基因演算法及圖形表示法在結構拓樸最佳化結構動力問題之研究

Abstract

本研究使用基因演算法搭配圖形表示法解決結構拓樸最佳化結構動力問題；基因演算法為常見之仿生演算法，其特性為全域式多點搜尋，雖然可以避免掉入局部最佳，但相對地其搜尋空間往往會應變數過多而使空間過大。本研究首先將基因演算法搭配圖形表示法使變數減少，並提出準初始隨機族群策略，藉由此策略使搜尋空間縮小，避免基因演算法浪費時間在探索沒有價值的區域以減少搜尋時間。最佳化過程中有限元素分析使用業界常用之分析軟體(SAP2000)做計算。最後為了驗證本研究所提出之準初始化隨機族群策略，使用兩個標準的結構動力拓樸最佳化問題來做測試，比對有使用策略與沒有使用策略之結果。結果驗證其最佳化之結構拓樸與文獻相同，且其第一特徵頻率亦達相對最大值。論文最後以一個新的三垮連續梁案例來驗證本文所提之最佳化模型。結果驗證在滿足體積比限制條件下，最佳化結構拓樸具有最大的相對第一特徵頻率值。

The genetic algorithm is the common bionic algorithm. Its feature is a global multi-search. Avoid falling into the local optimum. But its search space is often too large due to many variables. First, apply the genetic algorithms with a graphical representation to reduce the variable. And then, the new strategy-quasi random initial population is proposed. The search space will be become smaller by the new strategy. To avoid the genetic algorithm search the worthless search space. The optimization process is using finite element analysis software (SAP2000) to do the calculation. In order to verify the feasibility of the strategy, two benchmark problems are used to verify the performance of the proposed optimization algorithm. The last problem is new problem. The simulation results revel that the concluding topology of the structures are same as results in literature. The third problem also generated a final topology with a largest 1-st eigen frequency.