Abstract
A novel genetic algorithm (GA) utilizing independent component analysis
(ICA) was developed for x-ray reflectivity (XRR) curve fitting. EFICA was
used to reduce mutual information, or interparameter dependences, during
the combinatorial phase. The performance of the new algorithm was studied
by fitting trial XRR curves to target curves which were computed using
realistic multilayer models. The median convergence properties of
conventional GA, GA using principal component analysis and the novel GA
were compared. GA using ICA was found to outperform the other methods
with problems having 41 parameters or more to be fitted without additional
XRR curve calculations. The computational complexity of the conventional
methods was linear but the novel method had a quadratic computational
complexity due to the applied ICA method which sets a practical limit for
the dimensionality of the problem to be solved. However, the novel
algorithm had the best capability to extend the fitting analysis based on
Parratt’s formalism to multiperiodic layer structures.
(ICA) was developed for x-ray reflectivity (XRR) curve fitting. EFICA was
used to reduce mutual information, or interparameter dependences, during
the combinatorial phase. The performance of the new algorithm was studied
by fitting trial XRR curves to target curves which were computed using
realistic multilayer models. The median convergence properties of
conventional GA, GA using principal component analysis and the novel GA
were compared. GA using ICA was found to outperform the other methods
with problems having 41 parameters or more to be fitted without additional
XRR curve calculations. The computational complexity of the conventional
methods was linear but the novel method had a quadratic computational
complexity due to the applied ICA method which sets a practical limit for
the dimensionality of the problem to be solved. However, the novel
algorithm had the best capability to extend the fitting analysis based on
Parratt’s formalism to multiperiodic layer structures.
| Original language | English |
|---|---|
| Pages (from-to) | 6000-6004 |
| Number of pages | 5 |
| Journal | Journal of Physics D: Applied Physics |
| Volume | 40 |
| Issue number | 19 |
| DOIs | |
| Publication status | Published - 21 Sept 2007 |
| MoE publication type | A1 Journal article-refereed |
Keywords
- curve fitting
- genetic algorithm
- independent component analysis
- x-ray reflectivity