改良微分演化法於結構最佳化

Modified Differential Evolution for Structural Optimization

曾科穎(Ko-Ying Tseng)

指導教授 ： 吳俊瑩

大同大學/工程學院/機械工程學系所/博士(2010年)

摘要

微分演化法是一種啟發式的最佳化方法，目前該方法已被廣泛地應用在求解
各種最佳化問題上。它的演化機制中，突變與交配，與其他啟發式的最佳化方法
相較下具有相對簡單且有效的優點。本研究提出了兩種改良微分演化法，自調性
多群微分演化法與改良式二進制微分演化法，來求解不同型態的結構最佳化問
題。本研究首先提出了一個自調性多群的微分演化演算法，本研究首先提出了一
個自調性多群微分演化法來提升原本微分演化法求解不同型態桁架問題的效
率。雖然本研究所提出的自調性多群的微分演化演算法在求解桁架問題上能夠找
到比其他文獻更佳的結果，受到演算法本身是實數型態所影響，在處理二進制最
佳化問題時仍然會有困難。為了讓微分演化演算法可以同時求解實數與二進制最
佳化問題，本研究提出另一個擁有新突變機制的改良式二進位微分演化法。該機
制具備了簡單的演化特性並且能夠泛用在實數最佳化與二進制最佳化問題上。為
了驗證改良式二進制微分演化法在搜尋最佳化結果的適用性，本研究先採用了一
些實數最佳化問題，包括測試函式與熱壓頭表面均勻度最佳化問題，以證明所提
出的改良式二進制微分演化演算法可以適用在求解實數最佳化問題。針對二進制
最佳化問題部分，本研究使用不同的拓樸結構最佳化問題來證明改良式二進制微
分演化法在求解二進制最佳化問題上有很好的可行性。從這些本研究驗證的結果
可以得知，本文所提出的改良式二進位微分演化演算法可以適用在參數與二進制
IV
最佳化問題上。除此之外，本文所找到的結構拓樸最佳化的解比一些相關參考文
獻中的結果好。

關鍵字

結構最佳化 ； 改良式二進制微分演化法 ； 自調性多族群微分演化法 ； 微分演化法 ； 拓墣結構最佳化 ； 數值最佳化 ； 桁架結構最佳化

並列摘要

Differential evolution (DE) is a heuristic optimization method used to solve many optimization problems in real-valued search space. It has the advantage of incorporating a relatively simple and efficient form of mutation and crossover. In this study, two modified differential evolution algorithm, adaptive multi-population differential evolution and modified binary differential evolution, have been developed for dealing with different types of optimization problems. The adaptive multi-population differential evolution (AMPDE), including a proposed penalty-based self-adaptive strategy and multi-population mechanism, is developed in this study to enhance the performance of optimum search in truss structure optimization problems. Although the efficiency of proposed AMPDE is better than original DE and other population-based methods, 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 new modified binary differential evolution (MBDE) with a simple and new binary mutation mechanism based on a logical operation is proposed in this study. The developed MBDE is suitable for dealing with binary and real-valued optimization problems. Some numerical optimization problems, including test functions and a uniformity optimization of heat bonder, are first used to validate the correctness of architecture and performance of optimal search of the proposed MBDE algorithm. Different structural topology optimization problems are utilized to illustrate the high viability of the proposed algorithm in binary optimization problems. From the result of this study it is shown that the developed MBDE is suitable for dealing with real-valued and binary optimization problems. Besides, the proposed MBDE was observed to approach solutions better than those found in the references in the field of topology optimization of structures.

並列關鍵字

structural optimization ； modified binary differential evolution ； adaptive multi population differential evolution ； numerical optimization ； truss structure optimization ； topology optimization of structures ； differential evolution

參考文獻

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