基本粒子群演算法即為一種不含處理限制條件的仿生最佳化演算法。在近代粒子群演算的文獻中，以間接的方式處理限制函數居多。本文以仿生的觀念，發展替換數位資訊法處理粒子群演算中的限制條件處理問題，做法是藉由基因演化法則，將不可行個體與可行個體經由逐位元的資訊結合交換運算，使得不可行個體逐漸趨向且相似於一最佳可行個體。此法是直接處理限制函數，顯示穩健效果。另外本研究亦修改非支配排序策略，使其合理化。將限制條件違反量轉換為另一設計目標，與原目標函數使用非支配排序法求解，收斂於另一目標值為零。本文敘述整體最佳化解題程序，由數值題目驗證兩種限制處理策略，可有效且穩健的處理粒子群最佳化演算法含限制條件的問題。微致動器是微機電系統的一種動力源，大致可分為電熱式、壓電式、靜電式及電磁式。電熱式微制動器具有輸出力大，製作容易等優點。此微致動器若應用於夾取人體細胞，夾持點的溫度需限制在35℃以內，本研究設計電熱式微致動的結構，以最大化挾持點的位移量為目標，其中結合有限元素軟體ANSYS的分析，使用本文之粒子群演算法進行有限制條件的最佳化設計，可得到最佳的結果。本文之限制粒子群最佳化程序，可解一般含限制的工程設計問題。

Partical Swarm Algorithm (PSA) naturally is a unconstrained biocomputational optimization. In recent publications, several indirect constraints treatments were proposed named constrained partical swarm optimization (CPSO).The present thesis simulates birds flock communication to develop the information substitution strategy in treating constraints. This approach can gradually convert the infeasible individual becomes the feasible individual by refering the information of globally effective individual. The presenting strategy can be categorized to a direct method of constraints handling. Another approach presented here in is a modification of non-dominating strategy. The idea is that all constraints are transformed to an additional single objective, then non-dominating sorting technique can be applied. At the end, pareto front will converge to zero value of additional objective. Illustrative numerical examples shows that the proposed two approaches of constraint handling are effective and reliable for engineering optimization. Microthermal actuator is broadly used in MEMS, it has large power output and is easy to manufacture. It can be adapted for grasping human cell, however the 35°C is the high temperature limit on the grasping point. This thesis provides the optimum structural design by using CPSO proposed in the thesis with the aid finite of element analysis ANSYS.

致謝.......................................................I
中文摘要..................................................II
英文摘要..................................................IV
目錄......................................................VI
圖目錄..................................................VIII
表目錄.....................................................X
符號表....................................................XI
第一章	緒論.............................................1
1.1 動機與目的.............................................1
1.2 文獻回顧...............................................2
1.3 本文架構...............................................5
第二章	替換數位資訊法的粒子群最佳化.....................7
2.1 粒子群原理.............................................7
2.2 粒子群的數學模型與演算法...............................9
2.3 替換數位資訊法處理限制條件的原理......................13
2.4 替換數位資訊法的粒子群最佳化流程......................15
2.5 非支配排序策略的限制原理..............................20
第三章	含限制的粒子群最佳化數解........................38
3.1數值例題...............................................39
3.2比較討論...............................................66
第四章	含限制的粒子群最佳化應用........................68
4.1桁架結構最佳化設計.....................................68
4.2電熱微致動器有限元最佳化設計...........................79
第五章	結論............................................91
5.1綜合討論及結論.........................................91
5.2未來展望...............................................93參考文獻..................................................94

圖目錄
圖2.1	非支配排序法示意圖..................... ............................. .........21
圖2.2文獻[14]非支配排序法求解f(X)收斂迭........................ .....26
圖2.3文獻[14]非支配排序法求解Pareto結果圖..................... ....27
圖2.4本文非支配排序法求解f(X)收斂迭代圖..............................27
圖2.5本文非支配排序法求解Pareto結果圖........................... ......29
圖2.6文獻[14]非支配排序法求解例題二之f(X)收斂迭代圖........30
圖2.7本文使用文獻[14]非支配排序法求解Pareto結果圖...........33
圖2.8本文非支配排序法求解例題二之f(X)收斂迭代圖..............34
圖2.9本文非支配排序法求解Pareto結果圖..................................35
圖3.1例題一 之二維目標函數圖形...............................................39
圖3.2替換數位資訊法求解例題一之f(X)收斂迭代圖..................41
圖3.3非支配排序法求解例題一之f(X)收斂迭代圖......................42
圖3.4本文以改良飛回策略求解例題一之f(X)收斂迭代圖..........43
圖3.5Rastrigin 二維函數圖形........................................................45
圖3.6Rastrigin函數極值分佈圖......................................................46
圖3.7Rastrigin函數極值分佈與限制條件示意圖..........................47
圖3.8替換數位資訊法求解例題二之f(X)收斂迭代圖..................48
圖3.9非支配排序法求解例題二之f(X)收斂迭代圖......................49
圖3.10本文以改良飛回策略求解例題二之f(X)收斂迭代圖..........50
圖3.11替換數位資訊法求解例題三之f(X)收斂迭代圖..................53
圖3.12本文以改良飛回策略求解例題三之f(X)收斂迭代圖..........54
圖3.13替換數位資訊法求解例題四之f(X)收斂迭代圖..................57
圖3.14本文以改良飛回策略求解例題四之f(X)收斂迭代圖..........58
圖3.15壓力容器結構示意圖.............................................................60
圖3.16替換數位資訊法求解壓力容器之f(X)收斂迭代圖..............63
圖3.17非支配排序法求解壓力容器之f(X)收斂迭代圖..................64
圖3.18改良飛回策略求解壓力容器之f(X)收斂迭代圖..................65
圖4.110桿桁架結構及受力圖............................. ...........................68
圖4.2替換數位資訊法求解10之f(X)桿桁架迭代圖.....................70
圖4.3非支配排序策略求解10桿桁架之f(X)迭代圖.....................71
圖4.425桿桁架結構圖.....................................................................73
圖4.5替換數位資訊法求解10之f(X)桿桁架迭代圖.....................77
圖4.6非支配排序策略求解25桿桁架之f(X)迭代圖.....................78
圖4.7單臂電熱式微致動器示意圖............................. ...................80
圖4.8替換數位資訊法求解單臂微致動器收斂迭代圖.................83
圖4.9非支配排序法求解單臂微致動器收斂迭代圖.....................84
圖4.10雙臂電熱式微致動器示意圖................. ....... ....... ....... .......85
圖4.11替換數位資訊法求解雙臂微致動器收斂迭代圖.................88
圖4.12非支配排序法求解雙臂微致動器收斂迭代圖.....................89
	
表目錄
表2.1	例題一數值結果............................. .........................................30
表2.2例題二數值結果.......................................................................36
表3.1例題一之數值結果及比較............................. .........................44
表3.2例題二數值結果及比較...........................................................51
表3.3例題三之數值結果及比較............................. .........................55
表3.4例題四之數值結果及比較.......... .............. .............................59
表3.5壓力容器數值結果比較................................ ......... ................62
表4.110桿桁架結構最佳化分析結果表...................... ......... ..........72
表4.2設計變數與截面積對應表...... .... . ......... . ................. ...........75
表4.325 桿結構受力表..................................................................75
表4.425桿桁架設計結果比較...... ...............................................76
表4.5多晶矽材料性質... ..... .............................................................81
表4.6單臂設計變數與範圍... ..... .....................................................81
表4.7雙臂設計變數與範圍... ..... .....................................................86

[1]	J.Kennedy and R.C. Eberhart, “Particle Swarm Optimization,”International Conference on Neural Networks,IEEE,vol.4, pp. 1942-1948, November 1995.
[2]	Y. Shi and R. C. Eberhart, “A Modified Particle Swarm Optimizer,” IEEE, Evolutionary Computation, pp. 69-73, May, 4-9, 1998.
[3]	L.Wang, Q.Kang, H.Xiao, and Q.Wu, “A Modified Adaptive Particle Swarm Optimization Algorithm,” Industrial Technology ,IEEE, pp. 209-214, 2005.
[4]	R.C.Eberhart, and Y,Shi, “Comparing Inertia Weights and Constriction Factors in Particle swarm Optimization,” Evolutionary Computation,IEEE, vol 1, 84-88, 2000.
[5]	Y. Shi, and R.C.  Eberhart, .“Empirical Study Of Particle Swarm Optimization,” Evolutionary Computation, IEEE ,vol. 3,1945-1950,1999.
[6]	R. C. Eberhart and Y. Shi, “Particle Swarm Optimization: Development, Applications and Resources,” Evolutionary Computation,IEEE, vol. 1, pp. 81-86, 2001.
[7]	A.Ratnaweera, S.K Halgamuge, and H.C. Watson, “Self-Organizing Hierarchical Particle Swarm Optimizer with Time-Varying Acceleration Coefficients,” Evolutionary Computation, IEEE,vol.8
[8]	F. van den Bergh and A. P. Engelbrecht, “A Study of Particle Swarm Optimization Particle Trajectories,” Information Sciences,vol. 176,No. 8, pp. 937-971, April, 22, 2006.
[9]	M.Clerc and J.Kennedy,. “The particle swarm: Explosion, stability, and convergence in a multimodal complex space, ” Evolutionary Computation, IEEE ,vol. 6, 58-73,2000.
[10]	X.Hu, R. Eberhart, and Y. Shi, “Engineering Optimization with Particle Swarm,” Proceedings of the 2003 IEEE Swarm Intelligence Symposium, Indiana, USA, April 24-26, pp. 53-57,2003 .
[11]	P.Hajela, and J. Yoo, “Constraint Handling in Genetic Search Using Expression Strategies”, AIAA Journal, Vol. 34, No. 12, pp. 2414-2420, 1996.
[12]	管姿倫,“類免疫型生物演算法的最佳結構設計,”淡江大學機械與機電工程學系碩士班碩士論文,民國91年6月.
[13]	K.Deb, K.Srinivas, “Multi-Objective Optimization using Nondominated Sorting in Genetic Algorithms”, Evolutionary Computation, vol. 2, pp. 221-248,1994.
[14]	陳志忠,“含突變機制的粒子群演算法於多目標最佳化” 淡江大學機械與機電工程學系碩士班 碩士論文, 2010.
[15]	H. Guckel and J. Klein and T. Christenson and K. Skrobis, “Thermo-Magnetic Metal FlexureActuators,” Solid-State Sensor and ActuatorWorkshop, 5th Technical Digest., IEEE, pp. 73-75,1992.
[16]	M. K. Seyed and S. Mahnaz, “Optimal design analysis of Electro thermally Driven microactuators,” Microsystem Techonlogies, Vol. 16, No. 7, pp. 1062-1071, 2009.
[17]	R.Eberhart, and J.Kennedy,“Swarm Intelligence”, Morgan Kaufmann Publishers Inc,2001.
[18]	C.Reynolds, “Flocks, Herds and Schools: A Distributed Behavioral Model, ” ACM SIGGRAPH Computer Graphics, Vol.21, No. 4, pp. 25-34,1987.
[19]	I.L.Bajec, and F.H.Heppner, “Organized Flight in Birds,” Animal Behaviour, Vol. 78, No. 4, pp. 777-789,2009.
[20]	E, Selous., “Thought-transference (or What?) in Birds” Constable, London ,1931.
[21]	K.Deb, “Multi-Objective Optimization Using Evolutionary Algorithms”, John Wiley & Sons, Chichester, U.K.,2001.
[22]	K.Deb, “An Efficient Constraint Handling Method For Genetic Algorithms”, Computer Methods in Applied Mechanics and Engineering, Vol. 186, pp. 331-338,2000.
[23]	Z.Michalewicz, “Genetic Algorithms, Numerical Optimization and Constraints”, L. Eshelman (Ed.), Proceedings of the Sixth International Conference on Genetic Algorithms, Morgan Kauffman, San Mateo, pp. 151-158,1995.
[24]	Z.,Michalewicz, and M.Schienauer, “Evolutionary Algorithms for Constrained Parameter Optimization Problems”, Evolutionary Computation, Vol.4, No.1, pp.1-32,1996.
[25]	C.A.C. Coello, Constraint-handling using an evolutionary multiobjective optimization technique, Civ. Eng. Environ. Syst. 17 pp.319–346,2000.
[26]	K.Deb, and S.Gulati, “Design of truss-structures for minimum weight using genetic algorithms. ”Finite Elements in Analysis and Design, pp.447-465, 2001.
[27]	蘇育德,“可變長寬的電熱式微致動器最佳化設計” 中華明國機械工程學會第二十八屆全國學術研討會, 2010.
[28]	潘震澤，人體生理學，合記書局有限公司，台灣，2005.
[29]	蘇育德,“多目標策略限制的基因演算法於電熱微致動器最佳化” 淡江大學機械與機電工程學系碩士班 碩士論文, 2010.