Contact Professor: Yeh-Liang Hsu (徐業良)

# 82碩士論文：模糊理論在工程最佳化的應用

一般工程最佳化設計問題有兩種模糊性：" 評估、計算最佳化模型的目標函數與限制條件 "的不確定性及" 建立最佳化模型 "的不確定性。當設計者建立了工程最佳化設計問題的數學模型後，大部份是以數學規劃法來求取最佳數值解。而在一般的工程最佳化問題中，設計者每每在模糊的環境下作決策，此種模糊性與以明確數學定義中的數學規劃法並不能完全配合，將導致迭代沒有效率，甚至發散。因此設計者通常使用的方案是依其對此問題的認識以及由前面迭代結果所得的資訊來判斷，在此最佳化過程中對演算法作人為的調整。在本論文中將以模糊控制的原理來模擬此人為的調整。在" 建立最佳化模型 "的不確定性方面，本文將以多目標最佳化問題為例說明此種模糊性的處理方式，一般解多目標最佳化問題的基本原則是把多目標結合成單目標，其方式是將各子目標依其重要性，給予比重，加以正規化合併成單目標；而這些比重值充滿主觀的不確定性，本研究中將整合分析層級程序法以及模糊理論來處理此不確定性。

# Engineering Design Optimization Using Fuzzy Theory

Engineering design optimization problems often have two kinds of "fuzziness": the uncertainty in evaluating the function values of the objective and constrants of an optimization model, and the uncertainty in building the optimization model. In an engineering process, usually a designer constructs a methematical model, the uses mathematical programming methods to solve the model. But the mismatch between the fuzzy engineering optimization problem and the crisply defined mathematical programming methods often leads to inefficiency or divergence of the process. A common strategy for designers is to monitor and keep "tuning" the optimization process in an interactive manner, using their knowledge of the problem and judgment on the information obtained from the previous iterations. This paper presents how the heuristic of this human supervision can be modeled into the optimization algorithms using fuzzy concept. Multi-objective optimization is used to illustrate how to deal with the second type of fuzziness. A common way to salve multi-objective optimization problems is to assion weights to each objective according to its importance, them hormalize each objective, then combine into a single objective problem. Here how to determine the weights is a fuzzy decision. This vesearch uses Analytical Hierarchy Process and fuzzy theory to deal with this problem.