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系統識別號 U0026-0812200910400864
論文名稱(中文) 公路縱坡度與附屬設施配置最佳化模式
論文名稱(英文) none
校院名稱 成功大學
系所名稱(中) 土木工程學系碩博士班
系所名稱(英) Department of Civil Engineering
學年度 91
學期 2
出版年 92
研究生(中文) 黃笙玹
研究生(英文) Sheng-Xuan Huang
學號 n6690426
學位類別 碩士
語文別 中文
論文頁數 97頁
口試委員 口試委員-許瑞麟
口試委員-陳春益
口試委員-鄭瑞富
指導教授-李宇欣
中文關鍵字 公路縱坡度設計  爬坡車道  隧道  橋樑  最佳化  混合整數規劃  附屬設施 
英文關鍵字 vertical alignment  optimization  mixed integer programming  bridges  tunnels  climbing lanes  auxiliary facilities 
學科別分類
中文摘要 在公路設計時需考慮自然環境、社會狀態、交通量需求、行車安全性、經濟等方面的因素,以決定公路路線位置、幾何形狀與各項結構物或相關設施的配置。其中,幾何線形設計是公路設計的基礎,公路縱坡度設計更是幾何線形設計中重要的一環。公路縱坡度設計時會一併考慮附屬設施的設置,如在坡度陡峭的路段考慮爬坡車道的設置、在地形變化劇烈之路段考慮橋樑或隧道的興建等。然而,傳統上的公路設計較難系統化的考慮附屬設施設置與縱坡度相互之間的影響,往往需要由有經驗的工程師研擬少數幾個可行方案擇優採行。由於設計工作常需要作繁複、大量的計算,消耗大量的時間與人力,所以提昇幾何線形設計的效率與品質,對於整體公路工程建設具有重大的意義。

在過去的文獻中雖有針對考慮某一特定附屬設施所發展的模式,能以成本為考量做出最經濟的縱坡度設計,但這些模式彼此不完全相容,以至於無法同時考慮多種附屬設施,且若每次要考慮新的附屬設施就必須建構新的模式,則研究將變得沒有效率。因此本研究希望可以發展一套模式,此模式能夠加入佈設各種附屬設施的考量,同時考慮公路縱坡度與附屬設施的設置與否,以求得最佳化設計。

本研究利用混合整數規劃的方法,以總成本最小化為目標建構數學模式,所考慮的總成本為各設計樁成本之線性加總,各設計樁的成本包含挖方、填方、棄土、借土、擋土結構、邊坡處理、用地、附屬設施設置等費用。模式中考慮到的限制,除了符合公路設計規範外,尚需讓模式因為選擇佈設某一附屬設施,而使一些特定變數受到特定的限制,因此本研究建立一個選擇的機制來達到此項功能。在求解方面,是以門檻接受法為核心所發展的分層演算法,求解出公路縱坡度與附屬設施設置的最佳化設計。另外為了提高求解的效率,分別針對減少整數變數與減少混合整數問題求解次數,發展了變樁距求解與兩階段求解兩種求解策略。

最後自行以C語言撰寫程式,搭配線性規劃套裝軟體CPLEX 7.0所提供的函式庫,以求解本模式之問題,經由數個測試例驗證本研究的正確性,以及本研究的求解策略確實能大幅改善求解效率。
英文摘要 Many factors have to be taken into consideration to determine the alignment as well as auxiliary facilities of a highway segment. Some of the major factors are environment, situiation, traffic demand, safety, and economy. Geometric alignment is the base of highway design, and vertical alignment in turn plays a major role in geometric alignment. Auxiliary facilities are often deployed at the same time vertical alignments are designed. For example, climbing lanes can be used at places where the grade is steep, or bridges/tunnels can be deployed in a rolling terrain. However, designing the vertical alignment and the various auxiliary facilities at the same time is hard to be done systematically by engineers. Determining the vertical alignment of a highway remains an art and relies mostly on the judgement of experienced engineers. Due to the complexity of the problem, the highway design work often requires significant amount of labor and budget. Moreover, under time and financial pressure, human engineers often select from a handful of feasible designs without searching for the optimal design systematically. It is thus import to improve the efficiency and quality of vertical alignment design.

Literature in the past have proposed various models to optimize the vertical alignment and auxiliary facility concurrently. However, all these models are developed for one single auxiliary facility, and they are not fully compatible with each other. This makes it hard for the user to take multiple auxiliary facilities into consideration. Besides, each additional auxiliary facility will require one new model.

In this research, we develop a mixed integer programming model that simultaneously solves for an optimal highway vertical alignment and auxiliary facility deployment. Important cost items such as construction, cut/fill, earth borrow/dump, slope retaining structure, slope treatment, and land are taken into consideration. The model also accounts for the costs as well as design criteria of multiple auxiliary facilities. A set of variables and constraints built into the model enables it to optimally select from a set of given available auxiliary facilities, determine the location(s) of each facility, and enable/disable code requirements accordingly. The optimization goal is to minimize total cost. The model can be solved with a two-tiered heuristic. We developed two additional heuristics to further improve the efficiency. The variable station spacing heuristic reduces the number of integer variables, and the two stage heuristic seeks to cut down the number of mixed-integer optimization problem solved. The Threshold Accepting heuristic is center to all these models. Besides, we develop two strategies to improve the efficiency in solving.

The heuristics are implemented in the C language. The code calls the CPLEX 7.0 library as the solution engine. Several computational examples are provided to demonstrate the correctness of the model and efficiency of the heuristics.
論文目次 摘 要 I
Abstract III
誌 謝 V
目 錄 VII
表目錄 IX
圖目錄 XI

第一章 緒論1
1.1 研究動機與目的1
1.2 研究範圍與流程1
1.3論文架構2
第二章 文獻回顧3
2.1 公路縱坡度設計相關文獻3
2.1.1 一般公路縱坡度設計相關文獻3
2.1.2 整合附屬設施設置與公路縱坡度設計相關文獻5
2.1.3 小結6
2.2 公路縱坡度設計相關規範7
2.3 公路縱坡度設計基本模式13
2.3.1 模式簡介13
2.3.2 符號定義13
2.3.3 決策變數15
2.3.4 目標函數16
2.3.5 限制式22
2.4 載重車輛速率性能曲線的逼近25
第三章 問題定義27
3.1 公路設計流程27
3.2 公路縱坡度設計28
3.3 問題描述29
3.4 基本假設30
第四章 數學模式構建與求解33
4.1 基本概念33
4.2 符號定義34
4.3 決策變數37
4.4 目標函數38
4.4.1 成本計算方式39
4.4.2 一般路段工程費用函數40
4.4.3 一般路段淨土方量函數40
4.4.4 一般路段用地費用函數42
4.4.5 設置附屬設施的成本43
4.5 選擇機制44
4.6 限制式45
4.6.1 工程費用相關限制式45
4.6.2 土方量相關限制式47
4.6.3 用地相關限制式49
4.6.4 縱坡度線形限制式50
4.6.5 速率相關限制式58
4.6.6 設計高程相關限制式61
4.6.7 附屬設施相關限制式63
4.6.8 非負與整數限制式66
4.7 模式求解68
4.7.1 分層演算法68
4.7.2 變樁距求解70
4.7.3 兩階段求解73
第五章 模式測試75
5.1 單一附屬設施測試75
5.1.1 隧道測試77
5.1.2 爬坡車道測試81
5.2 多種附屬設施測試83
第六章 結論與後續研究87
6.1 結論87
6.2 後續研究88
參考文獻89
附 錄91
自 述97
參考文獻 1.交通部,公路路線設計規範,2001年。

2.李宇欣、伍裕華,整合式公路縱坡度與爬坡車道配置最佳化模式,中國土木水利工程學刊,第十一卷,第三期,第529 - 542頁,1999年。

3.李宇欣、施能豪,公路縱坡度設計之最佳化橋樑與隧道設置模式,中國土木水利工程學刊,第十卷,第二期,第351 - 360頁,1998年。

4.張仕龍,整合式公路縱坡度與車道數設計自動化模式,國立成功大學土木工程研究所碩士論文,2000年。

5.AASHO,"A Policy on Geometric Design of Rural Highways," American Association of State Highway and Officials, Washington, D.C., (1965).

6.Deck, G. and Scheuer, T., "Threshold Accepting: A General Purpose Optimization Algorithm Appearing Superior to Simulated Annealing," Journal of Computational Physics, Vol. 90, pp. 161 - 175(1990).

7.Easa, S. M., "Selection of Roadway Grades that Minimize Earthwork Cost Using Linear Programming," Transportation Research, Part A, Vol. 22, No. 2, pp.121 - 136(1988).

8.Fwa, T. F., "Highway Vertical Alignment Analysis by Dynamic Programmin," Highway Reseach Record 1239, HRB, National Research Council, Washington D.C., pp.1 - 9 (1989).

9.Goh, C. J., Chew, E. P. and Fwa, T. F., "Discrete and Continuous Models for Computation of Optimal Vertical Highway Alignment," Transportation Research, Part B, Vol 22, No. 5, pp. 399 - 409 (1988).

10.Hayman, R. W., "Optimization of Vertical Alignment for Highways Through Mathematical Programming," Highway Reseach Record 306, HRB, National Research Council, Washington, D.C., pp.1 - 9 (1970).

11.Lee, Y. and Cheng, J. F., "Modeling the Highway Vertical Alignment Design Process," Proceedings of XIIIth IRF world meeting(CDROM), Canada (1997).

12.Moreb, A. A., "Linear Programming Model for Finding Optimal Roadway Grades that Minimize Earthwork Cost," European Journal of Operational Research, Vol.93, No.1, pp.148 - 154 (1996).
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