本文主要針對連續變數、離散變數、混合變數之最佳化設計問題，提出一種結合和聲搜尋法(HS)與離散拉格郎日法(DLM)的混合式高階啟發式演算法，即HS-DLM。HS為一隨機搜尋法，具有全域搜尋的能力，其概念簡單且不需調整過多參數。然而隨機搜尋使得HS在局部搜尋精確性不足之外，含有約束條件之處理方式也為其缺點之ㄧ。為改善此缺失，本文採用DLM演算法來補強HS的局部搜尋的能力並提供處理束制函數的機制，以改善整體的搜尋性能。DLM處理束制函數和強健的局部搜尋能力，將使HS-DLM獲得全域最佳解或全域近似最佳解的機率大增。藉由數個結構輕量化設計問題分別來探討其適用性，並檢討影響求解效率的相關參數。數值算例的結果顯示，HS-DLM較單獨使用HS穩定，且求解品質亦較佳。與文獻結果比較，亦顯示HS-DLM的求解品質不差，甚至更好。

This report is devoted to the presentation of a hybrid meta-heuristic algorithm, namely HS-DLM, for optimum design of structures with continuous, discrete and mixed variables. The HS (Harmony Search) has the ability in performing global search. However, the main deficiencies of HS are lacking accuracy of local search and the way of dealing with constrains. To overcome these drawbacks, DLM is proposed to enhance the local search capacity of HS and repair violated constrains for the problem such that the probability of obtaining global optimum for the HS-DLM can be increased. More than ten typical structures studied in the literature were used to validate the effectiveness of the algorithm. The comparative studies of the HS-DLM against other optimization algorithms are reported to show the performance and the solution quality of the proposed HS-DLM algorithm. It shows that the performance of HS-DLM algorithm is reliable, and the solution quality of the optimum structural design problems studied in the literature is comparable to other meta-heuristic methods.

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