適應性網格基因演算法於結構拓樸最佳化之應用

Application of Genetic Algorithm in Structural Topology Optimization with Adaptive Mesh

10.29948/JAE.201010.0005

黃仲偉(Chang-Wei Huang)；陳北亭(Bei-Ting Chen)；吳啟誠(Chi-Cheng Wu)

基因演算法 ； 拓樸最佳化 ； 懲罰函數 ； 適應性網格 ； 影像處理 ； genetic algorithm ； structural topology optimization ； penalty function ； adaptive mesh ； image process

先進工程學刊

5卷4期（2010 / 10 / 01）

317 - 326

繁體中文

本研究利用基因演算法二進位編碼的特性於求解單一材料的結構拓樸最佳化設計問題。由於基因演算法屬於零階的最佳化方法，演進過程中無須計算目標函數和限制式的導數，配合懲罰函數的方式可在結構拓樸最佳化設計中考慮不同的功能限制式。數值模擬顯示基因演算法可提供設計者較佳的結構拓樸形狀，而所考慮的限制條件亦可適當的反映在最後所得的拓樸形狀之中。對於元素眾多結構所需的龐大演進世代數，本文所提之適應性網格的方式，可以有效減少傳統基因演算法得到最佳拓樸形狀所需的世代數。最後，本文利用影像處理的方式，可以有效解決棋盤式拓樸結構形狀的問題。

In this paper, the problem of structural topology optimization for single material is solved by making use of the binary codes characteristics of the genetic algorithm. Since the genetic algorithm is a zero-order optimization method, there is no need to calculate derivatives of both the objective function and the constraints in the iterative process. Different constraints can also be easily added by applying the concept of penalty function. Numerical examples demonstrate that the optimal structural topology can be obtained through the genetic algorithm. Also the topology obtained can properly reflect the presence of the constraints when different constraints are added to the pseudo-objective function. Moreover, for structures with large numbers of elements, the enormous computation time required for convergence in the genetic algorithm can be effectively reduced with the aid of the adaptive mesh proposed here. Finally, image process methods are adopted to solve the problem of the checkerboard pattern of structural topology.