根據衛福部的報告，在1982年到2016年間，癌症已經成為台灣死亡原因的首位，同時因癌症致死的比例呈現逐年上升的趨勢。強度調控放射線治療(IMRT)是目前治療癌症的主要手段之一，尤其是對於鼻咽癌、消化系統腫瘤和子宮頸癌有顯著的效果。對於確診的癌症患者來說，越能盡早的接受治療，康復的機會就越高。因此高效的病人排程方法能夠提高IMRT的治療和減少病人的等待時間。
本研究提出一個數學模型旨在提高病人排程的效率，減少病人的等待時間。本研究分為兩階段。第一階段是建立線上隨機的數學模型來改善醫院當前的排程方法，在本階段，我們考慮未來的治療排程需求來減少病人的等待時間。第二階段是發展出基因驗算法來解決該數學模型。
本研究還考慮了現實醫院的特點，並且適應從醫院收集到的數據對提出的數學模型的效度進行評估。本研究的結果可以為改善IMRT治療排程提出建議，並且該數學模型能為其他放射線治療排程作為參考。

According to Ministry of Health and Welfare Address of Taiwan, cancer has become the highest death rates among all causes of death in Taiwan from 1982 to 2016. And the death rate of cancer shows a steady growth every year. The Intensive-Modulated Radiation Therapy (IMRT) is one of the most important cancer’s radiotherapies, especially for Nasopharyngeal cancers, Digestive system cancers and Cervical cancers. It is important for cancer patients that they can receive the treatment as soon as possible while they were diagnosed with cancers. Therefore, the effective patient scheduling model can improve the IMRT treatment and reduce the patients’ waiting time.
This study proposed a mathematical model to improve patient scheduling efficiency. The research was divided into two stages. In the first phase, the mathematical model with online stochastic algorithm was proposed to improve the current scheduling system. In the phase, we considered impact of the future treatment requirements on scheduling to reduce patients’ waiting time. In the second phase, a genetic algorithm was proposed to solve the online stochastic scheduling problem.
This research took into account the practical characteristics in actual medical procedures. The mathematical model was validated in a specific case, but the same method can be applied in other radiotherapy scheduling.

摘要 I
Abstract II
致謝 III
Contents IV
List of Figures VI
List of Tables VIII
Chapter 1: Introduction 1
1.1 Background 1
1.2 Motivation 2
1.3 Organization of Thesis 3
Chapter 2: Literature Review 5
2.1 Patients Scheduling 5
2.1.1 Offline Scheduling 5
2.1.2 Online Scheduling 6
2.2 Radiotherapy Scheduling 7
2.2.1 Online Stochastic (OS) Scheduling for Radiotherapy 8
2.3 Genetic Algorithm (GA) 9
Chapter 3: Problem Definition 12
3.1 Problem Statement 12
3.1.1 Example Illustration 15
3.1.2 Uncertainty 19
3.2 Assumption and Notation 20
3.3 Problem Formulation 22
3.4 Model Validation 26
Chapter4: Methodology 28
4.1 Adaptive Genetic Algorithm 28
4.1.1 Encoding and Decoding 30
4.1.2 Initial Population 31
4.1.3 Evaluation of Fitness Value (FV) 31
4.1.4 Selection 32
4.1.5 Crossover 32
4.1.6 Mutation 33
4.1.7 Repair Mechanism 34
4.1.8 Local Search 35
4.1.9 Generation Replacement 36
4.1.10 Fuzzy Logic Control 37
4.2 Generation of Scenario 41
Chapter 5: Computational Study 45
5.1 Scenario Illustration 45
5.2 Comparison Results of LINGO and AGA 46
5.3 Comparison Results of Different Types GA 48
5.3.1 Objective Value Comparison 50
5.3.2 Runtime Comparison 52
5.3.3 Convergence Condition Comparison 53
5.4 Comparison Results of Current and Online Stochastic Scheduling 55
Chapter 6: Conclusion 58
Reference 60
Appendix 64
Appendix A: The data of the 25 scenarios 64
Appendix B: The data of the patient 68

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