改良式基因演算法對二維鋼構房屋結構斷面最佳化之研究

Abstract

使用基因演算法於鋼結構最佳化設計問題已經蓬勃發展多年，然於最佳化過程中大多使用未經業界認證自行編寫之結構分析程式。本論文嘗試發展一改良式基因演算法於鋼結構最佳化設計問題上，藉由兩個新的策略來改善基因演算法之搜尋效率：1.使用動態邊界逼近法掏選初始基因；2.使用機率式移民策略。前者試圖找出靠近局部極值之解為初始族群，後者則有效縮減移民之探索範圍，避免在無效解空間浪費運算時間。最佳化過程中結構分析程序將以業界常用之結構分析軟體(SAP2000)執行，希望能達成最佳化結果能直接運用於實務之目標。文中使用一個2D單跨十層樓鋼構房屋構架為測試與驗證之最佳化模型，並對於不同的初始族群產生方法混合比例(隨機產生+動態邊界逼近法產生)做了詳細的研究。結果顯示使用動態邊界逼近法產生所有初始族群者，可得最輕(最佳化)之桿件組合(33974Kg)，而隨機產生初始族群者最佳化桿件組合為41702Kg。再者，將研究中最佳化桿件組合與各文獻之結果比較，若將各文獻所求得的最佳斷面組合使用SAP2000分析時，發現文獻中最佳斷面組合皆有部分桿件違反限制條件。而本研究所提出的最佳斷面組合其各桿件斷面應力比(實際應力/容許應力)皆位於0.925~0.987範圍內，且未違反任何限制條件，研究證明此最佳化斷面組合之經濟性且可實際運用於工程實務中。而且，新的基因演算法在兩策略增強下，收斂次數與僅使用機率式移民策略者相較，至少加速了500個演化世代，證明在基因演算法中掏選初始基因可有效加速演化的進行。而藉由比較隨機移民與本研究所提出機率式移民之機率表可知，機率式移民策略成功縮減了搜尋空間，並減少無謂的時間浪費。 關鍵字：基因演算法、最佳化、SAP2000、剛架、動態邊界逼近法、DBA、機率式移民

This work presents an enhanced genetic algorithm (GA)-based optimization model for optimizing design of 2D nonlinear steel-framed structures by integrating two new strategies, dynamic boundary approach (DBA) and probability-based immigration strategy. The strategy of DBA is utilized to provide feasible initial individuals that close to local or global minimum as the initial population for GA within a small number of iterations. In order to increase the exploitation in search, probability-based immigration strategy settles new individual out of original population from a probability-based reduced search space. A case of optimal design of 2D nonlinear steel-framed structure, based on the requirements of the AISC-LRFD 99 specification, is used to verify the performance of the proposed GA. In engineering practical purpose, SAP2000 is employed in structural analysis process. The numerical results reveal that the DBA and probability-based immigration strategies can provide good initial population with a few steps and can provide good individual during later search steps, respectively. Comparing with other work, the proposed enhanced GA not only achieves a better optimal solution but also converge to the solution with less iteration. Keyword: Genetic algorithm, Optimization, SAP2000, Frame, Dynamic boundary approaching, DBA, Probability-based immigration