2006,Vol.19 No.1:34～36
[50]庄明强,金心宇,张昱,一种高效节能的无线传感网分簇路由协议,传感技术学报,2008, Vol.21 No.1:48~56
[51] Kennedy J,Eberhart R,Particle Swarm Optimization,IEEE 1995:1942~1948
[52] Shi Y,Eberhart R,A modified Particle Swarm optimization,IEEE World Congresson Computational Intelligenee,1998:69~73
[53] Clerc M,Discrete particle swarm optimization[A],Onwubolu GC,Babu BV,New Optimization Techniques in Engineering,Springer-Verlag,2004,219~240
[54]曾建潮,介婧,崔志华,微粒群算法,北京:科学出版社,2004
[55] L.Huang,K-p.Wang,C-g.Z.,Partical Swarm Optimization for Traveling Salesman Problems,Journal of JL University,2003,Vol.41 No.4:477~480
[2]于海斌,曾鹏,等,智能无线传感器网络系统(第一版),科学出版社,2006,5~30
[3] Ten emerging technologies that will change the world.Technology Review,2003,106(l):22-49,http://www.techreview.com/articles/emerging0203.asp
[4] Akyildiz I F,Su W,Sankarasubramaniam Y,et al,A survey on sensor networks,IEEE Communication Magazine,2002,40(8):102~105
[5]孙利民,李建中,陈渝,等,无线传感器网络,清华大学出版社,2005:3~24
[6] S.Avnaeha,J.Undereoeff,A.JoshinadJ Pinkston,Securiy to frsnesor Newtokrs,Wierless Snesor Newtokrs (C.S.Raghvaendaretaleds·),ChPater12,Jnauayr2004:253~275
[7]郑少仁,王海涛,赵志峰,等,Ad hoc网络技术(第一版)[M],人民邮电出版社,2005:97~102,109~111
[8] Kemal Akkaya,A Survey on Routing Protocols for Wireless Sensor Networks, the Elsevier Ad Hoc NetworkJournal,August 2003
[9]任丰原,黄海宁,林闯,无线传感器网络,软件学报,2003,Vol.14 No.7
[10] Kawadia V,Kumar P R,Principles and Protocols for Power Control in Wireless Ad hoc Network[J],IEEE Journal on Selected Areas in Communications,2005,23(1):76~88
[11]李建中,李金宝,石胜飞,传感器网络及其数据管理的概念、问题与进展,软件学报,2003,Vol.12 No.2:110~116
[12] VieiraM AM,Coelho C N,Survey on wireless sensor network devices[J],Emerging Technologies and Factory Automation 2003:Proceedings ETFA 03 IEEE Conference,2003,16-19(1):537~544
[13] Deborah E,Wireless Sensor Networks Tutorial Part IV:Sensor Network Protocols[C], Atlanta,Georgia,USA,2002:23~28
[14] Shakkottai S,Rappaport T S,Karlsson P C,Cross layer design for wireless networks[J],IEEE Communications Magazine,2003,41(10):74~80
[15] J.QiangFeng and D.Manivannan,Routing Protocols for sensor networks,Presented at Consumer communications and Networking Conferenee,CCNC2004,First.IEEE,2004
[16] Akkaya K,Younis M,A survey of routing protocols in wireless sensor networks,Ad HocNetworks,2005,3(3):325~349
[17] Al-Karaki JN,Kamal AE,Routing techniques in wireless sensor networks,A survey,IEEE Wireless Communications,2004,11(6):6~28
[18] Hedetniem IS,Liestman A,A survey of gossip ing and broadcasting in communication networks [M],Networks,1988
[19] S.Hedetniemi,A.Liestman,A Survery of Gossiping and Broadcasting in Communication Networks,Sensors,2002(2):286-293
[20] Shedetniemi,Liestman A,A survey of gossiping and broadcasting in communication networks,Networks,1988,18(4):319~349
[21] Heinzelman W R,Kulik J,Balakrishnan H, Adaptive protocols for information disseminati on in wireless sensor networks,In:Proc.of the ACM MobiCom’99,ACM Press,1999:174~185
[22] Intanagonwiwat C,Govindan R,Estrin D,Directed diffusion:A scalable and robust communication paradigm for sensor networks,In:Proc.6th Annual Int’1 Conf. on Mobile Computing and Networks,Boston,MA,August 2000
[23] Sohrabi K, Gao J,Ailawadhi V,Protocols for self-organization of a wireless sensor network,IEEE Personal Communications,2000,7(5):16~27
[24] Yu Y,Govindan R,Estrin D,Geographical and energy aware routing: A recursive data dissemination protocol for wireless sensor networks,UCLA Computer Science Department Technical Report UCLA/CSD-TR-01-0023,May 2001
[25] Hedetniem IS,Liestman A,A survey of gossip ing and broadcasting in communication networks [M],Networks,1988
[26] S.Hedetniemi,A.Liestman,A Survery of Gossiping and Broadcasting in Communication Networks,Sensors,2002(2):286-293
[27] http://www.autocontrol.com.cn/article/image/wuxianchuanganqiwang-luoluyouxieyifenxi.pdf
[28] Hairong Qi,The Development of Localized Algorithms in Wireless Sensor Networks,Sensors,2002(2):236-243
[29] Intanagonwiwat C,Govindan R,Estrin D,Directed Diffusion:A Scalable and Robust Connnunieation Paradigm for Sensor Networks,In:Proc. of ACM Conference on Mobile Computing and Networking,Boston,MA,2000
[30] Heinzelman W R,Chandrakasan A,Balakrishnan H,An application-specific protocol architecture for wireless micro-sensor networks , IEEE Transactions on Wireless Communications,2002,1(4):660~670
[31] Heinzehnman W,Chandrakasan A,Balakrishnan H,Energy-efficient routing protocols for wireless micro-sensor networks[C],In:Proc.of 33rd Hawaii Int Conf System Sciences (HICSS),USA,Jan 2000
[32] Lindsey S,Raghavendra CS,PEGASIS:Power efficient gathering in sensor information systems,In:Proc. of the IEEE Aerospace Conf. San Francisco:IEEE Computer Society,2002:1-6
[33] Karp.B,Kung.H,“Greedy Perimeter stateless routing for wireless networks”in MOBICOM,Boston,USA,2000(8):243~254
[34] Man jeshwar A,Agrawal D,TEEN:A protocol for enhance deficiency in WSNs,In Proceedings of the 1st International Workshop on Parallel and Distributed Computing Issues in Wireless Networks and Mobile Computing,San Francisco,CA,USA,April 2001
[35] Younis O,Fahmy S,HEED:A Hybrid Energy-efficient Distributed Clustering Approach for Ad hoc Sensor Networks[C],IEEE Trans on Mobile Computing,2004,3(4):660~669
[36] Gupta I,Riordan D,Sampalli S,Cluster-Head election using fuzzy logic for wireless sensor networks,In:Proc. of the 3rd Annual Communication Networks and Services Research Conf. Halifax:IEEE Computer Society,2005:255~260
[37] Manjeshwar A , Agrawal DP , APTEEN : A hybrid protocol for efficient routing and comprehensive information retrieval in wireless sensor networks,In:Proc.of the 2nd Int’l Workshop on Parallel Distributed Computing Issues in Wireless Networks and Mobile Computing,IEEE Computer Society,2002:195~202
[38] Ye F,Luo H,Cheng J,Lu S,et al,A two-tier data dissemination model for large-scale wireless sensor networks,In:Proc.of the 8th Annual Int’l Conf. on Mobile Computing and Networking,Atlanta:ACM Press,2002:148~159
[39] Chan H,Perrig A,ACE:An emergent algorithm for highly uniform cluster formation,In: Proc.of the 1st European Workshop on Wireless Sensor Networks,LNCS 2920,Berlin,2004:154~171
[40] Soro S,Heinzelman WB,Prolonging the lifetime of wireless sensor networks via unequal clustering,In:Proc.of the 19th IEEE Int’1 on Parallel and Distributed Processing Symposium,San Francisco:IEEE Computer Society Press,2005:236~240
[41] Ye M,Li CF,Chen G,EECS:An energy eficient clustering scheme in wireless sensor networks,In:Proc. of the IEEE IPCCC 2005.New York:IEEE Press,2005:535-540
[42]沈波,张世永,钟亦平,无线传感器网络分簇路由协议,软件学报,2006,Vol.17 No.7:188~200
[43] Amis A D,Prakash R.Load- balancing clusters in wireless ad hoc networks//Proceedings of ASSET 2000,Richardson,Texas,March 2000
[44] Chatterjee M,Das S K,Turgut D,WCA:a weighted clustering algorithm for mobile ad hoc networks,Journal of Cluster Computing,Special Issue on Mobile Ad hoc Networking,2002(5):193~204.
[45] Muruganathan S D,Ma DCF,Bhasin PI,and et al,A centralized energy-efficient routing protocol for wireless sensor networks,IEEE Communications Magazine,2005,43(3):8~13
[46] Foss S G,Zuyev S A,On a voronoi aggregative process related to a bivariate poisson process,Advances in Applied Probability,1996,28(4):965~981
[47] Basagni S,Distributed clustering for ad hoc networks,In:Proc.of the’99 Int’l Symp. on Parallel Architectures,Algorithms,and Networks,IEEE Computer Society,1999:310~315
[48] Arisha K A,Youssef M A,Younis M F.Energy-aware TDMA-based MAC for sensor networks,In:Proc. IEEE Workshop on Integrated Management of Power Aware Communications,Computing and NeTworking (IMPACCT),New York,May 2002
[49]吴臻,金心宇,无线传感器网络的LEACH算法的改进.传感技术学报,2006,Vol.19 No.1:34～36
[50]庄明强,金心宇,张昱,一种高效节能的无线传感网分簇路由协议,传感技术学报,2008, Vol.21 No.1:48~56
[51] Kennedy J,Eberhart R,Particle Swarm Optimization,IEEE 1995:1942~1948
[52] Shi Y,Eberhart R,A modified Particle Swarm optimization,IEEE World Congresson Computational Intelligenee,1998:69~73
[53] Clerc M,Discrete particle swarm optimization[A],Onwubolu GC,Babu BV,New Optimization Techniques in Engineering,Springer-Verlag,2004,219~240
[54]曾建潮,介婧,崔志华,微粒群算法,北京:科学出版社,2004
[55] L.Huang,K-p.Wang,C-g.Z.,Partical Swarm Optimization for Traveling Salesman Problems,Journal of JL University,2003,Vol.41 No.4:477~480