結合自適應共振理論與微分演算法於結構拓樸最佳化

Integrating Adaptive Resonance Theory with Differential Evolution for Topology Optimization of Structure

杜冠賢(Kuan-Hsien Du)

指導教授 ： 吳俊瑩

大同大學/工程學院/機械工程學系所/碩士(2011年)

摘要

微分演算法已被廣泛的應用到各個領域，但原始的微分演算法較適用於實數的最佳化問題，不能用在二進制的結構拓樸最佳化設計上，而改良微分演算法則可用在實數和二進制的最佳化問題。本研究結合自適應共振理論於改良微分演算法的架構，利用自適應共振理論的歸類能力保持搜尋時的廣度，以同一歸類族群的共同特徵以提升收斂速率。為了解自適應共振理論於改良微分演算法的特性及可行性，本研究採用數個與參考文獻相同終止條件的測試方程式以驗證正確性與執行效率。並將結合自適應共振理論的改良微分演算法應用在結構拓樸最佳化設計上。由結果顯示自適應共振理論不論在實數測試函數或是二進位結構拓樸最佳化問題都能提升改良微分演算法的搜尋廣度、收斂性及效能。

關鍵字

自適應共振理論 ； 微分演算法 ； 最佳化

並列摘要

Differential evolution has been applied in many engineering fields, but the original differential algorithm can be used only on the real number optimization problems. It still has a difficulty in dealing with binary optimization problems due to the fact that the representation of design variable is a real-value type. In order to develop a differential evolution algorithm which can be suitable for both real-valued and binary optimization problems, a modified binary differential evolution is integrated with adaptive resonance theory neural network in this study. The clustering capability of adaptive resonance theory can maintain population diversity during evolution process and the common characteristics of classified group can accelerate the convergence. In order to understand the performance and the viability of developed framework, several test functions are utilized for demonstration by using same stopping criteria applied in the reference. The developed modified binary differential evolution with adaptive resonance theory is also used in structural topology optimization problems. From results, it is shown that adaptive resonance theory can improve the modified binary differential evolution algorithm in population diversity, convergence rate and search performance simultaneously in dealing with real-valued test functions and binary topology optimization problems.

並列關鍵字

Adaptive Resonance Theory ； Differential Evolution ； Optimization

參考文獻

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