本研究旨在發展進階新型三點近似方法，建構替代目標函數或限制條件中無顯函數的最佳化問題，發展數學模型並探討求解策略。以新型三點近似法為基礎，改善其指數不可調整之性質，以可調整指數之中介變數，發展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。以三個參考點的方式，較大的近似區間，提升最佳化求解效率及較大機率得到全域解之可能性。 針對進階新型三點近似函數進行數值測試，並與發展基礎型的新型三點近似法做比較，討論其誤差情形及有效近似範圍。擬定一套序列近似最佳化策略，包括三個參考點的選取方式、搜尋區間的調整、移動限制縮減調整規則及收斂策略，探討其合理性及有效性。 本研究也探討有限元素分析軟體ANSYS及最佳化數值工具Visual Doc的結合性，使用參考文獻中的範例做測試，與文獻等研究工具比較得知，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，驗證進階新型三點近似法於最佳化設計的有效性與實用性。 Some optimization and finite element software are well-developed during last two decades that provide very efficient tools for engineering design and analysis. Although individual software is useful in its specialized function, however, it is not convenient of cooperating two soft wares into one phase for engineering application. This paper presents some examples of uniting two specialized software to perform engineering design optimization. Particularly, in a structural optimization problem takes considerable computation of finite element analysis and somehow increase the nonlinearity of problem characteristic. A general recognized strategy of dealing with this difficulty is to adopt the approximation method of transforming some mathematical functions. In design optimization model, the objective function or some constrained functions require to transform to approximate functions. One-point or two-point approximations are relatively simpler methods in this category. Because the desk-computer has a great computation speed, the recent development of those approximation techniques had explored three-point approximation technique. The most recent development is called the new three point approximation (nTPA). This thesis work applies the approximation to 2nd order term in Taylor series where only the diagonal items are included, as called advanced new three point approximation (AnTPA). The feature of AnTPA includes the computation of whole index parameters using for intervening variable. So that there comes up 3n+2 coefficients required to solve. The solution is complicated as compared with nTPA of 2n+2 coefficients. This thesis describes the complete mathematical modeling and the error analysis of proposed AnTPA with several numerical problems. The AnTPA is then applied to engineering design optimization. By considering the characteristic of AnTPA, an efficient optimization process is consequently developed and presented. The presented numerical processing shows the promotion of the solution efficiency for some structural optimization problems. The proposed AnTPA can be applied to large-scale structural optimization problems to verify the solution effectiveness.