臺灣博碩士論文加值系統

本論文考慮一個在電腦模擬實驗上具有多重極值的最佳化問題。為了要解決這個問題，在這提出了一個新的演算法。基本上這個新方法是利用在實驗區域中任意選取數個初始值後，同時進行數個反應曲面法，並輔以平行計算的技巧來節省計算成本。

In this thesis an optimization problems for finding multiple extremes in computer experiments (Sacks et al., 1989, and Koehler and Owen, 1996) are considered. To solve this kind of problems, a novel method is proposed. Basically the idea is to run multiple Response Surface Method (RSM) in the parallel environment at the same time.

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . .1
2 Response surface method . . . . . . . . . . . . . . . . . . . . . . . .2
3 Parallel response surface method . . . . . . . . . . . . . . . . . . . . . . . .4
3.1 Master-client parallel model . . . . . . . . . . . . . . . . . . . . . . . . 4
3.2 PRSM algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.3 Information Sharing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.3.1 Sharing the function value . . . . . . . . . . . . . . . . . . . . . 6
3.3.2 Share the path information . . . . . . . . . . . . . . . . . . . . . 8
3.4 Adding new initial point . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.4.1 Adding uniform design point . . . . . . . . . . . . . . . . . . . . 11
3.4.2 Using paths' directions . . . . . . . . . . . . . . . . . . . . . . . 11
3.4.3 Exploring unknown area . . . . . . . . . . . . . . . . . . . . . . 12
4 Estimation of trend . . . . . . . . . . . . . . . . . . . . . . . .13
4.1 Direct Ftting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.2 Fitting on modifed data . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.3 Extrapolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5 Numerical experiment . . . . . . . . . . . . . . . . . . . . . . . .15
5.1 Functional demonstration . . . . . . . . . . . . . . . . . . . . . . . . . 15
5.2 The performance of PRSM . . . . . . . . . . . . . . . . . . . . . . . . . 17
5.3 Trend estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.4 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . .26
References . . . . . . . . . . . . . . . . . . . . . . . .27

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5919.Synchronization