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研究生:黃中浩
研究生(外文):Chung-HaoHuang
論文名稱:正向座標法求解交通指派之非線性最佳化模式
論文名稱(外文):Solving Nonlinear Optimization Model of Traffic Assignment by Canonical Coordinates Method
指導教授:林珮珺林珮珺引用關係
指導教授(外文):Pei-Chun Lin
學位類別:碩士
校院名稱:國立成功大學
系所名稱:交通管理學系碩博士班
學門:運輸服務學門
學類:運輸管理學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:87
中文關鍵詞:正向座標法非線性最佳化交通指派
外文關鍵詞:Canonical Coordinates Method (CCM)Nonlinear OptimizationTraffic Assignment
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  本研究沿用Jahn et al. (2005)提出的靜態模式中,受限於容量限制、個別用路人需求下之最小化旅行時間的非線性函數,在顧及使用者的公平性下,針對多起迄對路網進行起迄對推估,整合使用者均衡與系統最佳化的優點,建構出系統總旅行時間最小化受限模式。研究方法則是採用學者Chang and Prabhu (2003)提出的正向座標法(Canonical Coordinates Method, CCM),此創新的演算法能夠在低計算成本下求解非線性最佳化模式,同時維持解的可行性。
  本研究以推估起迄對與路網相關數據輸入所建構的系統總旅行時間最小化受限非線性模式,並且將正向座標法的概念撰寫為實務上可以執行運算的程式進行求解,經由迭代求得最終局部最佳近似解的結果,提供交通指派策略的參考依據,以及歸納路徑導引的建議。
  求解結果分析顯示利用正向座標法的演算法求解交通指派非線性最佳化問題時,除了選擇一個較為適當的移步距離 值進行較有效率的運算之外,如果能夠給予合適起始點,將可以在求得相近近似解的情況下,得到較短的求解時間與較少的迭代次數。如此將能夠同時兼顧求解的精確性與求解效率,讓正向座標法可以更有效的發揮解決交通指派非線性最佳化問題的能力。
  歸納研究結果得到以下結論:決定一個合適的參數設定,讓求得可接受的可行解與求解效率之間取得平衡,將是在利用正向座標演算法求解此類非線性最佳化模式問題時,需要特別注意衡量的課題。同時可以顯示出正向座標法是相當具有潛力的演算法,具有一定的能力可以求解此類交通指派之非線性最佳化模式的問題,可以延伸應用至其他非線性最佳化模式的求解。
  This study follows the Jahn et al. (2005) proposed a static model, which is a nonlinear function to minimize travel time subjecting to restrictions of capacity and the demand of individual passers, and construct the constrained model with the advantages of user equilibrium and system optimization to minimize the total travel time by estimating the origins and destinations for multiple ODs of road network in the fairness of the users. Research methods is to adopt the innovative algorithms “Canonical Coordinates Method (CCM)”, which was proposed by scholar Chang and Prabhu (2003), for solving nonlinear optimization model in a low computational cost while maintaining the solution feasibility.
  This study input the data of estimated ODs and road network to the constrained nonlinear model, which was constructed to minimize the total system travel time, and to written program with the concept of CCM to solve the problem in practice. The results of obtained final local best approximate solution by iteration can be the reference of traffic assignment policy and the summarized recommendations of the Route Guidance.
  The results of solution show that when solving the nonlinear optimization problem of traffic assignment by CCM, in addition to select an appropriate step size for efficient operation, if we can give a suitable initial point, will be able to get a shorter computation time and less number of iterations under similar approximate solution. That will be balance between the solving accuracy and computational efficiency, and the CCM can be more ability to solve the traffic assignment of non-linear optimization problem effectively.
  We get the following conclusions by summarizing the research results: To strike a balance between acceptable feasible solution and solution efficiency by choosing an appropriate parameter settings, will be the important issue for solving such nonlinear optimization model of traffic assignment by CCM. Also, the results can show the CCM is quite promising algorithm with ability to solve the nonlinear optimization model of traffic assignment problem, and can be extended to be applied to other nonlinear optimization model problems.
目錄 I
表目錄 III
圖目錄 IV
第一章、 緒論 1
第一節、 研究背景 1
第二節、 研究動機 2
第三節、 研究目的 3
第四節、 研究流程與架構 4
第二章、 文獻探討 6
第一節、 路徑導引系統及準則 6
2.1.1 路徑導引系統 6
2.1.2 路徑導引準則 7
第二節、 交通指派模式 9
2.2.1 一般演算法的限制 9
2.2.2 系統最佳化與使用者均衡 10
2.2.3 動態與靜態交通指派 11
第三節、 非線性最佳化問題 12
2.3.1 一般問題求解方法 12
2.3.2 正向座標法求解概念 15
第三章、 研究方法 18
第一節、 模式構建 18
第二節、 演算法 20
第四章、 小型模擬路網模式與執行結果 23
第一節、 小型模擬路網模式 23
第二節、 小型模擬路網執行結果 27
4.2.1 第一組起始點迭代求解結果 27
4.2.2 第二組起始點迭代求解結果 31
4.2.3 模擬路網的執行結果分析 35
第五章、 真實路網模式與執行結果 37
第一節、 真實路網模式 37
第二節、 真實路網執行結果 44
5.2.1 迭代求解結果 44
5.2.2 真實路網的結果比較分析 47
第六章、 結論與建議 50
第一節、 結論 50
第二節、 建議 52
參考文獻 54
附錄一、 真實路網路段限制式 58
附錄二、 小型路網迭代數據(第一組起始點)(dt=0.01) 64
附錄三、 小型路網迭代數據(第一組起始點)(dt=0.005) 65
附錄四、 小型路網迭代數據(第一組起始點)(dt=0.001) 66
附錄五、 小型路網迭代數據(第二組起始點)(dt=0.01) 67
附錄六、 小型路網迭代數據(第二組起始點)(dt=0.005) 68
附錄七、 小型路網迭代數據(第二組起始點)(dt=0.001) 69
附錄八、 真實路網迭代數據 (dt=0.001) 70
附錄九、 真實路網迭代數據 (dt=0.0005) 76
附錄十、 真實路網迭代數據 (dt=0.0001) 82
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