本研究旨在用回應表面建構替代目標函數或限制條件中具有不明確資訊且無顯函數的最佳化問題，發展數學模型並探討解題程序。以有限元素為基的最佳化及回應表面法建構具有模糊參數及變數的數學模型，探討求解模糊參數與變數的方法與步驟。將原題目從模糊性質轉為明確性質，針對其中不完整與不合理處，利用合理穩健化階切解法，建構合理的歸屬函數，配合直接單切法，求取唯一的設計解。用回應表面最佳化求解時，選取適當的起始點並採用連續縮減空間法逼近最佳解，於最佳化迭代過程中，逐步將最佳點加入實驗點中，使回應表面逐漸改變。處理離散變數最佳化問題時，用回應表面法結合分支與邊界法的求解策略，求取局部最佳解並將其調整至靠近的離散值，重複的加入離散點至實驗群中並重新建構回應表面，將最終的收斂值調整至最靠近的離散解。文中以十桿桁架為例，楊氏係數為模糊參數，桿件截面積包含連續型(部分為模糊數)及離散型設計變數，限制條件中含有允許模糊值。以位移最小化為單目標設計，再同時考慮桿件結構重量最小化為雙目標設計，用有限元素為基的最佳化與應用回應表面法求解皆能獲得正確的結果。 A design optimization problem contains fuzzy information such as fuzzy parameters and variable is often confronted in engineering applications. Particularly in the modern engineering problems, finite element method is popular used for the analysis in various engineering optimization problems with fuzzy information. This thesis presents the study of finite-element based engineering design optimization containing fuzzy parameters and fuzzy design variables; and the crisp design variables contain a mix of real continuous variables and discrete variables. For dealing with such kind of problem, the optimization with approximation technique of applying the response surface method is developed and presented in this thesis. The simple first-order response surface approximation with suitable sequential searching technique including confidence move limit technique has been used for locating the optimum. There are three critical sides considerably influence the result. The first one is how to deal with the fuzzy optimization problem containing fuzzy information existing in design variables and parameters so that a crisp optimization can be solved. Because of the fuzzy region of each fuzzy variable is vary, it is required to consider a way of design control so that the performance robustness can be achieved. The second one is how to deal with the discrete variables in the approximation environment constructed by response surface function. The third one is how to perform the optimization searching process to obtain the optimum result. For applying the proposed design methodology to the two-objective problem, the important point is how to define and select the ideal solution corresponding to individual objective during the whole optimization searching process. All above three considerations are presented in the thesis. One ten-bar truss with finite element analysis optimization problem is adopted in the thesis as a model for proposed development and demonstrating the presented concept, process and application.
