隨機最佳化問題存在於許多領域上，舉凡財金、醫療、電子、製藥產業等，所謂的隨機問題為目標式內含著不確定性，由於不確定性的存在使得在搜尋全域性最佳解的過程中十分地困難，因此本研究目的為發展新的演算法以解決隨機最佳化問題。發展之演算法為使用全域性的搜索方式找出最佳解，其架構為建構序列性的克利金反應曲面以預測目標值，並結合了核密度估計的方式以建構最佳解所在位置之機率密度函數讓我們可以有效地搜尋到最佳解。數值實驗以及個案實證結果均顯示此方法能夠有效地解決隨機最佳化的問題。

Stochastic global optimization refers an iterative procedure in attempt to find the global optima in the parameter space when the objective function can be estimated with noise. Due to the noise inherent in the objective value, the problem is difficult to be solved, especially when the time given to solve the problem is limited, which is usually the case in practice. In this research, we propose a framework that allows the stochastic global optimization problem to be solved efficiently. The proposed framework sequentially builds a Kriging metamodel based on kernel density estimation for predicting the functional behavior of the objective function and solves for the optimal solution of the metamodel. Numerical experiments show that its efficiency is satisfactory.

摘要 I
Abstract II
目錄 III
圖目錄 IV
表目錄 V
一、 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 4
1.3 論文架構 5
二、 文獻探討 7
2.1 模擬最佳化 7
2.2 隨機Kriging模型 10
2.3 核密度估計 12
三、 問題定義 15
四、 SKM演算法 16
4.1 SKM之主架構 17
4.1.1 樣本抽樣計畫 18
4.1.2 隨機Kriging反應曲面 19
4.1.3 核密度估計 28
4.1.4 搜尋架構 29
五、 數值實驗 34
5.1 測試函數 34
5.2 比較指標 36
5.3 數值結果 36
六、 個案研究 42
七、 結論與未來研究 45
參考文獻 46

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