中文摘要
本文主要是針對含離散設計變數之結構最佳化設計問
題，提出一種結合離散拉格朗日法(DLM)和遺傳演算法(GA
)的混合式全域搜尋法。DLM為一種鄰點搜尋法，過去的研
究結果顯示此法在中、小型結構問題上的求解能力極佳，
惟處理多極值之大型問題時，雖然求解的品質不錯，但因
屬局部搜尋法，故若參數調整不當，則仍有落入較差局部
最佳解的缺憾。GA為一隨機搜尋法，具全域搜尋之能力，
但所使用之策略及可調整之參數甚多、處理大型結構相當
耗時、且缺乏強固數學理論所建立之收斂準則，故即使所
得之解為一局部最佳解，卻無從驗證。因此，本研究嘗試
利用GA全域搜尋的能力，配合DLM具備強固之數學收斂準
則，將此兩種演算法加以整合，以改善整體的搜尋效能。
研究中，首先針對大型結構提出一種合向量移動策略
，來加速DLM的求解效率，並提出一種淘汰策略和調整懲
罰參數的方法，藉以改善傳統GA求解的穩定性，最後再根
據結構最佳化設計問題的特性，提出一種連續次區域搜尋
觀念，同時修改DLM的鄰點搜尋方法，發展出GA-NB和DLM-
GA-NB兩種混合搜尋法。數個結構輕量化設計問題將分別
用來探討各種搜尋方法的適用性和影響各方法求解品質與
效率的相關參數，並藉由和文獻設計結果之比較來印證本
文所發展之搜尋方法的優缺點。結果顯示：(1) 合向量移
動策略可以大幅改善DLM求解大型結構問題的效能；(2)
連續次區域搜尋之GA-NB法較傳統GA具備更為強健且快速
的搜尋能力，非常適合求解中、小型結構系統的最佳化問
題；(3) DLM-GA-NB混合求解策略則可進一步改善DLM的求
解品質，非常適合求解中、大型結構系統之離散最佳化問
題。

Abstract
This report is devoted to the presentation of
two hybrid search algorithms, namely GA-NB and
DLM-GA-NB, for discrete sizing optimization of
structures. The structure is subject to stress and
displacement constraints under multiple load
cases. The DLM (discrete Lagrangian method) is an
adaptation of the usual Lagrange multiplier method
for continuous problems. Previous applications of
the method to structural optimization problems
using available sections have shown that it is
robust and validate for solving small- to medium-
scale structures. Although good quality solution
for large-scale structures can also be acquired
using the method, it strongly depends on the
weighting parameter selected by the user. On the
other hand, GA has the ability in performing
global search. However, the solution quality of
the method relies on many factors, such as selec-
tion, crossover and mutation schemes, probabili-
ties of crossover and mutation, and so on. It is
also computational expensive for solving large-
scale structures. To enhance the efficiency and
robustness of the search for optimal structural
design problems, an enhancing schemes for accele-
rating the search speed of the DLM and, the two
hybrid search algorithms are proposed. A novel se-
quential regional GA searching concept is also
developed and been implemented into the hybrid
search algorithms presented in this report. More
than ten typical structures studied in the litera-
ture are used to validate the effectiveness of the
algorithms. It is shown that the algorithms pro-
posed in the report are valid and robust in de-
signing structures of weight minimization problems
using available sections.

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