本論文提出結合粒子群演算法與差分演化演算法的雙演化演算法於結構最佳化設計中。粒子群演算法為仿生演算法，其特點為收斂速度快、參數設定少、搜尋範圍廣及具有記憶性。差分演化演算法為演化式演算法，其優勢在於參數設定及架構簡單、能維持母體的多樣性、高效能及高精確度等。雙演化演算法則是利用粒子群演算法與差分演化演算法兩者同時進行運算，優點在於互相補足缺點，利用差分演化演算法的多樣性使其跳脫區域最佳解，而利用粒子群演算法的記憶性使局部搜尋更加完善，利用兩者不同的搜尋方式，並將兩者演算法之最佳值做比較及分享，以獲得最佳值。本文中針對粒子群演算法提出變速因子的改良機制，藉由判斷粒子的區域最佳解與全域最佳解的距離來改變搜尋的步伐，以改善搜尋過程之收斂效率。本研究在差分演化演算法中，選取適合的突變方式可增加解的多樣性以彌補粒子群演算法之不足。 本研究將ANSYS有限元素分析軟體中的APDL語法與FORTRAN程式結合成一系統程式，並以五種不同的範例執行結構最佳化設計。範例中將結構最佳化問題轉為數學函數，再利用雙演化演算法對結構系統執行最佳化設計。由數值分析範例之結果，顯示雙演化演算法求出的解比單獨使用粒子群演算法和差分演化演算法求出的解為佳且應用在結構之最佳化設計上皆可得到不錯的結果。 The PSO-DE Dual Evolution Strategy was applied to optimum design of structures in this study. Particle Swarm Optimization (PSO) algorithm is a bionic technique which has fast convergence, less parametric setting and wide search range with memory. Differential Evolution (DE) algorithm is an evolutional technique that has advantages of easy to implement, little parameter tuning requirement, and also exhibits reliable, accurate and fast convergence. In this study, a Dual Evolution Strategy that includes an improved Particle Swarm Optimization algorithm and a Differential Evolution algorithm is proposed for structural optimal design. The improved Particle Swarm Optimization algorithm adopts an alternation velocity factor that changes with the particle distance between the local and the global optimal solution. In the Differential Evolution algorithm, an appropriate mutation is selected to increase domain flexibility and improve the deficiency of Particle Swarm Optimization algorithm. This Dual Evolution Strategy utilizes the domain flexibility offered by the Differential Evolution algorithm and the local search memory of the Particle Swarm Optimization algorithm. The two algorithms are computed independently , the best result is obtained and shared between the two algorithms at each iteration. Numerical analysis showed that the results obtained from the Dual Evolution Strategy are better than those obtained individually from the Particle Swarm Optimization algorithm or Differential Evolution algorithm.
