Combination of parallel stochastic algorithms and a deterministic nonlinear least squares algorithm for the analysis of extended x-ray absorption fine structure (EXAFS) data

An improved method is presented for the analysis of extended X-ray absorption fine structure (EXAFS) data. The new method is a combination of a stochastic algorithm and a deterministic nonlinear least squares (NLLSQ) algorithm. This method is an improvement over the previously used analysis, where an irregular solution space was searched manually and refined by using the NLLSQ algorithm. The stochastic search part of the new algorithm samples the solution space more thoroughly and faster than the previous manual search; the deterministic NLLSQ part then refines the approximate solution generated by the stochastic algorithm. Reanalysis of previously analyzed data sets demonstrated that the new method is capable of finding both known and new solutions.; The stochastic algorithm part of the new method was thoroughly investigated. Different stochastic algorithms, including genetic algorithms (GA), simulated annealing (SA), and combinations of GA and SA were compared. It was found that GA, GA with temperature control, and GA with distance-based mutation produce the best approximate solutions. It was shown experimentally and theoretically that the GA samples the solution space thoroughly. Both the components and the parameters of the GA were optimized. Gray encoding improved the performance of the GA in narrow ranges of the solution, but dynamic range limiting did not yield better solutions.; The stochastic algorithm part takes approximately an order of magnitude longer time than the NLLSQ port; thus speeding up the stochastic part reduces the run time of the whole algorithm. Experimental GA convergence curves were compared to different convergence models to determine the form of convergence. Speedup curves were used to evaluate the different convergence models. Initial results suggest an exponential convergence, but more research is needed to establish the correct convergence type. The multiple independent runs (MIR) parallel implementation of the algorithm is easy to code and produces good results, even though more efficient implementations are feasible. Various heuristics were given to establish an optimal switching point between the stochastic and the deterministic part of the algorithm.