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研究生:許政天
研究生(外文):Cheng-Tien Hsu
論文名稱:混合整數非線性規劃問題的求解方法
論文名稱(外文):A Global Optimization Scheme for Mixed-Integer Nonlinear Programming Problems
指導教授:陳奇中陳奇中引用關係
指導教授(外文):Chyi-Tsong Chen
學位類別:碩士
校院名稱:逢甲大學
系所名稱:化學工程學所
學門:工程學門
學類:化學工程學類
論文種類:學術論文
論文出版年:2005
畢業學年度:93
語文別:中文
論文頁數:78
中文關鍵詞:混合整數非線性規劃最佳化最適化
外文關鍵詞:nlpMixed-Integeroptimizationminlp
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對於一般的化工程序設計,限於產品規格的關係,常存在著不連續的變數,因此在做最適化設計時,也就產生了混合整數(Mixed Integer)非線性規劃的問題。而在對混和整數的處理上,傳統的模擬退火技術,並無特定針對不連續變數進行選取,而是加上新的限制條件,也因此造成限制條件處理的困難。本研究是以高效模擬退火技術,結合Sobol系統化搜尋法、訊息理論,以及混沌搜索與一般化的可行點策略,來處理含混合整數非線性規劃的最適化問題。在解題方面,我們採取兩步驟的解題策略。在第一步驟,我們透過高效模擬退火技術來找出離散變數解;而在第二步驟,我們再使用我們已開發完成的,結合Sobol系統化搜尋法、訊息理論,混沌搜索與及一般化的可行點策略的求解策略,來找出問題的全局最佳解。為驗證本研究所提出之最適化策略的優越性,吾人列舉數個混合整數非線性規劃問題進行模擬測試,並與傳統隨機法與及僅使用訊息理論做比較。最後,將此演算法實際應用於具混合整數非線性限制條件與含動態(dynamic)限制條件之化工程序上。而從模擬的結果顯示,無論是在解答品質及運算效率上,本文所提出之全局最適化策略明顯地較文獻中的方法更具優勢,因此可為解決全局最適化設計問題提供另一可行且更具效率的新途徑。
This thesis aims at the development of a global optimization algorithm for the solution of mixed-integer nonlinear programming (MINLP) problems. A novel two-stage global optimization scheme is proposed. In the first stage, the modified Simulated Annealing (SA) algorithm is used to allocate the exact values of the discrete variables, while in the second stage the global optimal solution is obtained through making use of the information theory, a chaotic algorithm and a feasible point strategy. The applicability and effectiveness of the proposed global optimization scheme have been tested with some typical MINLP problems and extensive comparisons with existing SA and/or information theory-based algorithms have also performed in this work. Simulation results reveal that, due to the advantages of the chaotic algorithm and the two-stage solution approach, the proposed global optimization scheme is more efficient and outperforms the conventional SA and/or information theory-based algorithms. To extend the proposed global optimization scheme to the solution of the dynamic MINLP problems, we introduce the orthogonal collocation strategy for converting the original dynamic problem into a conventional MINLP problem. With this conversion, each of the dynamical constraint is reformulated into a set of equivalent discrete constraint forms with decision variables being at the pre-specified collocations points. This effort leads the proposed two-stage global optimization scheme directly applicable to the solution of dynamic MINLP problem and makes the solution procedure quite easy. For demonstration, we applied the solution scheme to solve several optimal control problems of dynamic chemical processes having simultaneously the continuous and discrete variables. Extensive simulation results corroborate again the effectiveness and advantage of the proposed global optimization schemes for the solution of MINLP problems.
中文摘要
英文摘要
目錄
圖、表目錄
第一章 緒論
1-1 前言
1-2 混和整數的非線性規劃問題
1-3 研究動機
1-4 組織章節
第二章 改良式高效模擬退火策略
2-1 前言
2-2高效模擬退火理論基礎
2-3改良式模擬退火之建立
2-4範例證明與討論
第三章 兩段式策略求解技術
3-1 前言
3-2基於訊息理論之全局最適化策略的基本架構與理論基礎
3-3 結合高效模擬退火策略的兩段式解法
3-4 範例證明與討論
第四章 應用Collocation技術的最適化演算法
4-1 前言
4-2 Collocation基本架構之確立
4-3含動態限制條件的最適化問題
第五章 結論與未來展望
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