在本篇論文中，我們在最佳化的程序中比較了BRSM，DACE和TGP這三種替代曲面的方法。然後我們研究了DACE裡面基底函數的參數的適用性。我們還利用了這三種方法來比較固定點和直接最佳化後曲面的差異。根據微分的資訊，我們發展了幾種不同的停止機制。在四種已知的函數之中，我們發現每次加兩個點的方法，其中一點加曲面上最低點另外一點加曲面變化量最大的地方是最有效的方法。

In this thesis, we compare three surrogate construction methods, including: DACE, BRSM and TGP in optimization procedure. We then investigate the suitable radial basis parameter used in DACE method. We utilize these three methods to perform surface fitting with either fixed experimental points or directly generated from the optimization process. Based on the derivative information, we developed different stopping criterion. Within 4 different known functions, we found that adding two experimental points per cycle with one as the lowest point on the present grid and the other to be the point with largest variation in the function value to be the most effective.

Contents
1 Introduction 1
2 Three surrogate construction methods 2
2.1 Basis-based Response SurfaceMethod (BRSM) 2
2.2 Design andAnalysis of Computer Experiments (DACE) 3
2.3 Bayesian nonstationary, semiparametric nonlinear regression and design
by TreedGaussian Processmodels (TGP) 4
3 Basis Comparison in the optimization process by DACE 6
3.1 Optimization process with Design and Analysis of Computer Experiments(
DACE) method 7
3.2 The optimization θ in the DACE toolbox 9
3.3 Test Cases 10
3.4 Result 29
4 Surface fitting by DACE and BRSM 29
4.1 Choose initial points by Latin Hypercube 30
4.2 Optimization process with the four next points choosing methods 30
4.3 Numerical result of surface fitting 32
5 Three methods comparison with the oscillation surface 42
5.1 Results 48
6 Conclusion 48
Appendix 50

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