跳到主要內容

臺灣博碩士論文加值系統

(18.97.14.81) 您好!臺灣時間:2025/02/11 01:18
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

: 
twitterline
研究生:何英如
研究生(外文):Ying-Ju Ho
論文名稱:應用特定型態質群最佳化演算法於搜尋D-optimal最佳設計之研究
論文名稱(外文):Construct D-Optimal Designs Using Modified Particle Swarm Optimization
指導教授:范書愷范書愷引用關係
指導教授(外文):Shu-Kai S. Fan
學位類別:碩士
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:2006
畢業學年度:94
語文別:英文
論文頁數:119
中文關鍵詞:反應曲面法最佳化設計準則質群演算法保留區域可行解法
外文關鍵詞:Response surface methodology (RSM)design optimality criteriaparticle swarm optimization (PSO)feasible-solution method (FSM)
相關次數:
  • 被引用被引用:0
  • 點閱點閱:928
  • 評分評分:
  • 下載下載:32
  • 收藏至我的研究室書目清單書目收藏:0
最佳化實驗設計 (optimal design) 經常被廣泛地運用在化學製造業界。現今因為工業界經常有高度複雜且伴隨限制條件的問題發生,所以在實際操作時,不對稱的實驗區域設計方法 (asymmetrical design) 便有存在之必要性。然而為了建構這樣的最佳化設計,傳統的統計方法有其不足的地方。因此當因子設計 (factorial design) 、部分因子設計 (fractional factorial design) 與反應曲面方法 (response surface methodology) 不容易被應用時,借助電腦演算求得最佳設計為一個較佳的方式。許多不同的最佳化設計準則 (optimality criteria) 以不同且有意義的英文字母來表達,而不同的最佳化設計準則分別衡量不同標準的最佳化設計。這些以電腦輔助 (computer-generated design) 求算的最佳化設計中以D最佳化設計 (D-optimal designs) 是最常被使用。
在早期,Fedorov 與 Mitchell 二位學者的傳統演算法經常被應用在建構D最佳化設計上。但是如果遇到問題比較複雜或者其變數維度提高時,這些方法實際應用效率較低。在本文中,我們將利用修正後的質群演算法 (modified particle swarm optimization, MPSO) 於建構一連串D最佳化設計問題,並且在搜尋最佳解的過程中,試著避免落入區域最佳解以及找出適當方法平衡質群演算法在速度更新上的搜尋能力。此外,我們利用保留區域可行解法 (feasible solutions method, FSM) 並重新設定不可行解在實驗區域邊界上的方式來處理混合實驗 (mixture experiments) 與高複雜限制式的問題。
Optimal designs are applied extensively to the process industry. Asymmetrical designs are now widely used in practice since many engineering problems usually involve complex objective functions and several constraints simultaneously. Hence, the classical designs cannot be valid for this circumstance any more. Accordingly, computer-generated designs are the legitimate choice for situations where standard factorial, fractional factorial designs or response surface designs cannot be easily employed. Design optimality criteria are characterized by letters of the alphabet and as a result, are often called alphabetic optimality criteria. An optimality criterion can be interpreted as a measure of the goodness of the design. Those designs are the most typically used type of computer-generated designs, and of course, the D-optimal class of designs is the most popular one.

To construct the D-optimal designs, the Fedorov’s and Mitchell’s algorithm is broadly used. But in case of high dimensionality, this class of algorithms cannot be used adequately due to its efficiency. In this thesis, an optimization technique is introduced to generate D-optimal designs using the modified particle swarm optimization (MPSO). The modified algorithm is mostly developed from the basic particle swarm optimization (BPSO). Meanwhile, the goal of the thesis is to alleviate the risk of being trapped at a suboptimal design solution and further balance exploration and exploitation within the global search ability of MPSO. Furthermore, the constraint-handling mechanism in the mixture experiments demonstrated is tried out to resolve infeasible solutions in this study. Rejection of infeasible individuals and preservation of feasible solutions method (FSM) are used for constituting constrained optimization.
TABLE OF CONTENTS

摘要 i
ABSTRACT ii
ACKNOWLEDGEMENT iv
TABLE OF CONTENTS v
LIST OF FIGURES AND TABLES viii
NOMENCLATURE xii


Chapter

1. INTRODUCTION 1
1.1 Background 1
1.2 Motivation 3
1.3 Research Objectives 5
1.4 Outline of the Thesis 5
2. LITERATURE REVIEW 8
2.1 Optimal Design 8
2.2 D-optimal Criterion and D-efficiency 12
2.3 Algorithms for Construction of D-optimal Designs 17
2.3.1 Branch and Bound Approach 18
2.3.2 Silmulated Annealing 18
2.3.3 Exchange Algorithms 18
2.3.4 Coordinate Exchange Approach 22
2.3.5 Genetic Algorithm 22
2.4 D-optimal Designs for Mixture Experiment with Constrained Methods 23
2.4.1 Mixture Experiment 24
2.4.2 Algorithms for Constrained Methods 25
2.5 Particle Swarm Optimization 26
2.5.1 Basic Particle Swarm Optimization 26
2.5.2 Development of Particle Swarm Optimization 30
2.5.2.1 Inertia Weight PSO 30
2.5.2.2 Constriction PSO 31
2.5.2.3 Modification to Ordinary PSO 32
2.5.3 Parameters in Particle Swarm Optimization 33
2.5.3.1 Initialization 33
2.5.3.2 Inertia Weight 34
2.5.3.3 Stochastic Factors 35
2.5.3.4 Maximum Velocity 35
3. PROPOSED MODIFIED PARTICLE SWARM OPTIMIZATION FOR
SOLVING D-OTIMAL DESIGNS PROBLEMS 37
3.1 Overview 37
3.2 Modified Particle Swarm Optimization Method 39
3.2.1 Initialized Population in PSO for Constraints 39
3.2.2 Inflation Factor 40
3.2.3 The Modified PSO (MPSO) Method for Constructing D-optimal Designs 40
3.2.4 Stochastic Factor 43
3.2.5 Feasible Solutions Method 43
3.2.6 Brief Summary 44
3.3 Design Problems 46
3.3.1 An Irregular Experimental Region Problem 46
3.3.2 A Series of Factorial Region 48
3.3.3 A Mixture Problem with One Processing Variable 49
3.3.4 A Constrained Mixture Problem 51
3.3.5 A Quadratic Model for a Mixture Problem 52
3.4 Brief Summary 53
4. EXPERIMENT RESULTS AND PERFORMANCE EVALUATION 55
4.1 Design of Experiment for Parameters Setting in MPSO 55
4.1.1 Inflation Factor 55
4.1.2 Stochastic Factors 58
4.1.3 Local Investigation of Stochastic Factor 61
4.1.4 Recommendation of Parameters Setting 63
4.2 Computation Experiences and Comparisons of MPSO with Existing Methods 64
4.2.1 An Irregular Experimental Region Problem 64
4.2.2 A Series of Factorial Region 67
4.2.3 A Mixture Problem with One Processing Variable 78
4.2.4 A Constrained Mixture Problem 81
4.2.5 A Quadratic Model for a Mixture Problem 84
4.3 Summary 86
5. CONCLUSIONS AND FUTURE RESEARCH 88
5.1 Conclusions 88
5.2 Future Research 89

REFERENCES 90

APPENDIX A SAS PROC 94
APPENDIX B Random Initial Population for Constrained Mixture and Mixture Problem 113
APPENDIX C Comparison Performance of Different PSO Methods 115
Alifanov, O. M., Artyukhin, E. A. and Rumyantsev, S. V. (1995). Extreme Methods for Solving Ill-Posed Problems With Applications to Inverse Heat Transfer Problems, Begell house, New York.

Atkinson, A. C. and Donev, A.N. (1989). “The Construction of Exact D-optimum Experimental Designs with Application to Blocking Response Surface Designs,” JSTOR, 76, 3, 515-526.

Beck, J. V. and Arnold, K. J. (1977). Parameter Estimation in Engineering and Science, Wiley, New York.

Carlisle, A. J. (2002). “Applying the Particle Swarm Optimizer to Non-stationary Environments,” Auburn University, Auburn, Alabama.

Clerc, M. (1999). “The Swarm and The Queen: Towards a Deterministic and Adaptive Particle Swarm Optimization,” Proceedings of the Congress on Evolutionary Computation, 3, 1951-1957.

Coath, G. and Halgamuge, S. K. (2003). “A Comparison of Constraint-Handling Methods for The Application of Particle Swarm Optimization to Constrained Nonlinear Optimization Problems,” Proceedings of the Congress on Evolutionary Computation, 4, 2419-2425.

Cook, R. D. and Nachtsheim, C. J. (1980). “A Comparison of Algorithms for Constructing Exact D-Optimal Designs,” Technometrics, 22, 315-324.

Dykstra, O. (1971). “The Augmentation of Experimental Data to Maximize |X’X|,” JSTOR, 13, 3, 682-688.

Eberhart, R. C. and Shi, Y. (2000). “Comparing Inertia Weights and Constriction Factors in Particle Swarm Optimization,” Proceedings of the Congress on Evolutionary Computation, 1, 84-88.

Eberhart, R. C. and Shi, Y. (2001). “Particle Swarm Optimization: Developments, Applications and Resources,” Proceedings of the Congress on Evolutionary Computation, 1, 81-86.

Emery, A. F. and Nenarokomov, A. V. (1998). “Optimal experiment design,” Measurement Science and Technology, 9, 6, 864-876.

Eschenauer, H., Koski, J. and Osyczka, A. (1990). “Multicriteria design optimization: Procedures and applications,” Springer, Berlin. 504, 46042-46050.

Garcia, S. (1999). “Experimental Design Optimization and Thermo physical Parameter Estimation of Composite Materials Using Genetic Algorithms,” Ph.D. Dissertation, Virginia Polytechnic Institute and State University, Nantes, France.

Haines, L. M. (1987). “The Application of the Annealing Algorithm to the Construction of Exact Optimal Designs for Linear-Regression Models,” Technometrics, 29, 439-447.

Heredia-Langner, A., Carlyle, W. M., Montgomery, D. C., Borror, C. M. and Runger, G. C. (2003). “Genetic Algorithms for the Construction of D-Optimal Designs,” Journal of Quality Technology, 35, 28-46.

Ho, S. L., Yang, S., Ni, G., Lo, W.C. and Wong, H. C. (2005). “A Particle Swarm Optimization-Based Method for Multiobjective Design Optimizations,” IEEE Transaction on Magnetics, 41, 1756-1759.

Hu, X. and Eberhart, R. (2002). “Solving Constrained Nonlinear Optimization Problems with Particle Swarm Optimization,” 6th World Multiconference on Systemics, Cybernetics and Informatics (SCI 2002).

John, R. C. and Deraper, N. R. (1975). “D-optimality for Regression Designs: A review,” Technometrics, 17, 15-23.

Johnson, M. E. and Nachtsheim, C. J. (1983). “Some Guidelines for Constructing Exact D-optimal Designs on Convex Design Spaces,” Technometrics, 25, 271-277.

Kennedy, J. and Eberhart, R. (1995). “Particle Swarm Optimization,” Proceeding of the IEEE International Conference on Neural Networks, IEEE Service Center, Piscataway, NJ, 1942-1948.

Khuri, A.I. and Cornell, J. A. (1996). Response Surface: Design and Analyses, 2nd edition, Marcel Dekker, New York, NY.

Kiefer, J. and Wolfowitz, J. (1959). “Optimum Designs in Regression Problems,” JSTOR, 30, 2, 271-294.

Kiefer, J. (1959). “Optimum Designs in Regression Problems Ⅱ,” JSTOR, 32, 1, 298-325.

Kiefer, J. (1961). “Optimum Experimental Designs,” JSTOR, 21, 2, 272-329.

Kiefer, J. (1975). “Optimal Design: Variation in Structure and Performance Under Change of Criterion,” JSTOR, 62, 2, 277-288.

Lohman, T., Bock, H. G. and Schloder, T. P. (1992). “Numerical Methods for Parameter Estimation and Optimal Experiment Design in Chemical Reaction Systems,” Ind. Eng. Chem. Res., 31, 54-57.

Meyer, R. K. and Nachtsheim, C. J. (1995). “The Coordinate-Exchange Algorithm for Constructing Exact Optimal Experimental Designs,” Technometrics, 37, 1, 60-69.

Michalewicz, Z., Dasgupta, D., Riche, R. G. L. and Schoenauer, M. (1996). “Evolutionary Algorithms for Constrained Engineering Problems,” Computers and Industrial Engineering, 30, 4, 851-870.

Mitchell, T. J. (1974). “An Algorithm for the Construction of Exact D-Optimal Designs,” Technometrics, 20, 203-210.

Myers, R. H. and Montgomery, D. C. (2002). Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 2nd edition, John Wiley and Sons, New York, NY.

Nguyen, N. K. and Miller, A. J. (1992). “A Review of Some Exchange Algorithm for Constructing Discrete D-optimal Designs,” Computational Statistics & Data analysis, 14, 489-498.

Pronzato, L., Huang, C. Y., Walter, E., Roux, Y. L. and Frydman, A. (1989). “Planification d''expériences pour l''estimation de paramètres pharmacocinétiques,” Informatique et Médicaments, 2.

Pronzato, L. and Walter, E. (1994). “Minimum-volume ellipsoids containing compact sets: application to parameter bounding,” IFAC, 30, 11, 1731-1739.

Shi, Y. and Eberhart, R. (1998). “A Modified Particle Swarm Optimizer,” Proceedings of IEEE International Conference of Evolutionary Computation, Anchorage, Alaska, 69-73.

Snee, R. D. and Marquardt, D. W. (1974). “Extreme Vertices Designs for Linear Mixture Models,” Technometrics, 16, 399-408.

Snee, R. D. (1974). “Computer-Aided Design of Experiments— Some Practical Experiences,” Journal of Quality Technongy, 17, 222-236.

Sobieszczanski- Sobieski, J. and Haftka, R.T. (1997). “Multidisciplinary Aerospace Design Optimization: Survey of Recent Developments,” Structural Optimization, 14, 1-23.

Welch, W. J. (1982). “Branch-and-Bound Search for Experimental Designs Based on D-optimality and Other Criteria,” Technometrics, 24, 1, 41-48.

Welch, W. J. (1984). “Computer-Aided Design of Experiments for Response Estimation,” Technometrics, 26, 217-224.

Wynn, H. P. (1970). “The Sequential Generation of D-optimal Experimental Designs,” JSTOR, 41, 5, 1655-1664.
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top
無相關論文
 
1. 21. 徐享崑、李朝晉 (1984),「序率水資源系統離散行微分動態規劃模式之初步研究」,土木水利,11(3)。
2. 21. 徐享崑、李朝晉 (1984),「序率水資源系統離散行微分動態規劃模式之初步研究」,土木水利,11(3)。
3. 10. 李天岩 (1989),「熵(Entropy)(上)」,數學傳播,13(3)。
4. 10. 李天岩 (1989),「熵(Entropy)(上)」,數學傳播,13(3)。
5. 28. 郭振泰、林國峰 (1992),「台灣地區乾旱問題之回顧與前瞻」,土木水利,18(4)。
6. 28. 郭振泰、林國峰 (1992),「台灣地區乾旱問題之回顧與前瞻」,土木水利,18(4)。
7. 30. 陳莉、張斐章 (1995),「遺傳演算法優選水庫應用規線之研究」,中國農業工程學報,41(4)。
8. 30. 陳莉、張斐章 (1995),「遺傳演算法優選水庫應用規線之研究」,中國農業工程學報,41(4)。
9. 37. 張斐章、徐國麟 (1991),「利用模糊集理理論推估河川流量研究」,中國農業工程學報,30(4),1-12。
10. 37. 張斐章、徐國麟 (1991),「利用模糊集理理論推估河川流量研究」,中國農業工程學報,30(4),1-12。
11. 46. 黃文政、謝宏智 (1994),「旱季期間水庫入流量長期預報之研究」, 農業工程學報,40(3)。
12. 46. 黃文政、謝宏智 (1994),「旱季期間水庫入流量長期預報之研究」, 農業工程學報,40(3)。
13. 76. 蕭政宗 (2000),「乾旱時期水庫供水策略對缺水影響分析」,農業工程學報,46(2)。
14. 76. 蕭政宗 (2000),「乾旱時期水庫供水策略對缺水影響分析」,農業工程學報,46(2)。
15. 77. 蕭政宗 (2001),「以連續累積降雨量定義氣象乾旱之研究」,臺灣水利,49(3),52-64。