本文將多層最佳化觀念及平行處理技術，及結合混成遺傳學演算法，整合成更具效率的平行混成多層遺傳學演算法PHMGA(Parallel Hybrid Multilevel Genetic Algorithms)，應用於幾何非線性結構的最佳化設計問題，探討其適用性與平行計算效益。若以桁架分析為例，考慮真實情況之幾何大變形，其結果將比只以線性考量更為合理，但卻更為複雜而耗時。平行混成多層遺傳學演算法PHMGA，對大型複雜線性結構的最佳化應用成效相當好；若將其應用於更為複雜的非線性行結構最佳化設計問題上，平行效率與適用性，必將具顯著。因此，本文將針對混成遺傳演算法結合多層最佳化技術，並予以整合平行處理技術，建立之平行混成多層遺傳學演算法PHMGA方法應用於一些大型複雜非線性結構問題，於IBM SP6000超級電腦上執行，探討並驗證其平行計算效率與適用性。

The purpose of this study is to discuss the fitness of using PHMGA (Parallel Multilevel Hybrid Genetic Algorithm), which is a fast and efficient method, in the geometrically nonlinear structural optimization. Parallel genetic algorithms can solve the problem of traditional sequential genetic algorithms, such as premature convergence, large number of function evaluations, and a difficulty in setting parameters. By using several concurrent sub-population, parallel genetic algorithms can avoid premature convergence resulting from the single genetic searching environment of sequential genetic algorithms. It is useful to speed up the operation rate of joining timely multilevel optimization with parallel genetic algorithms. Because multilevel optimization can resolve one problem into several smaller subproblems, each subproblem is independent and not interference with one another. Then the subsystem of each level can be connected by sensitivity analysis. So we can solve the entire problem. Because each subproblem contains less variables and constrains, it can achieve the faster converge rate of the entire optimization. PHMGA integrates advantages of two methods including the parallel genetic algorithms and the multilevel optimization.

In this study, PHMGA is adopted to solve several design optimization problems for nonlinear geometrically trusses on the parallel computer IBM SP2. The use of PHMGA helps reduce execution time because of integrating a multilevel optimization and a parallel technique. PHMGA helps speed up the searching efficiency in solving structural optimization problems of nonlinear truss. It is hoped that this study will demonstrate PHMGA is an efficient and powerful tool in solving large geometrically nonlinear structural optimization problems.

第一章 緒論....................... 1
第二章 遺傳演算法簡介.............. 4
第三章 平行混成多層遺傳法簡介...... 22
第四章 非線性有限元素法分析模型.... 42
第五章 結構最佳化設計............. 48
第六章 實例分析與討論............. 52
第七章 結論...................... 72

1. John H.Holland., ”Adaptation in natural and artificial system”, Ann Arbar. The University of Michigan Press 1975.

2. David E. Goldberg, “Genetic Algorithms in Search Optimization and Machine Learning”, Addison Wesley Press 1989.

3. A.K.Dhingra and B. H. Lee, “Multi-object Design of Actively Controlled Structures using a Hybrid Optimization Method”, International Journal for Numerical Methods in Engineering, Vol. 38, pp. 3383-3401, 1995.

4. Pal-KF, “Genetic Algorithm with Local Optimization”, Biological Cybernetics, Vol. 73, Issue. 4, pp. 335-341, 1995.

5. Shyue-Jian Wu and Pei-Tse Chow, ”Integrated Discrete and Configuration Optimization of Trusses Using Genetic Algorithms”, Computers ＆ Structures. Vol.56. No.6. pp.979-991. 1995

6. J.J.Gerfenstette, “Parallel Adaptive Algorithms for Function Optimization”, Technical report on CS-81-19 Nashville Vanderbilt University. Computer Science Department 1981.

7. J. P. Cohoon. S.U. Heged, W.N. Martin and D.S. Richard, ”Punctuated Equilibrate: a Parallel Genetic Algorithm”, in Proceeding of the second international conference on Genetic Algorithms . pp. 148-154,1987.

8. M. Dariga and V. Maniezza, “Parallel Genetic Algorithms introduction and a review of current research”, in Stander’s .pp.5-42,1993.

9. Adeli, Hojjant and Cheng Nai-Tsang, “Concurrent genetic algorithm for optimization of large strustures”, Journal of Aerospace Engineering, Vol. 7, pp. 276-296, 1994.

10. Adeli, Hojjat, Kumar, Sanjay, “Distributed genetic algorithm for structural optimization “, Journal of Aerospace Engineering. Vol.8, pp. 156-163, 1995.

11. Enokizono-M Akinari-Y, “Estimation of current distribution by Hybrid genetic algorithm and sampled pattern-matching method”, IEEE transactions on magnetic, Vol. 31, Is. 3, pp. 2012-2015,1995.

12. Joachim Stender. Parallel Genetic Algorithms: Thoery and Applications. IOS Press.1993

13. D. Whitley. “The Genitor Algorithm and Selection Pressure: Why rank-based Allocation of reproductive trials is Best”, In Proceedings of the third international Conference on Genetic Algorithms. pp.116-121. 1989

14. 黃朝魁, ”分散式遺傳演算法於最佳化設計之研究”, 國立中山大學機械工程研究所碩士論文，1996

15. J. J. Grefenstette. “Optimization of Control Parameters for Genetic Algorithms”, IEEE Transactions on System. Man. and Cybernetics. SMA-16(1). pp.122-128. 1986

16. Shyue-Jian Wu and Pei-Tse Chow, “Steady-state Genetic Algorithms for Discrete Optimization of Trusses”, Computers ＆ Structures. Vol.56. No.4. pp.695-702. 1995

17. M. Dorigo and V. Maniezzo, ”Parallel Genetic Algo-rithms: Introduction and overview of current research”, in Stender's, pp.5-42, 1993

18. 戴如育, ”分散式遺傳演算法於最佳化設計之研究”, 國立中山大學機械工程研究所碩士論文，1994

19. Jasbir S. Arora, Introduction to optimum design, McGraw-Hill Press, pp.353-354, 1989

20. Garret N. Vanderplaats, Numerical optimization tech-niques for engineering design: With applications, McGraw-Hill Press, pp.122-128, 1984