簡易檢索 / 詳目顯示

回結果列表
研究生： 許愷宸
Hsu, Kai-Chen
論文名稱： 應用班德氏分解法於隨機混整數規劃
Benders decompositions in random-coefficients and mixed-integer programming
指導教授： 李雨青
Lee, Yu-Ching
口試委員: 陳勝一
Chen, Shen-I
朱建達
Zhu, Jian-Da
學位類別： 碩士
Master
系所名稱： 工學院 - 工業工程與工程管理學系
Department of Industrial Engineering and Engineering Management
論文出版年： 2019
畢業學年度： 107
語文別： 中文
論文頁數： 47
中文關鍵詞： 班德氏分解 、大規模最佳化 、混整數規劃 、典型BLP模型 、均衡約束數學規劃 、隨機係數混整數逆優化 、大規模限制式問題
外文關鍵詞： Benders decomposition, large scale optimization, mixed-integer programming, The BLP-type model, MPEC, random-coefficients and mixed-integer inverse optimization, large scale constraints problem
相關次數： 點閱：4  下載：0 
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報

    • 班德氏分解是一種將原問題分解為主問題與子問題的方法，可以應用於大規模最優化、混整數規劃、隨機最優化等...問題中。典型BLP模型是一種可以預測消費者對產品喜好的效用函數。現在我們擁有一個透過均衡約束數學規劃將典型BLP離散選擇模型建構為混整數規劃的逆優化問題，由於這個模型的目的在於分析2001-2015 UK汽車市場的消費者喜好，模型會隨著消費者人數與產品數量被建構成一個大規模限制式問題。我們將在此研究中提出如何透過班德氏分解法去分解此問題。

    Benders decomposition partitions original problem into master problem and subproblem. It can be applied to large scale optimization problem, mixed-integer programming, stochastic optimization, etc. The BLP type model is a utility function to predict consumer preferences for products. We change BLP-type discrete choice model into random-coefficients and mix-integer inverse optimization via mathematical programming with equilibrium constraints. The purpose of this model is to analyze consumer preferences of the UK vehicle market from 2001 to 2015. The model is constructed to a large scale constraints problem due to a large number of customers and products. In this study, the proposed algorithm provides a way of applying the Benders decomposition to solve this problem.

    摘要 目錄 第一章 緒論-------------------------1 第二章 文獻回顧-------------------------2 第三章 原問題-------------------------9 第四章 方法-------------------------14 第五章 數學證明-------------------------39 第六章 結論-------------------------44 Reference-------------------------46

    1. BARR, Donald R.; SHERRILL, E. Todd. Mean and variance of truncated normal distributions. The American Statistician, 1999, 53.4: 357-361.
    2. BENDERS, Jacobus Franciscus. Partitioning procedures for solving mixed-variables programming problems. Numerische mathematik, 1962, 4.1: 238-252.
    3. BERRY, Steven; LEVINSOHN, James; PAKES, Ariel. Automobile prices in market equilibrium. Econometrica: Journal of the Econometric Society, 1995, 841-890
    4. BERRY, Steven; PAKES, Ariel. The pure characteristics demand model. International Economic Review, 2007, 48.4: 1193-1225.
    5. CHU, Yingyi; XIA, Quanshi. Generating benders cuts for a general class of integer programming problems. In: International Conference on Integration of Artificial Intelligence (AI) and Operations Research (OR) Techniques in Constraint Programming. Springer, Berlin, Heidelberg, 2004. p. 127-141.
    6. CHOPIN, Nicolas. Fast simulation of truncated Gaussian distributions. Statistics and Computing, 2011, 21.2: 275-288.
    7. FLOUDAS, Christodoulos A. Nonlinear and mixed-integer optimization: fundamentals and applications. Oxford University Press, 1995.
    8. GEOFFRION, Arthur M. Generalized benders decomposition. Journal of optimization theory and applications, 1972, 10.4: 237-260.
    9. GREENBERG, Harold. Integer programming. Academic Press, 1971.
    10. HOEFFDING, Wassily. A class of statistics with asymptotically normal distribution. In: Breakthroughs in Statistics. Springer, New York, NY, 1992. p. 308-334.
    11. HOGG, Robert V.; MCKEAN, Joseph; CRAIG, Allen T. Introduction to mathematical statistics. Pearson Education, 2005.
    12. TASKIN,Z.Caner. Benders decomposition. Encyclopedia of Operations Research and Management Science. Wiley, New York, 2010, 1-15.
    13. KALVELAGEN, Erwin. Benders decomposition with GAMS. Amsterdam Optimization Modeling Group: Washington, DC, USA, 2002.
    14. KALVELAGEN, Erwin. Benders decomposition for stochastic programming with GAMS. 2003.
    15. KALVELAGEN, Erwin. Two-stage stochastic linear programming with GAMS. GAMS Corporation, 2003.
    16. LUO, Zhi-Quan; PANG, Jong-Shi; RALPH, Daniel. Mathematical programs with equilibrium constraints. Cambridge University Press, 1996.
    17. ROSENBLATT, Murray. A central limit theorem and a strong mixing condition. Proceedings of the National Academy of Sciences of the United States of America, 1956, 42.1: 43.
    18. ROY, Dilip. The discrete normal distribution. Communications in Statistics-theory and Methods, 2003, 32.10: 1871-1883.
    19. SAUNDERS, Michael A.; MURRAY, Walter; GILL, Philip E. MINOS: A Solver for Large-Scale Nonlinear Optimization Problems. 2002.
    20. SCHRIJVER, Alexander. Theory of linear and integer programming. John Wiley ; Sons, 1998.
    21. WOLSEY, Laurence A.; NEMHAUSER, George L. Integer and combinatorial optimization. John Wiley ; Sons, 2014.

    QR CODE