臺灣博碩士論文加值系統

本研究考慮了一個並行批量處理機器的問題，以在任意批量、不兼容系列、開始時間窗口的約束和適度決定下達到最小化製造時間。本研究首先通過混合整數程序化模型來格式化問題，並且也提供了所研究問題的下界。但因爲研究問題為NP-Hard且因應實務上須能解決大的問題，本研究亦將發展了一種基於分解的啟發式算法和進化算法，以便在計算時間作為一個側重點時獲得大規模問題的近似最優解。二維節約函數被引入來量化時間和容量空間被浪費的值。對於遺傳算法，我們提出了用於編碼的二維矩陣和一維表示，以及適當的二維交叉和突變以產生後代。此外，此遺傳算法旨在改善基於已開發分解的啟發式算法的解決方案品質，該啟發式被用作已開發遺傳算法的初始解。計算實驗表明，所提出的啟發式算法對於小規模問題的執行表現良好，並且可以在合理的計算時間內有效地處理大規模問題。此外，計算結果還表明，本研究提出的啟發式算法在答案品質 (Solution quality) 方面優於文獻中現有的啟發式算法。

This study considers a parallel batch processing machines problem to minimize the makespan under constraints of arbitrary lot sizes, incompatible families, start time windows, and machine eligibility determination. We first formulate the problem by a mixed-integer programming model and a lower bound for the studied problem is also provided. Due to the NP-hardness of the problem, we then develop a decomposition-based heuristic and an evolutionary algorithm to obtain a near-optimal solution for large-scale problems when computational time is a concern. A two-dimensional saving function is introduced to quantify the value of time and capacity space wasted. For the genetic algorithm, we propose a two-dimensional matrix and one-dimensional representation for encoding, and appropriate two-dimensional crossovers as well as mutations to generate offspring. In addition, the genetic algorithm aims to improve the quality of the solution found by the developed decomposition-based heuristic which is used as an initial solution for the developed genetic algorithm. Computational experiments show that the proposed heuristic algorithms perform well for small-size problems and can deal with large-scale problems efficiently within a reasonable computational time. Moreover, computational results also indicate that our proposed heuristics outperform an existing heuristic from the literature in terms of solution quality.

摘 要 i
Abstract ii
Acknowledgments iii
Table of Contents iv
List of Figures vii
List of Tables viii
Chapter 1. Introduction 1
1.1. Background and Motivation 1
1.2. Problem definition 4
1.3. Research objectives 5
1.4. Research methodology and framework 6
1.4.1. Research methodology 6
1.4.2. Research framework 6
Chapter 2. Literature Review 8
2.1. Parallel batch processing machines with incompatible families 8
2.2. Machine eligibility 10
2.3. Time window constraints 11
2.4. Decomposition-based method 13
2.5. Savings method 13
2.6. Genetic algorithm approach to scheduling problems 14
Chapter 3. MIP model and Decomposition-based Heuristic Algorithm 16
3.1. Mixed-integer programming model 16
3.1.1. Notations 16
3.1.2. MIP model formulation 17
3.1.3. Analysis of the size of the MIP model 19
3.2. Lower bound 19
3.3. Decomposition-based heuristic algorithm 20
3.3.1. Batch formation phase 20
3.3.2. Batch scheduling phase 24
Chapter 4. Genetic Algorithm 31
4.1. Chromosome representation 33
4.2. Encoding scheme 33
4.2.1. Batch sub-chromosome 33
4.2.2. Machine sub-chromosome 36
4.3. Decoding scheme 37
4.4. Initial population and Parent selection strategy
38
4.5. Crossover Operator 39
4.5.1. Batch sub-chromosome crossover 39
4.5.2. Machine sub-chromosome crossover 44
4.6. Mutation Operator 46
4.6.1. Batch sub-chromosome mutation 46
4.6.2. Machine sub-chromosome mutation 47
4.7. Feasibility test 49
Chapter 5. Computational Experiment 50
5.1. Experiment design 50
5.2. Parameter setting 51
5.3. Experimental results 51
5.3.1. Small-size instances 51
5.3.2. Large-size instances 56
Chapter 6. Conclusions 59
Bibliographies 61
Appendix 69
Appendix A. Additional notations used in DH and GA algorithms. 69
Appendix B. An illustrative example to demonstrate how a chromosome is generated. 70
Appendix C. Decoding scheme demonstration 76
Appendix D. Batching vector determination 78
Appendix E. Demonstration of batch sub-chromosome mutation
79

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