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研究生:林高正
研究生(外文):Lin, Kao-Cheng
論文名稱:網路系統之關鍵聯結與阻撓問題
論文名稱(外文):MOST VITAL EDGES AND INTERDICTION PROBLEMS OF NETWORK SYSTEMS
指導教授:陳茂生陳茂生引用關係
指導教授(外文):Chern, Maw-Sheng
學位類別:博士
校院名稱:國立清華大學
系所名稱:工業工程研究所
學門:工程學門
學類:工業工程學類
論文種類:學術論文
畢業學年度:81
語文別:英文
論文頁數:118
中文關鍵詞:關鍵聯結阻撓問題最小生成樹最小成本流量問題
外文關鍵詞:Most vital edgesInterdiction problemMinimum cost flow
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給一評估網路績效之測度,若某組聯結滿足給定的限制條件,且將它從網
路中移去會使網路之績效降低最多,則該組聯結稱為網路的關鍵聯結。在
網路規劃的實務中,聯結之可用性扮演著重要的角色。關鍵聯結問題之目
的在評估聯結可用性的重要程度。因此,它提供有關網路維護與破壞所需
的資訊。此外,本文也考慮一個更一般化的問題,稱為阻撓問題。該問題
是經由提高網路聯結之權數以降低網路績效。當問題的決策變數為二元變
數時,則稱為二元阻撓問題。換言之,二元阻撓問題之目的在決定應破壞
那些聯結。而當聯結遭破壞時,它的權數將增加一給定數量﹔否則,聯結
的權數維持不變。若所增加的聯結權數為足夠大時,則該問題變成一個關
鍵聯結問題。
Given a network performance measure, the most vital edges
problem is to find a set L* of edges whose removal from the
network results in the greatest decrease of the performance.
Furthermore, L* satisfies a set of specified constraints.
The availability of edges plays a key role in the design of
network systems. The most vital edges problem provides a means
by which the importance of edge''s availability can be
measured. Thus, it can be used in network maintenance and
network interdiction. In addition to the most vital edges
problem, it is natural to consider a generalized problem in
which the performance of a network is reduced via increasing
(or decreasing) the edge weights. Such a problem is called an
interdiction problem. When the decision variables of an
interdiction problem are binary, it is called a binary
interdiction problem. In other words, the purpose of a binary
interdiction problem is to determine which edges should be
interdicted. Moreover, when an edge is interdicted, its weight
is increased (or decreased) by a specified value. If the
specified values are sufficiently large, then the problem is
reduced to the most vital edges problem.
第一章 導論
第二章 最小生成樹之關鍵聯結
第三章 最經濟路徑問題之單一關鍵聯結的參數分析
第四章 模糊最短路徑問題之單一關鍵聯結
第五章 線性規劃之阻撓問題
第六章 流量網路之阻撓問題
第七章 網路關鍵聯結問題的演算複雜度
第八章 結論與後續研究
1. INTRODUCTION
1.1. The Most Vital Edges Problem
1.2. The Interdiction Problem
1.3. Theory of Computational Complexity
1.4. The Related Network Problem-A Review
1.5. The Proposed Problems-An Overview
2. FINDING A SET OF MOST VITAL EDGES IN THE MINIMUM SPANNING TREE PROBLEM
2.1. Introduction
2.2. Finding a Set of Most Vital Edges
2.3. Numerical Examples
2.4. Conclusions
3. THE SINGLE MOST VITAL EDGE IN THE MOST ECONOMICAL PATH PROBLEM-A PARAMETRIC ANALYSIS
3.1. Introduction
3.2. The Shortest-Path Simplex Method
3.3. The Single Most Vital Edge-A Parametric Analysis
3.4. A Numerical Example
3.5. Conclusions
4. THE SINGLE MOST VITAL EDGE IN THE SHORTEST PATH PROBLEM WITH FUZZY EDGE LENGTHS
4.1. Introduction
4.2. Linear Programs with Fuzzy Cost Coefficient
4.3. The Shortest Path Problem with Fuzzy Edge Lengths-A Fuzzy Linear Programming Approach
4.4. Finding the Single Most Vital Edge
4.5. A Numerical Example and Computational Results
4.6. Conclusions
5. INTERDICTING THE ACTIVITIES OF A LLINEAR PROGRAM
5.1. Introduction
5.2. Interdicting the Activities of a Linear Program-A Parametric Analysis
5.3. Economic Interpretations
5.4. Binary Interdiction Problems
5.5. Conclusions
6. INTERDICTING FLOW NETWORKS
6.1. Introduction
6.2. Interdictiog Flow Networks
6.3. An Algorithm for the Parametric Minimum Cost Flow Problem
6.4. 0-1 Mixed Intege Programming Formulation of the Most vital Edges Problem for Flow Networks
6.5. Conclusions
7.COMPUTATIONAL COMPLEXITY OF THE MOST VITAL EDGES PROBLEMS
7.1. Introduction
7.2. Computational Complexity of Finding a Set of Most Vital Edges in the Minimum spanning Tree Problem
7.3. Computational Complexity of Finding a Set of Most Vital Edges in the Maximum Flw Problem
7.4. Computational Complexity of Finding a Set of Most vital Edges in the Assignment Problem
7.5. Conclusions
8. CONCLUSIONS AND TOPICS FOR FURTHER RESEARCH
8.1. Conclusions
8.2. Topics for further Research
目錄
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摘要
英文摘要
參考書目
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