近二十年來所發展的多點搜尋最佳化解法，雖可得逼近的全域解，但普遍需要相當長的計算時間。傳統的單點搜尋法，雖求解計算時間較少，但卻無法確定得到全域解。尤其是應用最佳化於工程結構設計上時，需使用有限元素的分析，導致計算量遽增，需更多的計算時間，降低最佳化的實用性。本文即為探討多點搜尋的最佳化程序結合近似函數的可行性，藉由近似法的特性可減少有限元素分析的次數，減少最佳化程序的整體計算時間。 本文的多點搜尋最佳化方法是採用粒子群最佳化(PSO)，以改良飛回策略為處理限制的機制，合成含限制的粒子群最佳化(CPSO)。選用稱為Tana3的近似函數，建構該近似函數的C++程式，發展成可求解全域值的粒子群多點搜尋最佳化解法，稱為ACPSO。文中以十桿、二十五桿桁架及三維工具機床台等結構設計題目為例，建立有限元素分析模型，及應用ACPSO求解。同時與單點搜尋最佳化結果比較，並討論近似法的差異。比較討論的關鍵項目為全域最佳解的精確性有限元分析的次數與電腦計算時間，結果顯示ACPSO確實能有效率及得到全域解，適合應用於大型結構工程之最佳化設計。 In recent 20 years, multiple-points search optimization methods have been developed for possible global solutions. However, it is recognized that the computation is time consuming. In traditional single-point search optimization methods spend less computational time, but is easy falling into local optimum. In modern optimal engineering structural design, very often it requires the finite element (FE) analysis. This results in large amount computation time, and losing the efficiency. This thesis explores an selected multiple-points search optimization method including an approximation technique that can reduce the work of FE analysis as well as the computation time. The proposed multiple-points search optimization method in this thesis is particle swarm optimization (PSO). The improve flying back strategy for constraints handling developed in our research group had been combined in PSO resulted in CPSO. An approximation technique called Tana3 is adopted and developed in C++ programming. The CPSO combined Tana3 herein is named ACPSO. The structures of 10-bar truss, 25-bar truss and a two-pieces platform assembly for machine tool are utilized as examples to show the research work and performances. The mechanical analysis applied FE software named ANSYS that connected to ACPSO. The results are compares each other with or without Tana3 in multiple-points or single-point search optimization method. The final result shows that the presented ACPSO indeed can promote the computational efficiency and simultaneously the global design can be obtained. It is concluded that ACPSO is suitable for general large-scale engineering structural design optimization.
