Nonlinear fitness–space–structure adaptation and principal component analysis in genetic algorithms: an application to x-ray reflectivity analysis

Two novel genetic algorithms implementing principal component analysis
and an adaptive nonlinear fitness–space–structure technique are presented
and compared with conventional algorithms in x-ray reflectivity analysis.
Principal component analysis based on Hessian or interparameter covariance
matrices is used to rotate a coordinate frame. The nonlinear adaptation
applies nonlinear estimates to reshape the probability distribution of the trial
parameters. The simulated x-ray reflectivity of a realistic model of a periodic
nanolaminate structure was used as a test case for the fitting algorithms.
The novel methods had significantly faster convergence and less stagnation
than conventional non-adaptive genetic algorithms. The covariance
approach needs no additional curve calculations compared with conventional
methods, and it had better convergence properties than the computationally
expensive Hessian approach. These new algorithms can also be applied to
other fitting problems where tight interparameter dependence is present.