无线传感器网络三维全局定位算法研究
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摘要
随着无线传感器网络的广泛应用,作为传感器众多应用基础的传感器节点的位置信息变得越来越重要。针对传感器本身所具有的能量、存储、计算等资源相对有限的特点,如何用较低的能耗,准确的得到传感器节点的位置信息就显得越来越重要。到目前为止,传感器节点的定位算法主要分为两类:与锚节点相关的定位算法和与锚节点无关的定位算法。本文将会对这两类算法分别进行研究与改进,并提出新的算法。
首先,本文研究了与锚节点相关的定位算法。虽然目前已有的与锚节点相关的定位算法已经对节点的定位精度和能耗进行了改进,但通常无法对这两者兼顾,提高了定位精度的同时也增大了节点的能耗。线性最优化的方法计算量不大,但是节点的定位精度低,而使用非线性最优化的方法来定位的节点定位算法精度高,但是计算量大,针对如上问题,结合传感器的特性,本文提出一种改进的非线性最优化定位方法。仿真结果显示本文提出的对传统定位算法改进的两种算法,能够有效的缓解定位精度和节点计算量之间的矛盾。算法具有较高的定位精度和相对较低的计算消耗,不增加额外通信开销的优点。同时,考虑到集中式算法会造成某些节点的计算量大,能量消耗过多的情况,本文对与锚节点相关的定位算法中的分布式算法进行了研究,引入粒子群算法的思想,提出一种多种群并行粒子群算法(MPPSO),有效的解决了单一粒子群算法中某些节点能量消耗过多,且容易陷入局部最优化的问题。通过在多个信标节点上部署粒子群算法,有效的节约待定位节点的计算资源,实现算法的并行化,同时,通过使用多种群协同避免了局部最优问题。仿真结果表明当测距误差在30%以内时,MPPSO与某些传统的定位算法相比,能够提高定位精度8%到40%。
其次,考虑到传感器所在的恶劣环境,在没有GPS的情况下获得节点的位置也是非常重要的。本文研究了与锚节点无关的定位算法,提出了一种基于分簇机制的新的与锚节点无关的定位算法。本算法考虑到了节点的能量,连接度,以及三角形几何限制性原理来启发式的建簇,然后将这些簇融合成一个簇,建立起一个统一的全局坐标系。这个算法有效的解决了无锚节点的情况下节点定位问题,克服了在传统的与锚节点无关定位算法的累积性错误问题,提高了定位的精度,节约了节点的能量。仿真结果表明,在使用改善的簇融合技术之后,此定位算法相对于传统的与锚节点无关的ABC定位算法提高了30%到70%。
As the application of Wireless Sensor Network (WSN) is developing increasingly, the position of the sensors becomes more and more important as the basic of many applications of Wireless Sensor Network. According to the characteristic of the sensors which has limited energy, storage and computation ability and etc, it’s more and more important to get the sensor’s position quickly and accurately. Until recently, there are two categories of localization algorithm in WSN: range-based algorithm and range-free algorithm. This paper will do research and improving on the two categories of localization algorithm separately.
Firstly, this paper studies the range-based localization algorithm. Although the existed range-based localization algorithms improve the precision and computation cost, they can hardly do this at the same time, when they improve the precision of the localization, they will have a high computation cost. The linear optimization can achieve small calculating amount at the cost of reducing the positioning accuracy, and the traditional unconstrained nonlinear optimization has a better performance in accuracy but always demands large calculating amount. Basing on the characteristic of sensors, this paper proposes a modified nonlinear optimization method. Simulation results show that the two algorithms proposed in the paper are efficient to relieve the contradiction between calculating amount and localization accuracy by improving the traditional algorithms. This method has the advantages of high localization accuracy, relatively low calculating amount, and without requiring extra communicational cost. At the same time, considering that the centralized algorithm has the disadvantage of high computation cost and energy cost for some sensors, this paper studies the distributed algorithm in localization of WSN. By introducing the particle swarm algorithm, this paper proposes a Multi-population Parallel Particle Swarm Optimization Algorithm (MPPSO). Through deploying particle swarm in several beacons, we can reduce computation cost of sensors to be localized and achieve the parallelism of the algorithm, meanwhile, the local optimization problem can effectively being avoided by using the scheme of multi-population co-evolution. Simulation results show when ranging error is less than 30 percentages, MPPSO can improve location precision by 8% to 40% against some traditional algorithms.
Secondly, considering the hostile environment of the sensors, it is very important to acquire the node’s position without GPS. We propose one novel anchor-free algorithm based on cluster technique, node’s energy, connective degree, and the geometric limit principles of triangle inequality is also considered to heuristically build clusters, then fuse the clusters into one cluster and get one uniform global coordinate system. This algorithm effectively solves the position problem without any anchor node, conquer the cumulative error problem in traditional anchor-free algorithm, improve the localization precision and save the sensors energy. Simulation results show that after improving the fusion section, our algorithm can improve localization precision by 30% to 70% comparing to the traditional algorithm ABC.
首先,本文研究了与锚节点相关的定位算法。虽然目前已有的与锚节点相关的定位算法已经对节点的定位精度和能耗进行了改进,但通常无法对这两者兼顾,提高了定位精度的同时也增大了节点的能耗。线性最优化的方法计算量不大,但是节点的定位精度低,而使用非线性最优化的方法来定位的节点定位算法精度高,但是计算量大,针对如上问题,结合传感器的特性,本文提出一种改进的非线性最优化定位方法。仿真结果显示本文提出的对传统定位算法改进的两种算法,能够有效的缓解定位精度和节点计算量之间的矛盾。算法具有较高的定位精度和相对较低的计算消耗,不增加额外通信开销的优点。同时,考虑到集中式算法会造成某些节点的计算量大,能量消耗过多的情况,本文对与锚节点相关的定位算法中的分布式算法进行了研究,引入粒子群算法的思想,提出一种多种群并行粒子群算法(MPPSO),有效的解决了单一粒子群算法中某些节点能量消耗过多,且容易陷入局部最优化的问题。通过在多个信标节点上部署粒子群算法,有效的节约待定位节点的计算资源,实现算法的并行化,同时,通过使用多种群协同避免了局部最优问题。仿真结果表明当测距误差在30%以内时,MPPSO与某些传统的定位算法相比,能够提高定位精度8%到40%。
其次,考虑到传感器所在的恶劣环境,在没有GPS的情况下获得节点的位置也是非常重要的。本文研究了与锚节点无关的定位算法,提出了一种基于分簇机制的新的与锚节点无关的定位算法。本算法考虑到了节点的能量,连接度,以及三角形几何限制性原理来启发式的建簇,然后将这些簇融合成一个簇,建立起一个统一的全局坐标系。这个算法有效的解决了无锚节点的情况下节点定位问题,克服了在传统的与锚节点无关定位算法的累积性错误问题,提高了定位的精度,节约了节点的能量。仿真结果表明,在使用改善的簇融合技术之后,此定位算法相对于传统的与锚节点无关的ABC定位算法提高了30%到70%。
As the application of Wireless Sensor Network (WSN) is developing increasingly, the position of the sensors becomes more and more important as the basic of many applications of Wireless Sensor Network. According to the characteristic of the sensors which has limited energy, storage and computation ability and etc, it’s more and more important to get the sensor’s position quickly and accurately. Until recently, there are two categories of localization algorithm in WSN: range-based algorithm and range-free algorithm. This paper will do research and improving on the two categories of localization algorithm separately.
Firstly, this paper studies the range-based localization algorithm. Although the existed range-based localization algorithms improve the precision and computation cost, they can hardly do this at the same time, when they improve the precision of the localization, they will have a high computation cost. The linear optimization can achieve small calculating amount at the cost of reducing the positioning accuracy, and the traditional unconstrained nonlinear optimization has a better performance in accuracy but always demands large calculating amount. Basing on the characteristic of sensors, this paper proposes a modified nonlinear optimization method. Simulation results show that the two algorithms proposed in the paper are efficient to relieve the contradiction between calculating amount and localization accuracy by improving the traditional algorithms. This method has the advantages of high localization accuracy, relatively low calculating amount, and without requiring extra communicational cost. At the same time, considering that the centralized algorithm has the disadvantage of high computation cost and energy cost for some sensors, this paper studies the distributed algorithm in localization of WSN. By introducing the particle swarm algorithm, this paper proposes a Multi-population Parallel Particle Swarm Optimization Algorithm (MPPSO). Through deploying particle swarm in several beacons, we can reduce computation cost of sensors to be localized and achieve the parallelism of the algorithm, meanwhile, the local optimization problem can effectively being avoided by using the scheme of multi-population co-evolution. Simulation results show when ranging error is less than 30 percentages, MPPSO can improve location precision by 8% to 40% against some traditional algorithms.
Secondly, considering the hostile environment of the sensors, it is very important to acquire the node’s position without GPS. We propose one novel anchor-free algorithm based on cluster technique, node’s energy, connective degree, and the geometric limit principles of triangle inequality is also considered to heuristically build clusters, then fuse the clusters into one cluster and get one uniform global coordinate system. This algorithm effectively solves the position problem without any anchor node, conquer the cumulative error problem in traditional anchor-free algorithm, improve the localization precision and save the sensors energy. Simulation results show that after improving the fusion section, our algorithm can improve localization precision by 30% to 70% comparing to the traditional algorithm ABC.
引文
Ren FY, Huang HN, Lin C. 2003. Wireless sensor networks. Journal of Software, 14(7):1282-1291.
Business Week. 21 ideas for the 21st century. Business Week. pp.78-167, Aug30, 1999.
Haiqing Jiang, Renzhi Cao, Xingfu Wang. 2009. Apply Modified Method of Nonlinear Optimization to Improve Localization accuracy in WSN. The 5th International Conference on Wireless Communications, Networking and Mobile Computing, ISBN: 978-1-4244-3693-4.
TA Alhmiedat, SH Yang. 2007. A Survey: Localization and Tracking Mobile Targets through Wireless Sensors Network. PGnet,ISBN 1-9025-6016-7.
B. H. Wellenhoff, H. Lichtenegger and J. Collins. 1997. Global Positioning System: Theory and Practice: Springer Verlag.
A. Savvides, C. Han and M. B. Srivastava. 2001. Dynamic Fine-Grained Localization in Ad-Hoc Networks of Sensors. Proceedings of ACM MobiCom.
P. Bahl and V. N. Padmanabhan. 2000. RADAR: An In-Building RF-Based User Location and Tracking System. Proceedings of IEEE INFOCOM.
D. Niculescu and B. Nath. 2003. Ad Hoc Positioning System (APS) using AOA. Proceedings of IEEE INFOCOM, 2003.
SHI Qin-qin, HUO Hong. 2008.“Using steepest descent method to improve node localization accuracy of maximum likelihood estimation”,Application Research of Computers, Vol'25 No.7.
Kennedy J, Eberhart R C,Shi Y. 2001. Swarm Intelligence. San Francisco: Morgan Kaufman Publishers.
C Savarese, JM Rabaey,J Beutel. 2001. ICASSP IEEE INT CONF ACOUST SPEECH SIGNAL PROCESS PROC 4, 2037-2040.
Nissanka B. Priyantha, Hari Balakrishnan, Erik Demaine, and Seth Teller. 2003. Conference On Embedded Networked Sensor Systems. ISBN:1-58113-707-9.
Camillo Gentile. 2006. Distributed Sensor Location through Linear Programming with Triangle Inequality Constraints. IEEE International Conference on Communications, v 9, p 4020-4027. ISSN: 05361486
Hady S. AbdelSalam,Stephan Olariu. 2009. HexNet: Hexagon-Based Localization Technique For Wireless Sensor Networks. 7th Annual IEEE International Conference on Pervasive Computing and Communications, PerCom 2009.
Antonio Abramo, Franco Blanchini, Luca Geretti, and Carlo Savorgnan. 2008. A Mixed Convex/Nonconvex Distributed Localization Approach for the Deployment of Indoor Positioning Services. IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 7.
Radu Stoleru and John A. Stankovic. 2004. Probability Grid: A Location Estimation Scheme for Wireless Sensor Networks. 2004 First Annual IEEE Communications Society Conference on Sensor and Ad Hoc Communications and Networks, IEEE SECON 2004,ISBN-10: 078038796.
Ameer Ahmed Abbasi, Mohamed Younis. 2007. A survey on clustering algorithms for wireless sensor networks. Computer Communications 30 (2007) 2826–2841
Hongyi Wu, Member, IEEE, Chong Wang, Student Member, IEEE, and Nian-Feng Tzeng, Senior Member, IEEE. 2005. Novel Self-Configurable Positioning Technique for Multihop Wireless Networks. IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 13, NO. 3.
Adel Youssef and Ashok Agrawala,Mohamed Younis. 2005. Accurate Anchor-Free Node Localization in Wireless Sensor Networks. 24th IEEE International Performance, Computing, and Communications Conference, IPCCC.
Wang Shanshan, Yin Jianping, Cai Zhiping, Zhang Guomin. 2008, JOURNAL OF COMPUTER RESEARCH AND DEVELOPMENT. 2008 45(z1). TP393.
LIU Guang-yi, YU Hong-yi, PI Xing-yu, ZHANG Jian. 2010. COMMUNICATIONS TECHNOLOGY. 2010 43(3). TP301.
Liu Shujing, Luo Haiyong, Zhao Fang, Zhou Zhou, Liu Shaoshuai. 2010. JOURNAL OF COMPUTER RESEARCH AND DEVELOPMENT. 2010 47(z2). TP391.
J. Beutel. 1999. Geolocation in a PicoRadio Environment. M S Thesis. ETH Zurich Electronics Laboratory.
Meguerdichian S, Slijepcevic S, Karayan V, Potkonjak M. 2001. Localized algorithms in wireless ad-hoc networks: Location discovery and sensor exposure. Vaidya NH, ed. Proc. of the ACM Int’l Symp. On Mobile Ad Hoc Networking and Computing(MobiHOC). New York: ACM Press, 106-116.
Li H, Almeida L, Wang Z, et al. 2006. Relative positions within small teams of mobile units[A]. International Conference on Mobile Ad-hoc and Sensor Network[C], 1-9.
Nasipuri A, Najjar R E. 2006. Experimental evaluation of an angle based indoor location system[A]. Proceedings of the 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks[C], 1-9.
J Caffery. 2000. A new approach to the geometry of TOA location[A]. J Winters. IEEE VTS-FALL VTC2000[C]. Boston: IEEE Press, 1943-1949.
Sallai J, Balogh G, Maroti M, et al. 2004. Acoustic Ranging in Resource Constrained Sensor
Networks[R]. Technical Report ISIS-04-504, Institute for software Integrated Systems. Lewis Girod, Deborah Estrin. 2001. Robust range estimation using acoustic and multimodal sensing. Intelligent Robots and systems, 2001. Proceeding. 2001. IEEE/RSJ International Conference, Vol. 3: 1312-1320.
Steggles P, Ward A. 2001. Webster P. The Anatomy of a Context-Aware Application, Wireless Networks, Vol. 8: 187-197.
Nicolescu D, Nath B. 2001. Ad-Hoc positioning systems(APS). In: Proc. of the 2001 IEEE Global Telecommunications Conf. San Antonio: IEEE Communications Society. Vol.5. 2926.2931.
Langendoen K, Reijers N. 2003. Distributed localization in wireless sensor network: a quantitative comparison [J]. Computer Networks, 43(4): 499-518.
Andreas Savvides, Chih-Chieh Han, Mani B. Strivastava. 2001. Dynamic fine-grained localization in Ad-Hoc networks of sensors. Proceedings of the Seventh Annual ACM/IEEE International Conference on Mobile Computing and Networking(MobiCom 2001), Rome: ACM. Shi Qinqin, Huo Hong. 2008.“Using steepest descent method to improve node localization accuracy of maximum likelihood estimation”, Application Research of Computers, Vol'25 No.7, Ju1.
Lu Rui, Yang Xianhui. 2008.“Reduction of wireless sensor node localization errors”, Journal of Tsinghua Univ(Sci&Tech), V01.48.
Zhao Fengzhi. 2000. Numerical Optimization of Quadratic Approximation, Science Press, Beijing.
David Kincaid, Ward Cheney. 2005. Mathematics of Scientific Computing (third edition), China Machine Press, Beijing.
Whitehouse K, Culler D. 2002. Calibration aS p~ameter estimation in sensor networks, Proe of the 1st ACM International Workshop on WSN and Application, GA: ACM Press, Atlanta , 59-67.
Shi Y, Eberhart R C. 1998. A modified particle swarm optimizer. In: Proc. Of the IEEE CEC. Shi Y, Eberhart R C. 2001. Fuzzy adaptive particle swarm optimization. In: Proc. Of the IEEE CEC.
Clerc M, Kennedy J. 2002. The particle swarm: explosion, stability, and convergence in a multidimensional complex space.IEEE Trans. Evolut.Comput.
Xu Kaixin, HONG Xiaoyan, GERLAM. 2002. An Ad Hoc network with mobile backbones[C]. IEEE International Conference on Communication.
Anthony Carlisle and Gerry Dozier. 2001. An off-the-shelf pso. In: Proceedings of theWorkshop onParticle Swarm Optimization, Purdue School of Engineering and Technology, Indianapolis, USA.
Business Week. 21 ideas for the 21st century. Business Week. pp.78-167, Aug30, 1999.
Haiqing Jiang, Renzhi Cao, Xingfu Wang. 2009. Apply Modified Method of Nonlinear Optimization to Improve Localization accuracy in WSN. The 5th International Conference on Wireless Communications, Networking and Mobile Computing, ISBN: 978-1-4244-3693-4.
TA Alhmiedat, SH Yang. 2007. A Survey: Localization and Tracking Mobile Targets through Wireless Sensors Network. PGnet,ISBN 1-9025-6016-7.
B. H. Wellenhoff, H. Lichtenegger and J. Collins. 1997. Global Positioning System: Theory and Practice: Springer Verlag.
A. Savvides, C. Han and M. B. Srivastava. 2001. Dynamic Fine-Grained Localization in Ad-Hoc Networks of Sensors. Proceedings of ACM MobiCom.
P. Bahl and V. N. Padmanabhan. 2000. RADAR: An In-Building RF-Based User Location and Tracking System. Proceedings of IEEE INFOCOM.
D. Niculescu and B. Nath. 2003. Ad Hoc Positioning System (APS) using AOA. Proceedings of IEEE INFOCOM, 2003.
SHI Qin-qin, HUO Hong. 2008.“Using steepest descent method to improve node localization accuracy of maximum likelihood estimation”,Application Research of Computers, Vol'25 No.7.
Kennedy J, Eberhart R C,Shi Y. 2001. Swarm Intelligence. San Francisco: Morgan Kaufman Publishers.
C Savarese, JM Rabaey,J Beutel. 2001. ICASSP IEEE INT CONF ACOUST SPEECH SIGNAL PROCESS PROC 4, 2037-2040.
Nissanka B. Priyantha, Hari Balakrishnan, Erik Demaine, and Seth Teller. 2003. Conference On Embedded Networked Sensor Systems. ISBN:1-58113-707-9.
Camillo Gentile. 2006. Distributed Sensor Location through Linear Programming with Triangle Inequality Constraints. IEEE International Conference on Communications, v 9, p 4020-4027. ISSN: 05361486
Hady S. AbdelSalam,Stephan Olariu. 2009. HexNet: Hexagon-Based Localization Technique For Wireless Sensor Networks. 7th Annual IEEE International Conference on Pervasive Computing and Communications, PerCom 2009.
Antonio Abramo, Franco Blanchini, Luca Geretti, and Carlo Savorgnan. 2008. A Mixed Convex/Nonconvex Distributed Localization Approach for the Deployment of Indoor Positioning Services. IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 7.
Radu Stoleru and John A. Stankovic. 2004. Probability Grid: A Location Estimation Scheme for Wireless Sensor Networks. 2004 First Annual IEEE Communications Society Conference on Sensor and Ad Hoc Communications and Networks, IEEE SECON 2004,ISBN-10: 078038796.
Ameer Ahmed Abbasi, Mohamed Younis. 2007. A survey on clustering algorithms for wireless sensor networks. Computer Communications 30 (2007) 2826–2841
Hongyi Wu, Member, IEEE, Chong Wang, Student Member, IEEE, and Nian-Feng Tzeng, Senior Member, IEEE. 2005. Novel Self-Configurable Positioning Technique for Multihop Wireless Networks. IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 13, NO. 3.
Adel Youssef and Ashok Agrawala,Mohamed Younis. 2005. Accurate Anchor-Free Node Localization in Wireless Sensor Networks. 24th IEEE International Performance, Computing, and Communications Conference, IPCCC.
Wang Shanshan, Yin Jianping, Cai Zhiping, Zhang Guomin. 2008, JOURNAL OF COMPUTER RESEARCH AND DEVELOPMENT. 2008 45(z1). TP393.
LIU Guang-yi, YU Hong-yi, PI Xing-yu, ZHANG Jian. 2010. COMMUNICATIONS TECHNOLOGY. 2010 43(3). TP301.
Liu Shujing, Luo Haiyong, Zhao Fang, Zhou Zhou, Liu Shaoshuai. 2010. JOURNAL OF COMPUTER RESEARCH AND DEVELOPMENT. 2010 47(z2). TP391.
J. Beutel. 1999. Geolocation in a PicoRadio Environment. M S Thesis. ETH Zurich Electronics Laboratory.
Meguerdichian S, Slijepcevic S, Karayan V, Potkonjak M. 2001. Localized algorithms in wireless ad-hoc networks: Location discovery and sensor exposure. Vaidya NH, ed. Proc. of the ACM Int’l Symp. On Mobile Ad Hoc Networking and Computing(MobiHOC). New York: ACM Press, 106-116.
Li H, Almeida L, Wang Z, et al. 2006. Relative positions within small teams of mobile units[A]. International Conference on Mobile Ad-hoc and Sensor Network[C], 1-9.
Nasipuri A, Najjar R E. 2006. Experimental evaluation of an angle based indoor location system[A]. Proceedings of the 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks[C], 1-9.
J Caffery. 2000. A new approach to the geometry of TOA location[A]. J Winters. IEEE VTS-FALL VTC2000[C]. Boston: IEEE Press, 1943-1949.
Sallai J, Balogh G, Maroti M, et al. 2004. Acoustic Ranging in Resource Constrained Sensor
Networks[R]. Technical Report ISIS-04-504, Institute for software Integrated Systems. Lewis Girod, Deborah Estrin. 2001. Robust range estimation using acoustic and multimodal sensing. Intelligent Robots and systems, 2001. Proceeding. 2001. IEEE/RSJ International Conference, Vol. 3: 1312-1320.
Steggles P, Ward A. 2001. Webster P. The Anatomy of a Context-Aware Application, Wireless Networks, Vol. 8: 187-197.
Nicolescu D, Nath B. 2001. Ad-Hoc positioning systems(APS). In: Proc. of the 2001 IEEE Global Telecommunications Conf. San Antonio: IEEE Communications Society. Vol.5. 2926.2931.
Langendoen K, Reijers N. 2003. Distributed localization in wireless sensor network: a quantitative comparison [J]. Computer Networks, 43(4): 499-518.
Andreas Savvides, Chih-Chieh Han, Mani B. Strivastava. 2001. Dynamic fine-grained localization in Ad-Hoc networks of sensors. Proceedings of the Seventh Annual ACM/IEEE International Conference on Mobile Computing and Networking(MobiCom 2001), Rome: ACM. Shi Qinqin, Huo Hong. 2008.“Using steepest descent method to improve node localization accuracy of maximum likelihood estimation”, Application Research of Computers, Vol'25 No.7, Ju1.
Lu Rui, Yang Xianhui. 2008.“Reduction of wireless sensor node localization errors”, Journal of Tsinghua Univ(Sci&Tech), V01.48.
Zhao Fengzhi. 2000. Numerical Optimization of Quadratic Approximation, Science Press, Beijing.
David Kincaid, Ward Cheney. 2005. Mathematics of Scientific Computing (third edition), China Machine Press, Beijing.
Whitehouse K, Culler D. 2002. Calibration aS p~ameter estimation in sensor networks, Proe of the 1st ACM International Workshop on WSN and Application, GA: ACM Press, Atlanta , 59-67.
Shi Y, Eberhart R C. 1998. A modified particle swarm optimizer. In: Proc. Of the IEEE CEC. Shi Y, Eberhart R C. 2001. Fuzzy adaptive particle swarm optimization. In: Proc. Of the IEEE CEC.
Clerc M, Kennedy J. 2002. The particle swarm: explosion, stability, and convergence in a multidimensional complex space.IEEE Trans. Evolut.Comput.
Xu Kaixin, HONG Xiaoyan, GERLAM. 2002. An Ad Hoc network with mobile backbones[C]. IEEE International Conference on Communication.
Anthony Carlisle and Gerry Dozier. 2001. An off-the-shelf pso. In: Proceedings of theWorkshop onParticle Swarm Optimization, Purdue School of Engineering and Technology, Indianapolis, USA.