Global minima stochastic methods

To approximately locate the global minimum i.e., to obtain a good quality crystal structure solution) in a reasonable amount of time, grid search methods should be replaced by the stochastic ones, based on a random sampling of the parameter space. This technique, called Monte Carlo MC), has been widely used in other scientific fields to simulate the behavior of complex systems. Its application to crystal structure determination from powder diffraction data has been developed by many authors the main strategies are outlined below. 

We consider first unconstrained problems, and then treat constraints. Here, the focus is upon methods that identify local minima i.e., points that are lower in cost function than their neighbors. The stochastic methods of Chapter 7 return (eventually) global minima therefore, the reader is referred to that discussion if identifying the global minimum is necessary. 

REMD, the authors point to [38], Briefly, REMD is an enhanced sampling method that acts to vary the temperature stochastically through a simulation. This allows for the RNA molecule to sample faster and obtain a more global energy minimum structure. 

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