基因演算法於鋼構斜張橋斷面及幾何最佳化設計之應用

Abstract

本文為研究鋼構斜張橋最小重量的最佳化設計，以橋之纜索、主桁、橋塔之橫斷面為設計 參數，在滿足設計應力的限制下，使用基因演算法仿傚自然界隨機選擇及基因機制的搜尋 技術，藉由隨機性的篩選後代(複製)、基因配對交換、基因突變以及個體由外界環境評估 其適應程度的結果產生新個體，再根據物種競爭原則以「適者生存，不適者淘汰」來演化 ，將這些新產生出來的族群當作是搜索的新出發點，對不同特性空間的點進行逐次的搜索 ，可嚴密的解釋自然系統中的選擇性及適應性，易設計一個具有和自然系統機制類似特性 的智慧系統軟體。由橋身幾何固定的線性初形分析的結論得知突變率及懲罰因子的改變， 其橋的最小重量也隨之不同。由此，選擇一最適當的突變率及懲罰因子，分析線性與非線 性橋身幾何變化最小重量的情況，發現考慮橋身幾何變化比幾何固定的最小重量值更為經 濟。經由這些例子，可知基因演算法可快速搜尋至不錯的結果，但發現有多條纜索拉應力 遠小於容許拉應力。為改善此缺陷，利用由基因演算法所得最小重量，依據滿載應力設計 (Fully Stress Design) 修正斷面，可得更佳的最小重量。 An approach for optimization design of steel cable-stayed bridge is developed, with the cable anchor position on the main girder, pylon as well as the sectio nal dimensions of the member elements as the design variables. The weight mini mization problem under stress constraintsis solved by using a modified genetic algorithm with penalty function.The penalty function is employed in the modifi ed genetic algorithm(GA)to amend the objective function and transform a popula tion of individualswith its associated value of fitness. The modified GA algor ithm is based on the Darwinian principle of survival of fittest and it isimple mentedin three base operators, reproduction, crossover, and mutation. Two ex amples, fixed and variable geometry of bridges, havebeen used to verify the pe rformance of the modified GA algorithm.Investigating from illustrative example s, it is shown thatthe minimum weight of bridges is highly depend upon the mut ation rateand penalty factor used. Moreover, the design variable, pylon height , demonstrated its significant role in determination of minimumweight. In addi tion, the solution obtained by the modified GA algorithm is acceptable in a r apid convergence rate. Finally, a robust modified GA is presented by integrati ng Fully Stress Design approach and a near-globaloptimum solution is obtained.