本研究以進階新型三點近似法為基礎，改善最佳化過程中可能會遇到的奇異點，引入移位技術作為中介變數，發展加強進階新型三點近似法數學模型，並可滿足目前參考點及另兩參考點的函數值與靈敏度值，提升最佳化求解的準確性及穩健性。針對加強進階新型三點近似函數進行數值測試，並與進階新型三點近似法做比較，討論其誤差性及準確性。研擬定序列近似最佳化策略，其中包括參 考點的選取及收斂策略，以及探討求解的合理性與有效性。 接著應用在工程設計例題，以加強進階新型三點近似法求解，證明加強三點近似法的求解過程，能有效避免在最佳化過程中可能發生的奇異點，得到較準確的最佳化結果。本研究應用有限元素分析軟體ANSYS及最佳化數值工具Visual Doc結合，並用來求解光學檢測結構最佳化，並與參考文獻做比較。本文提出的近似方法及求解策略，能以較少的數值迭代次數得到最佳化收斂結果，驗證近似法於最佳化設計的有效性與實用性。同時進一步對體積及位移雙目標最佳化設計，得到距離理想點最靠近的平衡解，以達到光學檢測機構的設計需求。 On the basis of the advanced new three-point approximation method, this thesis presents a shifting level technique combined the advanced new three-point approximation applying on structural optimization problems. Numerical examples show that the singularity can be effectively avoided by shifting level technique during optimization process. From the examination, it is verified that fewer iterations is required than other approximation optimization. The numerical error and the numbers of convergence can be reduced as well. The completed optimization process including moving region are re-examined and proposed in the thesis. A large-scale optical inspection structure for modern wafer manufacture is presented in the thesis. To promote the precision of quality measurement and inspection, it is necessary to increase the structural stiffness and to optimize the structural behavior control. In the beginning, the finite element analysis must be successfully applied to the correct model, and then an appropriate optimization model must can be proposed. Thus, to minimize the structural weight and minimize critical deflection are two design objectives are assigned in the numerical optimization process. Consequently, the proposed enhanced three-point approximation optimization is applied to the solution process. A satisfactory result can be obtained in proposed approximated design optimization process.
