PSO-SA混合搜尋法與其他結構最佳化設計之應用

A PSO-SA Hybrid Searching Algorithm for Optimization of Structures

莊玟珊(Wen-Shan Chuang)

指導教授 ： 莊德興

國立中央大學/工學院/土木工程學系/碩士(2007年)

摘要

本文主要是針對連續變數、離散變數、混合變數之最佳化設計問題，提出兩種以結合粒子群演算法(PSO)與模擬退火法(SA)的混合搜尋法，即PSO–SA–Pg與PSO–SA–Pi。PSO為一隨機搜尋法，具有全域搜尋之能力，其概念簡單且不需調整過多參數。過去研究結果顯示，PSO常在求解最佳化問題的搜尋初期收斂速度較快，但後期搜尋階段隨著所有粒子逐漸往搜尋空間之整體最佳解靠近，因而喪失整體搜尋之多樣性，導致後期收斂速度變慢且容易陷入局部最佳解。為了改善此缺失，本文採用SA演算法作為局部搜尋工具，並將PSO與SA兩種演算法加以整合，期望能使粒子有效地進行全域和局部搜尋，以改善整體的搜尋性能。數個結構輕量化設計問題將分別用來探討其適用性和影響求解品質與效率的相關參數，並藉由設計結果之比較，來探討本文所發展之兩種混合搜尋策略的優缺點。比較結果發現PSO–SA–Pg的求解品質較佳，而PSO–SA–Pi在求解多數混合變數之最佳化問題時，其求解穩定性相對較優。

關鍵字

結構輕量化設計 ； 模擬退火法 ； 粒子群演算法 ； 混合搜尋法

並列摘要

This report is devoted to the presentation of two hybrid search
algorithms, namely PSO–SA–Pg and PSO–SA–Pi, for optimum design of
structures with continuous, discrete and mixed variables. The PSO
(Particle Swarm Optimization) is an evolutionary computation technique
which has ability in performing global search. The main deficiency of
PSO is that all particles have the tendency to fly to the current best
solution which may be a local optimum or a solution near local optimum.
In this case, all particles will move toward to a small region and the
global exploration ability will be weakened. To overcome the drawback
of premature convergence of the method and to make the algorithm
explore the local and global minima thoroughly at the same time, two
hybrid search algorithms are proposed. More than ten typical structures
studied in the literature are used to validate the effectiveness of the
algorithms. The results from comparative studies of the PSO–SA against
other optimization algorithms are reported to show the solution quality of
the proposed PSO−SA algorithms. The advantages and drawbacks of the
two PSO–SA algorithms are also discussed in this report.

並列關鍵字

optimum structural design ； particle swarm optimization ； simulated annealing ； hybrid search algorithms

參考文獻

[1] Pedersen, P., “Optimal Joint Positions for Space Trusses,” Journal of the Structural Division, ASCE, Vol. 99, No. 12, pp. 2459