改良式粒子群優化演算法於桁架結構最佳化設計之應用

Abstract

最近十年，粒子群優化演算法(Particle Swarm Optimization, PSO)是一款在結構最佳化設計問題上被探討的新方法。它是一種模擬群體智慧概念的仿生演算法，粒子群先是以全域搜尋的方式在搜尋空間內移動並且蒐集資訊，再逐漸轉成局部搜尋，最後則收斂到粒子群經驗中最好解的位置。粒子群優化演算法與其他仿生演算法相比具有參數設定簡單與快速收斂的優點，但是太過快速收斂有可能造成引導到局部最佳解。為了改善粒子群優化演算法在桁架結構最佳化設計問題上的效能，本論文提出兩個策略有效率的控制粒子群收斂過程。第一個策略取名「邊界移動法」，它是利用結構設計最佳解常位於搜尋空間內合理解與不合理解交界的特性，將全域搜尋階段的粒子瞬間移動到鄰近的交界區，因此降低粒子群在不重要區域搜尋的時間。第二個策略稱做「粒子飛離法」，將靠近收斂中心的粒子隨機拋離有限的距離，使得粒子與收斂中心的距離在指定的搜尋半徑內均勻分布，藉此避免粒子群過早收斂。為了測試改良式粒子群優化演算法在桁架結構最佳化設計問題上的效能，數個經典的桁架設計問題在本論文中被測試。測試結果指出，改良式粒子群優化演算法較傳統粒子群優化演算法能更有效率找到桁架設計最佳解。

The particle swarm optimization (PSO), simulating the flying of avian for searching food, is one of bionic algorithms and a popular method for finding the optimal design of structures in the last decade. The convergence speed of PSO is fast for the PSO gradually turns global search into local search. In the early search stage of PSO, a population particles move in the different regions of search space to collects information. Then, the particles converge to the same search region to search solutions according to their best experience and the best solution of swarm. However, the PSO may converge to the local minimum if its convergence speed is too fast. Therefore, how to balance the global search and local search in the PSO is an important research issue. This work proposes two novel strategies to improve the capacity of PSO for solving truss optimization design problems. The first strategy is quickly moving the particle to the boundary between feasible and constrains region. The other strategy is forcing the particle to a random position with random distance which closes to convergence center. Four examples of optimal design of truss structures are employed to verify the performance of the proposed improved-PSO algorithm. The analytic results reveal that particles can move quickly in early search stage based on the first strategy. Moreover, based on the second strategy, particles can keep converging to the global minimum when bounding to local minimum. The analytic results also expose that the proposed PSO algorithm outperforms standard PSO algorithm in convergence speed and the obtained optimal solutions.