本文針對連續變數、離散變數、混和變數等最佳化問題，以杜鵑鳥演算法(Cuckoo Search Algorithm, CS)為基礎，提出改良式杜鵑鳥演算法(Modified cuckoo search, MCS)。CS演算法為一種全域的隨機搜尋法，其構想來自於杜鵑鳥的寄生雛幼行為，並結合列維飛行(Lévy flight)擾動機制，列維飛行為源自模擬果蠅和鳥類在飛行時的移動狀態之數學方法。然而，CS演算法和其他高階啟發演算法類似，在求解最佳化問題時存在著局部搜索能力差，接近最佳解時搜索效率下降，以及求解高度非線性問題時可能陷入局部最佳而使演化停滯等缺失。為改善此二缺失，本文乃提出MCS演算法，期可加速局部搜尋效率，並維持鳥巢的多樣性。為驗證MCS演算法的可行性，本文藉由不同類型的算例，包含數學式及結構輕量化設計的問題等，探討CS及MCS演算法方法之優劣。最後，本文亦將MCS演算法應用於製作矩形鋼管混凝土構材之軸壓與雙向彎矩互制圖，以克服在考慮局部挫屈時使用割線法於高軸壓下不易收斂的缺失。

This article is devoted to the presentation of a modified cuckoo search (MCS) algorithm for solving optimization problems with discrete, continuous and mixed variables. The cuckoo search (CS) algorithm is based on the obligate brood parasitic behaviour of some cuckoo species in combination with the Lévy flight behaviour of some birds and fruit flies. The main deficiency of CS algorithm is that all nests have the tendency to converge to the current best solution which may be a local optimum or a solution near local optimum. In this case, all nests 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 thoroughly at the same time, a MCS algorithm is proposed. More than ten typical optimization problems studied in the literature are used to validate the effectiveness of the algorithm. The results from comparative studies of the MCS algorithm againsts other optimization algorithms are reported to show the solution quality of the proposed MCS algorithm. The advantages and drawbacks of the MCS algorithm is also discussed in this report. Finally, the MCS algorithm is also used to construct P-M curves for concrete-filled steel tubular (CFT) columns. The results show that the MCS algorithm can effectively applied to construct P-M curves for CFT columns.

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