近年來，市場的快速變遷與激烈的競爭，專案管理變得日漸重要。專案排程作為專案管理的重要部分，具有網路結構特點，各個專案成員係分布在網路的各個節點上，負責整個專案的一項或多項工作，且擁有各自的資源或是共享某些公共資源，而專案成員的共同目標即是使專案達到最佳化運籌，藉此快速響應市場以獲得最佳經濟效益。其中，最具代表性的一類經典問題─資源限制下專案排程問題(Resource-Constrained Project Scheduling Problem, RCPSP)也在近年逐漸成為了研究的熱點，其係專注於研究如何在滿足專案中各活動時序限制和資源限制的條件之下，適當地安排出所有活動的開工期和完工期，以達到訂定之最佳目標(如，工期最短、成本最小等)。該問題也已被證明是為一NP-hard問題。

本研究主要目的係提出了一種新的簡化群體最佳化算法(SSO)，用以解決經典的資源限制之專案排程問題(RCPSP)。在這項研究中，我們提出了一個基於混合式的優先權規則(CPR)之啟發式方法來決定演算法的初始群體，藉以綜合運用不同優先權規則在生成排程時的優勢。此外，對於在求解該問題上，進一步採用了過去文獻上，效能良好的雙向對齊技術，同時結合了我們所採用的粒子群雙向搜索策略來提升整體解的品質。最後，我們應用了知名的PSPLIB基準實例資料庫來提供測試結果的數值比較。在與文獻上近年且知名的演算法的相比之下證明了我們所提出的方法在求解RCPSP方面之有效性。

In recent years, with the economic development, project management has become increasingly important. Project scheduling is an important part of project management. It has the characteristics of network structure. Each project member is distributed on each node of the network and responsible for one or more tasks of the entire project and has its own resources or shares some public resources. The common goal of the project members is to quickly respond to the market for obtaining the best economic benefits. Therefore, the Resource-Constrained Project Scheduling Problem (called RCPSP) has become a research hotspot. The scheduling target of RCPSP is to determine the start-up and completion of all activities subjected to precedence and resources constraints for achieving the best goal. RCPSP also has been proved to be NP-hard problem.

This research presents a novel simplified swarm optimization algorithm (SSO) to solve the classical resource-constrained project scheduling problem (RCPSP). In our method, a combine priority-rule-based (CPR) heuristic is proposed to initialize the population for obtaining promising activity lists. Moreover, the double justification (DJ) which has been proven to be effective in the literature will be combined with the bidirectional search strategy to enhance the quality of solutions. Numerical testing results are provided by using three sets of PSPLIB benchmark instances. The comparisons to the existing algorithms demonstrate the effectiveness of the proposed SSO in solving the RCPSP.

LIST OF CONTENTS
中文摘要 I
ABSTRACT II
LIST OF CONTENTS III
LIST OF TABLES V
LIST OF FIGURES VI
CHAPTER 1 INTRODUCTION 1
1.1 BACKGROUND AND MOTIVATION 1
1.2 PROBLEM DESCRIPTION 2
1.3 SCOPE OF THIS WORK 2
1.4 OUTLINE 3
CHAPTER 2 LITERATURE REVIEW 4
2.1 SCHEDULING 4
2.2 CLASSIFICATION OF SCHEDULING PROBLEMS 4
2.3 RESOURCE-CONSTRAINED PROJECT SCHEDULING PROBLEM (RCPSP) 5
2.3.1 Notations 5
2.3.2 Mathematical formulation of RCPSP 6
2.4 SOLUTION APPROACHES 7
2.5 VISUAL REPRESENTATIONS OF PROJECT NETWORK 8
2.5.1 Activity on the Node diagram (AON) 8
2.5.2 Gantt charts 9
CHAPTER 3 METHODOLOGY 10
3.1 NOTATIONS 10
3.2 SIMPLIFIED SWARM OPTIMIZATION (SSO) 11
3.3 SOLUTION REPRESENTATION SCHEME 14
3.4 SCHEDULE GENERATION SCHEME (SGS) 16
3.5 PRIORITY-RULE-BASED (PRB) HEURISTIC 16
3.6 IMPROVEMENT SCHEMES 21
3.6.1 Double Justification (DJ) 21
3.6.2 Forward and backward scheduling 23
3.7 THE PROPOSED SSO ALGORITHM 24
CHAPTER 4 EXPERIMENTAL RESULTS 28
4.1 BENCHMARK DATASET 28
4.1.1 Problem File 28
4.1.2 Criterion 30
4.2 PARAMETERS SETTING 31
4.3 IMPROVEMENT SCHEME TEST RESULTS 35
4.4 PRB HEURISTIC TEST RESULTS 37
4.5 COMPARISONS OF SSO WITH OTHER EXISTING ALGORITHMS 40
CHAPTER 5 CONCLUSIONS 42
5.1 DISCUSSIONS AND CONCLUSIONS 42
REFERENCES 43

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