本研究嘗試將離散拉格朗日法應用於含有離散設計變數之結構最佳化設計，使結構物在符合應力及位移束制條件下，達輕量化設計之目標，其設計變數則為桿件截面積。文中首先介紹離散發格朗日法的基本理論，並探討此法影響求解品質以及收斂速度之參數。數個數值計算例的演算結果將用來說明此法求解的效率與品質。經與其他離散最佳化方法之結果比較，本文發現若適當調整目標函數之權因子與拉格朗日乘子的更新速度，則離散拉格朗日法經常可獲得較佳之解，同時亦具備非常強健之搜尋能力。 This research studies the minimum weight design of structures with discrete variables using the discrete Lagrangian method (DLM). The design variables are members’ cross-sectional areas. The constraints include stress, displacement and size constraints. In this report, the theory of the DLM is presented first, and parameters that influence convergence speed and solution quality of this method are investigated and discussed. The feasibility of the DLM is validated by several design examples. The results from comparative studies of the DLM against other discrete optimization algorithms are reported to show the solution quality of the DLM. It is shown that the DLM can often find better solution for the structural optimization problems than those reported in previous literature by using appropriate weighting and the changing speed for objective function.
