# 臺灣博碩士論文加值系統

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 近年來，無線感測網路在於諸多應用上都具有其優越性。然而，在硬體和環境的限制下，感測器對於能源消耗具有高度限制性。採用資料集縮(data aggregation)能夠有效率地降低資料傳送量，以達到節省能耗的目的。本篇論文研究在感測器具有資料集縮能力之無線感測網路中，使用集縮樹的適當路由分配以完成最大化系統生命週期。我們將問題化為一個數學模式，目的函式為最大化系統生命週期，並採用拉格蘭日鬆馳法獲得近似最佳解。
 In recent years, wireless sensor networks have the advantages in a variety of applications. However, due to the limitations of hardware and the environment, the sensors are highly energy-constrained. By adopting data aggregation, we can effectively reduce the amount of data and thereby save energy consumption.In this thesis, we adopt data aggregation trees to efficiently arrange routing assignments in order to maximize the system lifetime of data-centric WSNs. We model the problem a mathematical formulation, where the objective function is to maximize the system lifetime, and use Lagrangean Relaxation method to derive an optimal solution.
 謝 詞 I論文摘要 IITHESIS ABSTRACT IIITable of Contents IVList of Tables VIList of Figures VIIChapter 1 Introduction 11.1 Background 11.2 Motivation 31.3 Literature Survey 41.3.1 Data Aggregation Tree 41.3.2 Clustering 61.3.3 Genetic Algorithm 7Chapter 2 Problem Formulation 92.1 Problem Description 92.2 Problem Notation (IP) 122.3 Problem Formulation (IP) 14Chapter 3 Solution Approach 173.1 Introduction to Lagrangean Relaxation Method 173.2 Lagrangean Relaxation (LR) 193.4.1 Subproblem 1 (related to decision variable 、 ) 213.4.2 Subproblem 2 (related to decision variable ) 223.4.3 Subproblem 3 (related to decision variable 、 ) 233.4.4 Subproblem 4 (related to decision variable ) 243.3 The Dual Problem and the Subgradient Method (IP) 25Chapter 4 Getting Primal Feasible Solutions 274.1 Lagrangean Relaxation Results 274.2 Getting Primal Feasible Solutions 274.3 Simple Heuristic Algorithms 30Chapter 5 Computational Experiments 315.1 Experiment Environment 315.2 Random Network 335.2.1 Network Topology 335.2.2 Solution Quality 345.3 Grid Network 375.3.1 Network Topology 375.3.2 Solution Quality 385.4 Result Discussion 41Chapter 6 Conclusion and Future Work 436.1 Conclusion 436.2 Future Work 44References 47
 [1] Bhaskar Krishnamachari and Fernando Ord´o˜nez, “Analysis of Energy-Efficient, Fair Routing in Wireless Sensor Networks through Non-linear Optimization”, Workshop on Wireless Ad hoc, Sensor, and Wearable Networks, in IEEE Vehicular Technology Conference, October 2003.[2] K. Kalpakis, K. Dasgupta and P. Namjoshi. “Efficient Algorithms for Maximum Lifetime Data Gathering and Aggregation in Wireless Sensor Networks.” Computer Networks Journal, 42(6):697–716, August 2003.[3] H. O. Tan and I. Korpeoglu, “Power Efficient Data Gathering and Aggregation in Wireless Sensor Networks”, ACM SIGMOD Record, vol. 32, no. 4, pp. 66-71, 2003.[4] B. Krishnamachari, D. Estrin, and S.Wicker, "Modelling Data-Centric Routing in Wireless Sensor Networks." IEEE INFOCOM 2002.[5] M.L. Fisher, “The Lagrangean Relaxation Method for Solving Integer Programming Problems,” Management Science, Volume 27, Number 1, pp. 1-18, January 1981.[6] M.L. Fisher, “An Application Oriented Guide to Lagrangian Relaxation,” Interfaces, Volume 15, Number 2, pp. 10-21, April 1985.[7] A.M. Geoffrion, “Lagrangean Relaxation and its Use in Integer Programming,” Mathematical Programming Study, Volume 2, pp. 82-114, 1974.[8] M.S. Bazaraa, H.D. Sherali, and C.M. Shetty, “Lagrangian Duality and Saddle Point Optimality Conditions”, Nonlinear Programming: Theory and Algorithms, 2nd Edition, pp. 199-242, John Wiley & Sons, Inc, Singapore, 1993.[9] B. Jourdan and Olivier L. de Weck, “Layout Optimization for a Wireless Sensor Network Using a Multi-Objective Genetic Algorithm” IEEE Semiannual Vehicular Technology Conference, Milan, Italy, May 17-19, 2004.[10] James R. Yee and Frank Yeong-Sung Lin, “Routing Algorithms for Circuit Data Networks”, Computer Networks Journal, p185-p208, 1992.[11] W. Heinzelman, A. Chandrakasan and H. Balakrishnan, "Energy-Efficient Communication Protocol for Wireless Microsensor Networks", the 33rd Hawaii International Conference on System Sciences, Jan. 2000.[12] Jamal N. Al-Karaki and Ahmed E. Kamal, "Routing Techniques in Wireless Sensor Networks: A Survey", IEEE Wireless Communication, Dec. 2004.[13] S. Lindsey and C. S. Raghavendra, "PEGASIS: Power-Efficient Gathering in Sensor Information Systems", IEEE Aerospace Conference, March 2002.[14] Hong-Hsu Yen, Frank Yeong-Sung Lin, “Near-optimal tree-based access network design”, Computer Communication 28(2) 236-245, 2005.[15] H.S. Yen, F.Y.S. Lin and S.P. Lin, “Efficient Data-centric Routing in Wireless Sensor Networks”, IEEE ICC, 2005.
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