本文主要是針對離散變數、連續變數、混合變數之結構最佳化設計問題，提出以粒子群演算法(Particle Swarm Optimization , PSO)為基礎結合差分演化法(Differential Evolution , DE)的一種混合啟發式搜尋法，稱為PSO-DE。PSO和DE均為一隨機搜尋法，且都具有全域搜尋的能力。從以往的研究結果中可看出PSO的缺點，即在求解最佳化問題的搜尋初期收斂速度較快，到了後期搜尋階段隨著粒子群逐漸往群體最佳解的粒子靠近，因而喪失了整個群體的多樣性，導致搜尋後期收斂速度變慢且粒子易陷入局部最佳解。為了解決此一缺點，本文將採用DE演算法來增加PSO群體中之多樣性，期望能降低粒子容易陷入局部最佳解的機率。然後藉由多種不同設計變數類型的結構輕量化設計問題來探討其適用性和影響求解品質與效率的相關參數，並由設計結果之比較，來探討本文所發展之PSO-DE的優缺點。比較結果發現PSO-DE在求解多數混合變數和離散變數之結構最佳化問題時，都具有不錯的求解穩定性和搜尋性能。 This article is devoted to the presentation of a hybrid heuristic searching algorithm, namely PSO-DE, for the optimum design of structures with discrete, continuous and mixed variables. PSO (Particle Swarm Optimization) and DE (Differential Evolution) are both the random search methods and capable of performing global search. The main deficiency of the PSO is that all particles have the tendency to fly to the current best solution which may be a local optimum or a solution near local optimum. In this case, all particles will move toward to a small region and the global exploration ability will be weakened. To overcome the drawback, this research uses the DE algorithm to increase the diversity of PSO groups, hoping to reduce the probability of particles that trapped in local minimum. More than ten typical structures in the literature are used to validate the effectiveness of the algorithms. The results from comparative studies of the PSO-DE against other optimization algorithms are reported to show the solution quality of the proposed PSO-DE algorithm.
