# 臺灣博碩士論文加值系統

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 近年來由於能源的短缺，所以節能的概念越來越受到人們的重視，在本篇論文中，我們主要針對Ad-hoc無線網路節能問題做最佳化的研究和探討。首先，我們根據跨層最佳化的概念考慮點對點流量分配、排程與功率控制等問題來制定節能問題，並將它用數學模型來表示。接下來，觀察我們所建立的模型，發現我們的問題是一個NP-hard 的混整數非線性規劃問題，所以我們透過重新制定線性化技術 (Reformulation-Linearization Technique) 將非線性項放鬆，並利用增廣拉格朗日演算法(Augmented Lagrange Algorithm)來解決最大最小分數型規畫(Max-Min Fractional Programming)問題，如此一來我們就可以得到放鬆後的最佳解。最後，我們將呈現實驗數據來說明無線節能問題是可以被規畫出來的。
 Recently, due to the shortage of energy, people pay more attention to the concept of energy saving. In this thesis, we focus on the optimization of energy saving problem for the wireless ad-hoc network. First, we consider the end-to-end flow distribution, scheduling, and power control base on the concept of cross-layer optimization to formulate the energy saving problem into mathematical models. Secondly, we observe problem is an NP-hard mixed integer nonlinear programming problems. We employ the “Reformulation Linearization Technique” (RLT) to relax the nonlinear term and employ the “Augmented Lagrange Algorithm” to solve the induced min-max fractional problem. In this way, we can approximate the optimal solution. Finally, our numerical results indicate that the energy saving problem of wireless network can be planned with our proposed model and method.
 1 Introduction 52 System Model and Problem Formulation 82.1 AD-HOC Network System….………………………………………82.2 Network Topology….……………………………............102.3 Constraints…………………………………………………….........112.3.1 Scheduling…………………………………………….........112.3.2 Power Constraints….……………………………………...122.3.3 Half-Duplex Constraints………………………………….122.3.4 Capacity Constraints……………………………………...132.3.5 Flow Conservation……………………………...................142.4 Objective……………………………………………………………152.5 Mathematical Models......................152.6 Analysis of the Mathematical Models.……………………………162.6.1 Capacity Formulas..……………………………………….162.6.2 Fractional Programming………………………………….183 Solution Method 193.1 Linear Relaxation…………………………………………………..193.1.1 Remove “log” Term……………………………………….193.1.2 Reformulation Linear Technique………………………...213.2 Linear Fractional Programming………………………………….233.2.1 Fractional Programming..………………………………..243.2.2 Augmented Lagrange Method for our Models………….263.2.3 Main Flow Chart for the Solution Method………………304 Numerical results 324.1 Parameters…………………………………………….....................324.2 Some Topology Results…………………………………………….335 Conclusion 45Bibliography 46
 [1]J. Y. Lin and R. L. Sheu. “Augmented Lagrange Primal-Dual Approach for Generalized Fractional Programs, Journal of Industrial and Management Optimization.[2]R. Madan, S. Cui, S. Lall, and A. Goldsmith. “Cross-Layer Design for Lifetime Maximization in Interference-Limited Wireless Sensor Networks, IEEE, 2005.[3]L. Bui, A. Ery1lmaz, R. Srikant, and X. Wu. “Joint Asynchronous Congestion Control and Distributed Scheduling for Multi-Hop Wireless Networks, IEEE, 2006.[4]M. L. Sichitiu. “Cross-Layer Scheduling for Power Efficiency in Wireless Sensor Networks, IEEE, 2004.[5]L. Chen, S. H. Low, M. Chiang, and J. C. Doyle. “Cross-Layer Congestion Control, Routing and Scheduling Design in Ad Hoc Wireless Networks, IEEE, 2006.[6]M. Chiang. “To Layer or Not To Layer: Balancing Transport and Physical Layers in Wireless Multihop Networks, IEEE, 2004.[7]M. Chiang, C. W. Tan, D. P. Palomar, D. O'Neill, and D. Julian. “Power Control by Geometric Programming, IEEE Transactions on Wireless Communications, Vol. 6, No. 7, pp. 2640-2651, July, 2007.[8]J. P. Crouzeix, J. A. Ferland, and S. Schaible. “Duality in Generalized Linear Fractional Programming, Mathematical Programming 27(1983), pp. 342-354.[9]J. P. Crouzeix, J. A. Ferland, and S. Schaible. “An Algorithm for Generalized Fractional Programs, Journal of Optimization Theory and Applications: Vol. 47, No. 1, September 1985.[10]B. Johansson, P. Soldati, and M. Johansson. “Mathematical Decomposition Techniques for Distributed Cross-Layer Optimization of Data Networks, IEEE Journal on Selected Areas in Communications, Vol. 24, No. 8, pp. 1535-1547, August 2006.[11]M. Johansson and L. Xiao. “Cross-Layer Optimization of Wireless Networks Using Nonlinear Column Generation, IEEE Transactions on Wireless Communications, Vol.5, No. 2, pp. 435-445, February 2006.[12]S. J. Kim, X. Wang, and M. Madihian. “Cross-Layer Design of Wireless Multihop Backhaul Networks with Multiantenna Beamforming, IEEE Transactions on Mobile Computing, Vol. 6, No. 11, pp. 1259-1269, November 2007.[13]J. Papandriopoulos, S. Dey, and J. Evans. “Optimal and Distributed Protocols for Cross-Layer Design of Physical and Transport Layers in MANETs, IEEE/ACM Transactions on Networking, Vol. 16, No. 6, pp. 1392-1405, December 2008.[14]H.D. Sherali and W.P. Adams. “A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems, Chapter 8. Kluwer Academic Publishers, 1999.[15]Maurice Sion. “On the General Minimax Theorems, Pacific J. Math. , pp. 171-176, 1958.[16]B. Radunovic and J.-Y. Le Boudec. “Optimal Power Control, Scheduling, and Routing in UWB Networks, IEEE Journal on Selected Areas in Communications, Vol. 22, No. 7, pp. 1252-1270, September 2004.[17]Y. Shi, Y. T. Hou, S. Kompella, and H. D. Sherali. “Maximizing Capacity in Multi-Hop Cognitive Radio Networks under the SINR Model, IEEE.
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