桁架結構最佳化設計使用基因演算法與窄化空間技術

Abstract

基因演算法(Genetic algorithm，GA)是一種有效的全域搜尋技術，不僅可以處理離散變數(discrete variables)的最佳化問題，同時具有克服局部最小化的能力。以基因演算法處理離散斷面尺寸桁架結構最佳設計已是一個很普及的方法，然而隨著桁架結構桿件數目不斷增加，基因演算法搜尋空間亦隨之擴大，造成全域搜尋過程收斂緩慢。本論文針對桁架結構最佳化問題提出一個窄化空間技術，利用縮小搜尋空間的策略以提高基因演算法的收斂速度。首先以滿載應力設計(Fully stress design, FSD)概念建立最佳桁架拓樸，接著將滿載應力桁架結構透過一組啟發式法則放大其桿件斷面尺寸並將放大後的斷面尺寸作為搜尋空間的中心點，最後使用基因演算法於中心點鄰近空間進行搜尋。本論文所建立的窄化空間技術對最大與最小斷面尺寸限制、單載與多組載重條件、壓力桿件挫屈等問題上均有著墨。經由八個平面與空間桁架的數值案例測試，證實窄化空間技術確能輔助基因演算法讓桁架結構最佳化設計的電腦計算成本大幅減少。

Genetic algorithm (GA) is an efficient search technique in global space. It can not only deal with optimization problems with discrete variables, but also has ability to overcome the local minimization problems. Using GA to process the optimization design of discrete cross-section size for trusses has become a popular approach.For this problems the search space of GA may expand as the number of members of truss increasing; consquently it makes the process of global searching to converge slowly. This study proposes a narrowing search space technique for optimization design of trusses; it based on the strategy that reduces search space of GA to improve the speed of convergence. First it uses concept of fully stress design (FSD) to figure out optimal topology of a truss; then it takes a set of heuristic rules to enlarge cross-section sizes of a truss structure that was designed by FSD and takes the cross-section size that was enlarged to be the center of search space; finally it searches solutions of the problem nearby the center by GA. The narrowing space techniques that were implemented by this study were applied to solve constrainted optimization problems that include maximum and minimum cross-section size constraints, single load and multi-load case, and buckling stress constraints etc. Total eight planar and space truss design problems have been adapted to verify the performance of the porposed approach. The result reveales that the narrowing space techniques assist GA to reduce a lot of computational costs of optimization designs of truss structures.