臺灣博碩士論文加值系統

針對解決最佳化的問題上，我們提出了一新的演算法，稱為基底建構反應曲面法。主要的策略是使用所有已知訊息在整個實驗區域內建構代理模型，再從代理模型中選擇可能的最佳點。我們將實驗區域分成多個格點，並僅考慮格點上的得到的反應值，使得能夠將問題視為一影像，進而應用一些影像處理技巧建構代理模型，其中Matching Pursuit演算法、Gabor function與均勻設計在我們提出的新演算法中有著重要的應用。我們針對平滑與不平滑與有多重極值點之反應曲面均進行一些測試，並且同時與傳統反應曲面法RSM進行比較。數值實驗結果也呈現了新演算法能夠有效率的搜尋到單一最佳點及同時搜尋多個最佳點。

Here we proposed a new algorithm named Basis-based response surface method(BRSM) that aiming at solving optimization problems arising in computer experiments. Techniques taken from experimental design, statistical approximation, and image representation are incorporated carefully in the proposed algorithm. The method iteratively construct surrogate surfaces over the whole experimental region by using overcomplete basis functions to predict possible optimum points and next experiments. We do test on some typical response surface and comparison between the RSM and the BRSM. Numerical result show that BRSM is quite efficient for finding single or multiple optima of smooth response surfaces.

目錄
中文摘要 ii
Abstract iii
1 前言 1
2 Basis-based Response Surface Method(BRSM) 3
2.1 BRSM演算法描述 4
2.2 Matching-Pursuit演算法 12
2.3 BRSM演算法的主要改進 18
2.4一個以Matching Pursuit法建構代理模型的例子 20
2.5一個詳細的BRSM實作過程 27
3 反應曲面法(RSM) 36
3.1 反應曲面法簡述 36
3.2 計算機實驗上之反應曲面法 39
3.3 最陡上升(或下降)過程 41
3.4 一個詳細的RSM實作例子 53
4 BRSM與RSM在一些例子上的數值實驗與比較 94
4.1 Smooth function with single extreme 94
4.2 Smooth function with two local extreme values 97
4.3 Oscillatory surface with multiple extreme values 100
5 討論 105
Appendix A : Basis Dictionary of Gabor function 107
Appendix B :在本篇文章中所用來供模擬之反應曲面 109
參考文獻 113

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