Monte Carlo methods global minima

It is rather difficult to find the global minimum of such a multivariable function. The gradient method normally used is problematic in that only the next local minimum can be reached. On the other hand, the Monte-Carlo methods, which make guesses by means of random numbers, are not reliable enough with such a large number of variables. Thus, evolutionary algorithms represent an interesting alternative. 

We sample from this distribution using the Metropolis Monte Carlo method, starting initially at a very high temperature so that the system is able to move efficiently around parameter space. We then slowly decrease the temperature to zero, to allow the system sufficient time to escape from higher-lying local minima and find the global minimum (which is easier... 

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. 

---