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  • 學位論文

結合粒子群算法與人工蜂群算法於最佳化設計軟體之斜張橋設計

Applications of PSO and ABC Algorithm Using Optimal Design Software in Cable-Stayed Bridge Design

指導教授 : 呂良正

摘要


斜張橋因其外形美觀、建造經濟,在中長跨度橋樑選型中經常獲得設計者的青睞。然而,由於斜張橋屬於高度靜不定結構,在結構設計過程中參數眾多,計算複雜,同時又受限於設計時程,故設計方案的經濟性及合理性很難確保。 本研究主要關注於斜張橋的結構最佳化設計,利用並拓展研究團隊開發之最 佳化設計軟體 SODIUMM,結合兩種全域搜尋演算法:粒子群算法和人工蜂群算法,分析典型的斜張橋模型,提出最佳化結果及其結構參數。 本文從結構最佳化基本概念開始,淺談最佳化設計軟體 SODIUMM 的特點與 功能,闡述一般的最佳化流程,並介紹 B-spline 方法。接著著重介紹粒子群算法 與人工蜂群算法,包括兩者的算法描述、參數選擇、適應值的評估、算法流程及 虛擬程式碼,同時通過九個典型的函數最佳化問題對它們進行模擬實驗,測試算 法的最佳化性能及穩定性。 將兩種算法新增到 SODIUMM 中,利用結構分析軟體 SAP2000 建立單塔斜 張橋有限元素初始模型,以斜張橋鋼索預力最佳化作為目標,進行最佳化設計。 除了粒子群算法和人工蜂群算法的最佳化結果,本研究中還利用了 COBYLA 演 算法的最佳化結果作為對照組。綜合比較最佳化結果可得到結論如下:粒子群算 法收斂速度快,但穩定性較差,會得到極好與極差的解;人工蜂群算法全域搜索 能力強,解的質量較高,但需求的運算量較大;兩種算法均比對照組結果優化 40% 左右。 在斜張橋實務設計中,可根據設計週期長短、模型複雜程度、經濟性目標等不同設計需求選擇合適的算法。

並列摘要


Cable-stayed bridge is one of the most popular bridge types chosen by architects and structure engineers in modern bridge design because of its aesthetic appeal and economy. However, the design of cable-stayed bridge is very complex due to its highly statically indeterminate. Design of such complex structure with a large number of design variables and constraints with traditional methods is inevitably time consuming and cannot guarantee the optimality of the final design. The research mainly focuses on the optimization design of cable-stayed bridge. A flexible structure optimization software, SODIUMM, is used and expanded with two global search algorithms, Particle Swarm Optimization (PSO) and Artificial Bee Colony (ABC). By applying these two global search algorithms, some specific problems of cable-stayed bridges can be solved and provide engineers better optimization pattern than by applying local search algorithms. Basic concept of structure optimization, main features of SODIUMM, optimization procedure and the B-spline technique are briefly introduced in sequence. Then PSO and ABC are thoroughly discussed, including algorithm description, parameter selection, fitness evaluation, algorithm process, and pseudo code. In order to test PSO and ABC about their optimize performance and stability, simulations are made by using 9 typical functions. After adding PSO and ABC into SODIUMM, SAP2000 is used to set up initial model of single pylon cable-stayed bridge, then choose the total bending energy of structure as objective function and analyze. In this research, a third algorithm named COBYLA is used for comparison. From the optimization results it is concluded that PSO will reach convergence fast, but with a relatively poor stability. Meanwhile, ABC is an effective global optimizer, but with relatively low efficiency. However, both PSO and ABC could get results 40 percent better than that getting from COBYLA. During an optimization design of cable-stayed bridge, engineers could choose a suitable algorithm according to the need for design time, the complexity of the model or the economic goal.

參考文獻


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