近年來由於車子數量迅速地增加，各個城市面臨嚴重的交通擁擠問題。交通號誌設定問題主要是研究如何設定各個路口上的交通號誌使得車子的全部等待時間為最少。我們使用一個簡單的圖形模型來表示城市的交通網路，並且提出和分析交通號誌設定問題在此模型上的一些性質。首先我們利用這些性質提出了一個分支界定演算法(the branch and bound algorithm)來求得交通號誌設定問題的最佳解。另外，我們也使用了基因演算法、粒子族群最佳化演算法以及螞蟻演算法在此模型中找到近似最佳解。在此圖形模型中，我們還增加車子轉彎的假設條件讓此模型更現實化。在實驗中，藉由比較這些演算法對於交通號誌設定問題的影響，結果顯示出基因演算法是一個好的策略在我們的模型中來求得較好的解。最後，我們也轉換台灣高雄市的部份地圖在我們的圖形模型中並且測試比較各個演算法。

As the number of vehicles increases rapidly, traffic congestion has become a serious problem in a city. Over the past years, a considerable number of studies have been made on traffic light setting. The traffic light setting problem is to investigate how to set the given traffic lights such that the total waiting time of vehicles on the roads is minimized. In this thesis, we use a graph model to represent the traffic network. On this model, some characteristics of the setting problem can be presented and analyzed. We first devise a branch and bound algorithm for obtaining the optimal solution of the traffic light setting problem. In addition, the genetic algorithm (GA), the particle swarm optimization (PSO) and the ant colony optimization (ACO) algorithm are also adopted to get the near optimal solution. Then, to extend this model, we add the assumption that each vehicle can change its direction. By comparing the results of various algorithms, we can study the impact of these algorithms on the traffic light setting problem. In our experiments, we also transform the map of Kaohsiung city into our graph model and test each algorithm on this graph.

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0
Chapter 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Chapter 2. Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Related Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 The Branch and Bound Strategy . . . . . . . . . . . . . . . . . . . . 6
2.3 Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 Particle Swarm Optimization . . . . . . . . . . . . . . . . . . . . . . 11
2.5 Ant Colony Optimization Algorithm . . . . . . . . . . . . . . . . . . 13
Chapter 3. The Traffic Graph Model and Its Properties . . . . . . . 17
3.1 The Traffic Graph Model . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 The Stable Traffic Graph Model . . . . . . . . . . . . . . . . . . . . . 20
3.3 The Definition of Our Problem . . . . . . . . . . . . . . . . . . . . . 22
Chapter 4. Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.1 Input Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.2 The Branch and Bound Method . . . . . . . . . . . . . . . . . . . . . 26
4.3 The Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.4 The Particle Swarm Optimization Method . . . . . . . . . . . . . . . 31
4.5 The Ant Colony Optimization Algorithm . . . . . . . . . . . . . . . . 34
Page
Chapter 5. The Extended Traffic Graph Model . . . . . . . . . . . . . 37
Chapter 6. Experimental Results and Discussion . . . . . . . . . . . . 39
Chapter 7. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

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