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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳正剛 | |
| dc.contributor.author | Yen-Ting Chen | en |
| dc.contributor.author | 陳彥廷 | zh_TW |
| dc.date.accessioned | 2021-05-20T20:26:02Z | - |
| dc.date.available | 2018-01-01 | |
| dc.date.available | 2021-05-20T20:26:02Z | - |
| dc.date.copyright | 2008-09-02 | |
| dc.date.issued | 2008 | |
| dc.date.submitted | 2008-08-27 | |
| dc.identifier.citation | REFERENCE
[1] M. Avriel, Nonlinear Programming: Analysis and Methods, Dover Publications, 2003. [2] M. S. Bazaraa, H. D. Sherali, C. M. Shetty and Wiley InterScience (Online service), Nonlinear programming [electronic resource] : theory and algorithms, Wiley-Interscience, Hoboken, N.J., 2006. [3] A. D. Belegundu and T. R. Chandrupatla, Optimization concepts and applications in engineering, Prentice Hall. [4] R. H. Byrd, H. F. Khalfan and R. B. Schnabel, Analysis of a Symmetric Rank-One Trust Region Method, SIAM, 1996, pp. 1025. [5] R. H. Byrd, R. B. Schnabel and G. A. Shultz, Approximate Solution of the Trust Region Problem by Minimization over Two-Dimensional Subspaces, Mathematical Programming, 40 (1988), pp. 247-263. [6] A. Chen, P. S. Guo and P. Lin, Statistical analysis and design of semiconductor manufacturingsystems, 2000, pp. 335-338. [7] N. R. Draper, Ridge analysis of response surfaces, JSTOR, 1963, pp. 469-479. [8] J. Y. Fan, W. B. Ai and Q. Y. Zhang, A line search and trust region algorithm with trust region radius converging to zero, Journal of Computational Mathematics, 22 (2004), pp. 865-872. [9] S. K. S. Fan, A different view of ridge analysis from numerical optimization, Engineering Optimization, 35 (2003), pp. 627-647. [10] S. K. S. Fan, THE HOUSEHOLDER TRIDIAGONALIZATION STRATEGY FOR SOLVING A CONSTRAINED QUADRATIC MINIMIZATION PROBLEM, Taylor & Francis, 2001, pp. 261-277. [11] D. G. Luenberger, Linear and Nonlinear Programming, Springer, 2003. [12] D. C. Montgomery and D. C. Montgomery, Design and analysis of experiments, Wiley New York, 1991. [13] J. J. More and D. C. Sorensen, Computing a Trust Region Step, Siam Journal on Scientific and Statistical Computing, 4 (1983), pp. 553-572. [14] J. Nocedal, S. J. Wright and SpringerLink (Online service), Numerical Optimization [electronic resource], Springer Science+Business Media LLC., New York, NY, 2006. [15] J. Nocedal and Y. Yuan, Combining trust region and line search techniques, Berlin: Kluwer, 1998, pp. 175. [16] J. M. Rabaey, A. Chandrakasan and B. Nikolic, Digital integrated circuits, Prentice Hall Upper Saddle River, NJ, 2002. [17] M. Rojas and D. C. Sorensen, A Trust-Region Approach to the Regularization of Large-Scale Discrete Forms of Ill-Posed Problems, 2002, pp. 1843-1861. [18] J. Semple, Optimality conditions and solution procedures for nondegenerate dual-response systems, Springer, 1997, pp. 743-752. [19] J. M. B. Walmag and E. J. M. Delhez, A Note on Trust-Region Radius Update, SIAM, 2005, pp. 548. [20] R. A. Waltz, J. L. Morales, J. Nocedal and D. Orban, An interior algorithm for nonlinear optimization that combines line search and trust region steps, Mathematical Programming, 107 (2006), pp. 391-408. [21] W. Wolf, Modern VLSI Design: Systems on Silicon, 2nd Editon Prentice Hall, Inc, 1996. [22] J. Zhang and C. Xu, A Class of Indefinite Dogleg Path Methods for Unconstrained Minimization, SIAM, 1999, pp. 646. [23] Q. Zhang, K. Poolla and C. J. Spanos, Across Wafer Critical Dimension Uniformity Enhancement Through Lithography and Etch Process Sequence: Concept, Approach, Modeling, and Experiment, 2007, pp. 488-505. [24] 陳彥良, 使用一般化縮減脊線搜尋與Zoutendijk方法於多目標統計模型最佳化, 工業工程學研究所, 臺灣大學, pp. 60. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/9509 | - |
| dc.description.abstract | 一般化縮減梯度(Generalized Reduced Gradient)法是一個廣受喜愛的非線性規劃問題解法，但於具有四次目標式之多目標統計最佳化(Statistical Multi-objective Optimization)問題中，一般化縮減梯度法容易出現搜尋路徑曲折(Zigzagging)的現象。於本研究中，我們改善了信賴域(Trust Region)搜尋法，並發展了一般化縮減信賴域(Generalized Reduced Trust Region)搜尋法。此方法結合了一般化縮減梯度與信賴域搜尋法，將具有限制式的非線性規劃問題，轉化成由非基礎變數(Nonbasic variable)所構成的不具現制式的非線性規劃問題，並且在縮減空間(Reduced Space)中獲得最佳改善的方向，且於案例中克服了一般化縮減梯度法的缺點，此外，我們也結合了一般化縮減信賴域搜尋法與Zoutendijk’s搜尋法以改善搜尋效果。最後，為了驗證該演算法的成效，我們利用一個眾所皆知且具四次目標式的測試問題：Rosenbrock’s function與三個案例來測試，第一個案例是關於半導體可製造性設計(DFM)之問題，而第二個案例是半導體供應鏈穩健配置之案例，最後一個案例為半導體製造過程中，臨界尺寸均勻度(CDU)在軌道系統之曝光後烘烤(PEB)步驟下之最佳化。經由與商業套裝軟體Lingo的結果比較，我們可以在相似的計算時間內獲得同樣甚至更好的最佳解。 | zh_TW |
| dc.description.abstract | “Generalized Reduced Gradient” method is a popular NLP method, but it often incurs a zigzagging search path especially for the statistical multi-objective optimization (SMOO) problem where the objective function is a quartic function. In this study, we improve the “Trust Region (TR)” search method and develop the “Generalized Reduced Trust Region” (GRT) search method which combines the GRG method and the improved TR method. The GRT search transforms the constrained NLP problem to an unconstrained NLP problem consisting of only the nonbasic variables and searches the best improving direction in the reduced space. The proposed method is shown to overcome the zigzagging problem of the GRG method. To verify the performance of our methods, we study a well know test problem and three cases. The test problem is called Rosenbrock’s function which has a quartic objective function with two decision variables. The first case is a semiconductor design for manufacturing (DFM) problem. The second case is the problem to configure a robust semiconductor supply chain. The final case is the “Track System PEB CDU Optimization”. Compared against the result of the commercial software “Lingo”, the same or better solutions are obtained by our methods with comparable computation time. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-20T20:26:02Z (GMT). No. of bitstreams: 1 ntu-97-R95546024-1.pdf: 3900875 bytes, checksum: 3801d8daa3c3e848be13a41c35f1c61b (MD5) Previous issue date: 2008 | en |
| dc.description.tableofcontents | TABLE OF CONTENTS
TABLE OF CONTENTS III LIST OF FIGURES V LIST OF TABLES VII 1 Introduction 1 1.1 Problem Definition and Formulation 1 1.2 Current NLP Methods Review 6 1.2.1 Generalized Reduced Gradient (GRG) Method 7 1.2.2 Ridge Analysis and Ridge Search Method 15 1.2.3 Zoutendijk Method 20 1.3 Shortcomings of Current NLP Methods 23 1.3.1 Shortcomings of Generalized Reduced Gradient Method 23 1.3.2 Shortcomings of Ridge Search Method 28 1.4 Research Objectives 31 1.5 Thesis Organization 34 2 Trust Region Method 35 2.1 Trust Region Method 35 2.2 Iterative Solution of Trust Region Subproblem (TRS) 39 2.3 The Hard Case 43 2.4 Modifications of Trust Region Algorithm 49 3 Generalized Reduced Trust Region (GRT) Search 63 3.1 Trust Region Search Method 63 3.2 Generalized Reduced Trust Region Method 71 3.3 Convergence Proof of Generalized Reduced Trust Region Method 94 4 Case Study 98 4.1 Geometric Layout Design for Semiconductor Manufacturability 98 4.2 Robust Configuration of Semiconductor Supply Chain 104 4.3 Track System PEB CDU Optimization 112 5 Conclusions 121 REFERENCE 124 Appendix A. Proof of the solution to the Hard Case 126 Appendix B. Trust Region Algorithm 127 Appendix C. Proof of Theorem 3.1 (Convergence to Stationary Point) 129 Appendix D. Problem Formulation of DFM Case 132 Appendix E. Expected Cycle Times and Raw Process Time of Supply Chain 133 Appendix F. Problem Formulation of Supply Chain Case 135 | |
| dc.language.iso | en | |
| dc.title | 一般化縮減信賴域搜尋及其在多目標統計模型最佳化之應用 | zh_TW |
| dc.title | Generalized Reduced Trust-region Search and Its Applications to Statistical Multi-Objective Optimization | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 96-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 張時中,柯志明,蔡雅蓉,范書愷,吳政鴻 | |
| dc.subject.keyword | 非線性規劃,多目標統計最佳化,一般化縮減梯度法,一般化縮減信賴域法,信賴域法, | zh_TW |
| dc.subject.keyword | Nonlinear Programming,Statistical Multi-Objective Optimization,Generalized Reduced Gradient Method,Generalized Reduced Trust Region Method,Trust Region Method, | en |
| dc.relation.page | 138 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2008-08-27 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 工業工程學研究所 | zh_TW |
| 顯示於系所單位： | 工業工程學研究所 | |
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