臺灣博碩士論文加值系統

Michaelis-Menten 模型和其相關模型目前被廣泛的使用在生物學研究當中。在此篇文章當中，我們將專注於此類非線性模型的最適設計問題，首先對觀測值具有相關的Michaelis-Menten 模型，找尋最適正合設計。另外針對Michaelis-Menten也考慮了，標準化最大最小D-最適準則的設計。除了Michaelis-Menten模型之外，對於另外四種相關模型的局部D-最適設計與標準化最大最小D-最適設計亦進行探討。為了有效率地計算數值結果，本論文中利用粒子群最佳化演算法來執行相關數值計算。

The Michaelis-Menten model and its related models are widely used in biology studies. In this thesis, we focus on the optimal design issues for these nonlinear models. First we study the exact designs for the correlated Michaelis-Menten model and the standardized maximin D-optimal designs for Michaelis-Menten model. Then the locally D-optimal designs and the standardized maximin D-optimal designs for four different inhibition models are studied. Here particle swarm optimization approach is used to obtain the numerical results.

1. Introduction ........................................1
2. Optimal Designs for Nonlinear Models ................4
3. Particle Swarm Optimization .........................6
3.1 PSO for the Minimization or Maximization Problem ...7
3.2 Nested PSO for the Maximin or Minimax Problem.......8
4. Optimal Designs for Michaelis-Menten Model .........11
4.1 Locally Exact D-optimal Designs for Correlated Observations ..........................................11
4.2 Standardized Maximin D-optimal Designs ............15
5. Optimal Designs for Four Inhibition Models .........22
5.1 Locally D-optimal Designs .........................22
5.2 Standardized Maximin D-optimal Designs ............25
6. Conclusion .........................................33
References ............................................34
Appendix ..............................................36
Appendix A. Testification for Convergency of PSO with Correlated Observations ...............................37

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