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研究生:張煒嵩
研究生(外文):Wei-Shung Chang
論文名稱:結合配對理論與萬用啟發式演算法於多目標非相關平行機台排程問題求解之研究
論文名稱(外文):Optimizing Multi-Objective Scheduling Problems of Unrelated Parallel Machines via Archived Metaheuristics with Matching Techniques
指導教授:徐旭昇徐旭昇引用關係
學位類別:博士
校院名稱:元智大學
系所名稱:工業工程與管理學系
學門:工程學門
學類:工業工程學類
論文種類:學術論文
論文出版年:2011
畢業學年度:99
語文別:英文
論文頁數:126
中文關鍵詞:多目標排程問題柏拉圖式支配非相關平行機台排程問題啟發式演算法配對解碼模式
外文關鍵詞:Multi-objective scheduling problemsPareto dominanceunrelated parallel machine schedulingmeta-heuristicsevolutionary algorithmsperformance metrics
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非相關平行機台排程問題(unrelated parallel machine scheduling problems)常見於現實環境中,諸如: 玻璃裁切業,木材裁切業,偏光板裁切等,且生產管理者所考量的生產目標往往是多重的。但過去幾年,學者針對非相關平行機台排程問題大部分僅考慮單一個目標目問題,較少探討多目標且具不確定性之非相關平行型機台排程問題。本論文之主旨在於開發新的啟發式演算法與依照不同目標特質設計相對應之配對解碼模式(matching-based decoding),以求解多目標與具不確定性之非相關平行型機台排程問題。本論文依照機台稼動率、即時化生產(JIT)、顧客交期滿意度與在製品持有成本等目標特質,將問題目標組合分為四個類型研究。
針對第一與第二類型研究,本論文提出 (1) 演化式演算法 : PCGA、NSGAII、SPEA2與CEMA;(2) 多目標模擬退火法 : UMOSA與SMOSA,求解最小化(minimizing) 兩目標特質均為和 (sum-type) 之非相關平行機台排程問題,諸如:權重式總流程時間(在製品持有成本)與權重式總延遲時間(顧客交期滿意度),並探討Weighted bipartite matching (WBM) 配對解碼模式於演算法效果之表現。實驗結果顯示,演化式演算法優於多目標模擬退火法,另外CEMA為本研究所發展之重點演算法,其使用配對解碼模式表現優於此案例其他演算法。
第三類型研究為求解最小化三目標之非相關平行機台排程問題,其目標型特質分為兩種: (1) 最大化特質(max-type),目標式包括最大完工時間(機台稼動率)、最大延遲時間與提前完工時間 (即時化生產);(2) 混合型特質 (mixed- type):目標式,其一為最大化特質 - 最大完工時間,另兩個為和之特質 – 此為第一、二類型研究之兩目標式。本論文在類型研究提出SPEA2、CEMA與CRASP演算法,結合min-max matching (MMM) 配對解碼模式求解最大化特質目標;另外結合MMM-WBM求解混合型特質目標。實驗結果顯示, CEMA使用配對解碼模式表現最佳。
第四類型研究主旨為探討模糊雙目標(fuzzy bi-objective)之非相關平行機台排程問題,提出以GRAS、F-MOSA以及D-MOSA演算法,求解目標式為:最大化決策者生產滿意度與顧客平均延遲滿意度問題,並探討配對解碼模式Max-Min matching與WBM使用於演算法之影響與效果表現。實驗結果顯示,演算法使用配對解碼模式表現較佳,其中F-MOSA表現最佳,GRASP表現次佳。
整體而言,本論文所提出之配對解碼模式可提升演算法之效果表現,但當求解機台數增加時則必須花費較多的求解時間。


Over the years, parallel machine scheduling problems with a single objective or weighted sum of selected objectives have been widely studied. In practice, the layout of unrelated parallel machines is more common than that of their identical counterparts in real manufacturing environments, and management concerns of production scheduling are often multi-fold. In addition, there have been relatively few studies on unrelated parallel machine scheduling problems (UPMSP) considering multiple objectives and uncertain production situation. The research area of multi-objective unrelated machine scheduling problems (MO-UPSMP) is fertile, not only in development of theories and problem solving techniques, but also in practical applications. The main purpose of this thesis is to develop new algorithms for MO-UPMSP, and demonstrate that they are more effective than several popular algorithms.
The thesis presents four studies on MO-UPMSP with sequence- and machine-dependent setup times. The first two studies present different evolutionary algorithms with matching-based decoding scheme to solve UPMSP with two minimization objectives: total weighted tardiness and total weighted flow time. In the two studies, the performances of the proposed hybrid evolutionary algorithms are compared with other metaheuristics, such as multi-objective simulated annealing (MOSA), and two well-known multi-objective population-based evolutionary algorithms.
The third study aims to solve UPMSP with two configurations of three objectives: (1) three min-max objectives; (2) one min-max and two weighted-sum objectives. Three algorithms with matching-based decoding schemes are employed to solve the tri-objective UPMSPs, including SPEA2, CEMA (developed in this research), and GRASP. The GRASP has been successfully applied to solve many single-objective combinatorial optimization problems, but relative few research articles are published on multi-objective scheduling problems. We develop two matching-based decoding schemes, one for three min-max objectives and the other for mixed-type objectives. The experimental results indicate that CEMA with matching-based decoding is superior to the others in terms of several performance metrics often used in multi-objective optimization theory.
The fourth study applies fuzzy approach to solve MO-UPMSP involving uncertainties on job processing times and job due dates. Two objectives are to maximize the decision maker’s satisfaction grade of production makespan and average satisfaction grade of jobs’ tardiness. The solution methods include archived MOSA and GRASP with path-relinking. The numerical results indicate that the GRASP technique has potentials to find good quality solutions for the problem under study.


TABLE OF CONTENT
摘要 i
ABSTRACT iii
誌謝 v
TABLE OF CONTENT vi
LIST OF FIGURES ix
LIST OF TABLES xi
CHAPTER 1 INTRODUCTION 1
1.1 DISSERTATION MOTIVATION 1
1.2 DISSERTATION SCOPES AND GOALS 2
1.3 STRUCTURE OF THE DISSERTATION 4
CHAPTER 2 BASIC CONCEPTS, METHODS AND LITERATURE REVIEW 7
2.1 DOMINANCE AND PARETO-OPTIMALITY 7
2.1.1 Concept of Domination 7
2.1.2 Pareto Optimality 10
2.2 FUNDAMENTAL SOLUTION METHODS 10
2.2.1 Weighted Sum Method (WSM) 11
2.2.2 ?-constraint Method 13
2.2.3 Evolutionary Algorithms 15
2.2.3.1 Non-Dominated Sorting Genetic Algorithm (NSGA II) 15
2.2.3.2 Strength Pareto Evolutionary Algorithm 16
2.3 PERFORMANCE METRICS 18
2.3.1 Proximity 19
2.3.3 Proximity and Diversity 23
2.3.4 Other Metrics 25
2.4 LITERATURE REVIEW 26
CHAPTER 3 METAHEURISTICS WITH MATCHING TECHNIQUES FOR MULTI-OBJECTIVE UNRELATED PARALLEL MACHINE SCHEDULING 30
3.1 INTRODUCTION 30
3.2 PROBLEM DESCRIPTIONS 30
3.3 SOLVING BI-OBJECTIVE WFT-UPMSP 33
3.3.1 Study 1 on Model 1 - PCGA 34
3.3.1.1 Hybrid Pareto Converging Genetic Algorithm 34
3.3.1.2 Multi-Objective Simulated Annealing Algorithm 39
3.3.1.3 Numerical Results 40
3.3.1.3.1 Data Generation 41
3.3.1.3.2 Algorithm Parameters 42
3.3.1.3.3 Performance Metrics and Comparisons 43
3.3.1.5 Concluding remarks 49
3.3.2 Study 2 on Model 1 - CEMA 50
3.3.2.1 Common Components of Algorithms 51
3.3.2.2 The CEMA Algorithm 52
3.3.2.2.1 Competitive Evolution 53
3.3.2.2.2 Fuzzy C-means Clustering 54
3.3.2.2.3 Fitness Assignment 54
3.3.2.3 Other MOHEAs 55
3.3.2.4 Numerical Results 56
3.3.2.4.1 Generating Test Instances 56
3.3.2.4.2 Performance Metrics 57
3.3.2.4.3 Experimental Results 57
3.3.2.5 Concluding Remarks 63
3.4 SOLVING TRI-OBJECTIVE UPMSP 72
3.4.1 Matching Techniques for Tri-Objective UPMSP 73
3.4.1.1 MMM Decoding for MET-UPMSP 73
3.4.1.2 MMM-WBM Decoding for MFT-UPMSP 75
3.4.2 GRASP for Tri-Objective UPMSP 78
3.4.2.1 The Basic GRASP 78
3.4.2.1.1 Greedy Function 80
3.4.2.2 Construction of the RCL 81
3.4.2.3 Reactive GRASP 82
3.4.2.4 Local Search 83
3.4.2.5 Path-Relinking 84
3.4.3 Numerical Results 84
3.4.4 Conclusion Remarks 93
CHAPTER 4 SOLVING MULTI-OBJECTIVE UNRELATED PARELLEL MACHINE SCHEDULING PROBLEMS UNDER FLEXIBLE CONSTRAINTS AND UNCERTAIN DATA: THE FUZZY APPROACH 94
4.1 PROBLEM DESCRIPTION 95
4.1.1 Notations 95
4.1.2 Problem Description and Objective Definition 95
4.2 SOLUTION METHODS 100
4.2.1 Encoding and Decoding Schemes 100
4.2.2 Neighborhood Solutions 103
4.2.3 Search Direction 104
4.2.4 Algorithm F-MOSA 104
4.2.5 Algorithm D-MOSA 105
4.2.6 GRASP 105
4.2.6.1 Construction Phase 106
4.2.6.2 Local Search 108
4.2.6.3 Path Relinking 108
4.3 NUMERICAL RESULTS 109
4.3.1 Data Set Generation 109
4.3.2 Algorithm Parameters 109
4.3.3 Numerical Results 110
4.4 CONCLUDING REMARKS 115
CHAPTER 5 CONCLUSIONS 117
5.1 Conclusions 117
5.2 Future Research Directions 118
REFERENCES 119

LIST OF FIGURES
Fig. 2.1 Mapping from decision space to objective space 9
Fig. 2.2 An illustrative example for domination and weighted-sum objective 9
Fig. 2.3 WSM for producing efficient solutions 12
Fig. 2.4 Drawback of exact algorithm using WSM 12
Fig. 2.5 Weighted matching and non-dominated set for sum-type MO-UPMSP 13
Fig. 2.6 ?-method and min-max matching for bottleneck-type UPMSP 15
Fig. 2.7 NSGA-II Trimming procedure 16
Fig. 2.8 Crowding distances of individuals q2 and p6 16
Fig. 2.9 SPEA fitness assignment 18
Fig. 2.10 SPEA2 fitness assignment 18
Fig. 2.11 Computation for generational distance of algorithm B 20
Fig. 2.12 Spread measure of algorithm A 22
Fig. 2.13 Spread measure of algorithm B 22
Fig. 2.14 G1R measure of algorithm B 23
Fig. 2.15 Hypervolume of algorithm A 25
Fig. 2.16 Example of PFRO measure 26
Fig. 3.1 Coding scheme of PCGA-JL involving WBM 37
Fig. 3.2 Biased uniform crossover of PCGA-JL 37
Fig. 3.3 Coding scheme of PCGA-RKL involving WBM 38
Fig. 3.4 An example of crossover of PCGA-RKL 38
Fig. 3.5 Pseudo code of PCGA 39
Fig. 3.6 Pseudo code of SMOSA 40
Fig. 3.7a job due date distribution of ? = 0.8 and R = 0.8 42
Fig. 3.7b job due date distribution of (? = 0.8, R = 0.2) 42
Fig. 3.7c job due date distribution of (? = 0.2, R = 0.8) 42
Fig. 3.8 Performance of algorithms on instance 1 (100 x 5) 46
Fig. 3.9 Performance of algorithms on instance 2 (100 x 10) 46
Fig. 3.10 Performance of algorithms on instance 3 (200 x 10) 47
Fig. 3.11 Performance of algorithms with WBM on instance 1 48
Fig. 3.12 Performance of algorithms with WBM on instance 2 48
Fig. 3.13 Performance of algorithms with WBM on instance 3 49
Fig. 3.14 An example of recombination operation 52
Fig. 3.15 Fitness assignment for CEMA 55
Fig. 3.16 Reference Pareto optimal fronts for instance MT01 58
Fig. 3.17 Reference Pareto optimal fronts for instance LT01 58
Fig. 3.18 rt value fluctuations of CEMA for instance MT01 61
Fig. 3.19 rt value fluctuations of CEMA for instance LT01 61
Fig. 3.20 Min-max matching decoding for MET-UPMSP 74
Fig. 3.21 MMM-WBM decoding for MFT-UPMSP 76
Fig. 3.22 Pseudo code of basic GRASP 79
Fig. 3.23 Pseudo code of GRASP constructive heuristic 80
Fig 4.1 Two possible satisfaction levels of job j tardiness 98
Fig 4.2 Nine possible cases to calculate satisfaction level 99
Fig. 4.3a Max-min matching for weighted sum objective with w = 0.4 102
Fig. 4.3b Qualified pairs with minimum makespan satisfaction = 0.74 103
Fig. 4.3c Pairs with makespan satisfaction ? 0.74 in 4.3b 103
Fig. 4.3d Hungarian method for maximum total tardiness satisfaction 103
Fig. 4.4 Fuzzy due date subtracted from completion time and rank 107

LIST OF TABLES
Table 1.1 Acronym List 4
Table 1.2 Summary of the four studies 6
Table 3.1 Outline of algorithm components for Study 1 34
Table 3.2 Performance measures of the algorithms for instance 1 (100 x 5) 44
Table 3.3 Performance measures of the algorithms for instance 2 (100 x 10) 44
Table 3.4 Performance measures of the algorithms for instance 3 (200 x 10) 45
Table 3.5 Computation times of algorithms with WBM for instances (3 replications) 45
Table 3.6 Computation times without WBM for instances (3 replications) 45
Table 3.7 Outline of algorithm components for Study 2 51
Table 3.8 Problem instance information 57
Table 3.9 Evaluation of WBM and non-WBM reference sets for MT01 and LT01 59
Table 3.10 NHV of algorithms for 100 x 10 instances 59
Table 3.11 NHV of algorithms for 200 x 10 instances 59
Table 3.12 Computation time of eight algorithms for 100 x 10 problems 59
Table 3.13 Computation time of eight algorithms for 200 x 10 problems 60
Table 3.14 Algorithm performance in Purity for 100x10 instances 63
Table 3.15 Algorithm performance in Purity for 200x10 instances 64
Table 3.16 Algorithm performance on GD for 100x10 instances 64
Table 3.17 Algorithm performance on GD for 200x10 instances 64
Table 3.18 Algorithm performance on Spread for 100x10 instances 65
Table 3.19 Algorithm performance on Spread for 200x10 instances 65
Table 3.20 PDC measures of algorithm pairs for ML instances (100 x 10) 65
Table 3.21 PDC measures of algorithm pairs for MM instances (100 x 10) 66
Table 3.22 PDC measures of algorithm pairs for MT instances (100 x 10) 67
Table 3.23 PDC measures of algorithm pairs for LL instances (200 x 10) 68
Table 3.24 PDC measures of algorithm pairs for LM instances (200 x 10) 69
Table 3.25 PDC measures of algorithm pairs for LT instances (200 x 10) 70
Table 3.26 Competition results for ML instances (100 x 10) 70
Table 3.27 Competition results for MM instances (100 x 10) 71
Table 3.28 Competition results for MT instances (100 x 10) 71
Table 3.29 Competition results for LL instances (200 x 10) 71
Table 3.30 Competition results for LM instances (200 x 10) 72
Table 3.31 Competition results for LT instances (200 x 10) 72
Table 3.32 Summary of three algorithms for Study 3 73
Table 3.33 Example of MMM decoding for a 5 x 5 MET-UPMSP 75
Table 3.34a Configuration of (100, 61, 30) 75
Table 3.34b Configuration of (100, 55, 29) 75
Table 3.35 Example of MMM-WBM decoding for a 5 x 5 MFT-UPMSP 76
Table 3.36a SC =103 for matrix 77
Table 3.36b SC =103 for matrix 77
Table 3.37a SC =110 for matrix 77
Table 3.37b SC =110 for matrix 77
Table 3.38a Normalized with 77
Table 3.38b Normalized with 77
Table 3.39a WBM with 78
Table 3.39a WBM with 78
Table 3.40 Nadir distances on 200x5 instances with different α and due date factors 83
Table 3.41 Nadir distances on 200x5 instances with Path-relinking 84
Table 3.42 Problem instance information 85
Table 3.43 NHV of algorithms for 100 x 3 instances 86
Table 3.44 NHV of algorithms for 200 x 5 instances 86
Table 3.45 Computation time for 100 x 3 instances of MET-UPMSP 86
Table 3.46 Computation time for 200 x 5 instances of MET-UPMSP 87
Table 3.47 Computation time for 100 x 3 instances of MFT-UPMSP 87
Table 3.48 Computation time for 200 x 5 instances of MFT-UPMSP 87
Table 3.49 Purity performance for 100 x 3 instances of MET-UPMSP 88
Table 3.50 Purity performance for 200 x 5 instances of MET-UPMSP 88
Table 3.51 GD performance for 100 x 3 instances of MET-UPMSP 89
Table 3.52 GD performance for 200 x 5 instances of MET-UPMSP 89
Table 3.53 Spread performance for 100 x 3 instances of MET-UPMSP 89
Table 3.54 Spread performance for 200 x 5 instances of MET-UPMSP 90
Table 3.55 Purity performance for 100 x 3 instances of MFT-UPMSP 90
Table 3.56 Purity performance for 200 x 5 instances of MFT-UPMSP 91
Table 3.57 GD performance for 100 x 3 instances of MFT-UPMSP 91
Table 3.58 GD performance for 200 x 5 instances of MFT-UPMSP 92
Table 3.59 Spread performance for 100 x 3 instances of MFT-UPMSP 92
Table 3.60 Spread performance for 200 x 5 instances of MFT 92
Table 4.1 Outline of algorithm components for study 4 100
Table 4.2 Algorithm performance on 100x5 instances with different due date parameters. 111
Table 4.3 Algorithm performance on 200x10 instances with different due date parameters. 111
Table 4.4 PFRO comparison on 100x5 instances with loose due date factors 113
Table 4.5 PFRO comparison on 100x5 instances with moderate due date factors 113
Table 4.6 PFRO comparison on 100x5 instances with tight due date factors 114
Table 4.7 PFRO comparison on 200x10 instances with loose due date factors 114
Table 4.8 PFRO comparison on 200x10 instances with moderate due date factors 114
Table 4.9 PFRO comparison on 200x10 instances with tight due date factors 115



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