本文主要是針對連續變數、離散變數、混合變數之最佳化設計問題，提出以結合改良過後的粒子群演算法(MPSO)與模擬退火法(SA)的混合高階啟發式演算法，即MPSO-SA。PSO為全域隨機性的搜尋法，其概念簡單且不需調整過多參數。從過去的研究中顯示出，PSO在求解最佳化問題時，粒子隨群體最佳解來移動，然而搜尋過程中的群體最佳解可能僅是局部最佳解或近似局部最佳解，使得粒子逐漸往局部小區域靠近而喪失整體的多樣性，將導致搜尋後期收斂速度過慢，落於局部次佳解中。為了改善此缺失，本文採用了避開較差解的概念來改良PSO，再將改良過的PSO(MPSO)與SA兩種演算法加以混合，期望能藉SA的跳躍機制，使得於搜尋過程中能有效地進行全域和局部搜尋，以加強整體的搜尋性能。藉由數個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，並在設計結果之比較，來探討本文所發展之MPSO-SA的優缺點。比較結果顯示MPSO-SA求解多數混合變數之最佳化問題時，具有良好的求解能力及穩定性。

Particle Swarm Optimization has been used effectively for many types of optimization problems. The PSO is an evolutionary computation technique which has ability in performing global search. Many challenges arise when the algorithm is applied to heavily constrained problems where feasible regions may be sparse or disconnected. This report is devoted to the presentation of a hybrid search algorithm, namely MPSO–SA, for optimum design of structures with continuous, discrete and mixed variables. 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 of premature convergence of the method and to make the algorithm explore the local and global minima by the simulated annealing method (SA) and a modified PSO (MPSO), respectively. More than ten typical structures are used to validate the effectiveness of the algorithm. The results from comparative studies of the MPSO-SA against other optimization algorithms are reported to show the solution quality of the proposed algorithm.

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