結合鯨魚演算法與模擬退火法於結構最佳化設計之研究

Optimum Design of Structures by A Hybrid Whale Optimization Algorithm and Simulated Annealing

邱垂泯(Chuei-Min Chiu)

指導教授 ： 張永康

淡江大學/工學院/航空太空工程學系碩士班/碩士(2023年)

https://doi.org/10.6846/TKU.2023.00012

摘要

本論文結合鯨魚演算法與模擬退火法於結構最佳化設計中。鯨魚演算 法是一種
模擬自然界中座頭鯨獨特的獵捕行為所構築出來的仿生演算法。 鯨魚演算法擁有三
種搜尋方式，分別為探勘階段以及開發階段中的收縮環繞機制和螺旋更新位置，其
架構簡單且擁有較少的參數設定，以隨機的方式進行搜尋，因此可以做大範圍之全
域搜尋。模擬退火法為 根據金屬物質在退火過程中的物理現象和最佳化問題的求解
過程非常相似而啟發的方法， 並透過波茲曼函數判斷問題解被接受機率，以增加跳
脫區域最佳解往全域最佳解的機會 。鯨魚退火演算法則為結合鯨魚演算法與模擬退
火法進行最佳化運算，利用鯨魚演算法 特殊的更新方式搜索最佳解做為參考，並且
透過模擬退火法中的波茲曼函數最為突變機制提供給鯨魚演算法更多的求 解機會
改善鯨魚演算法容易落入區域最佳解之缺點。 本研究結合兩種演算法之優點，並由
數值分析計算的結果顯示鯨魚退火法應用於結構最佳化設計可得到不錯的結果。

關鍵字

鯨魚演算法 ； 模擬退火法 ； 最佳化設計

並列摘要

The Hybrid Whale Optimization Algorithm (WOA) and Simulated Annealing (SA) were adopted in optimum design of structures in this study. The Whale Optimization Algorithm is a bionic algorithm constructed by mimicking the unique hunting behavior of humpback whales in nature. The main features are exploration phase, shrinking phase and spiral update position, to execute global search.SA is a method inspired by the similarity between the physical phenomenon of the metal substance in the annealing process and the solution process of the optimization problem. The possibility of local optimum jump to global optimum can be determined by the probability of Bozemann function. This hybrid method combines the advantages of the two algorithms; first the WOA was applied to search the best solution, then using SA to find the probability of global optimum. The final results in numerical analysis showed that near optimum solution can be obtained by the hybrid method.

並列關鍵字

Whale Optimization Algorithm ； Simulated Annealing ； Optimum Design

參考文獻

[1]Mirjalili, S. and Lewis, A., “The Whale Optimization Algorithm,” Advances in Engineering Software,Vol. 95,pp.51-67,2016.

[2]Mirjalili, S., Mirjalili, S. M. and Lewis, A., “Grey wolf optimizer, ” Advances in Engineering software, pp. 46-61, 2014.

[3]Trivedi, I.,Jangir, P., Kumar, A.,Jangir, N. and Totlani, R.,“A Novel Hybrid PSO-WOA Algorithm for Global Numerical Functions Optimization”Advances in Computer and Computational Sciences,Vol. 554 , pp.53-60 , 2016

[4]Kaveh, A. and Ilchi Ghazaan, M.,“Enhanced Whale Optimization Algorithm for Sizing Optimization of Skeletal Structures,”Mechanics Based Design of Structures and Machines, Vol. 45, issue 3, pp. 345-362, 2016.

[5]Jadhav, A. N. and Gomathi, N., “ WGC: Hybridization of Exponential Grey Wolf Optimizer with Whale Optimization for Data Clustering,” Alezandria Engineering Journal. pp. 1-16, 2017.