Searching potential energy surfaces by simulated annealing

Many problems in physics1, chemistry, biology2 and mathematics3 involve the determination of the absolute minimum of a certain multidimensional function. In most cases of practical interest this is a complicated matter, owing to the presence of local minima, and even more so because the number of local minima often increases exponentially with the problem size. Standard techniques apply local optimizers to many random initial configurations, but soon become intractable as the dimensionality increases. Here I show how the simulated annealing method can be used to guide a search towards the absolute minimum. The method is illustrated on a problem recently discussed in this journal, namely the minimum-energy configuration of equal charges confined to a sphere. This problem, although easy to visualize, can be used to simulate much of the complexity of the above problems by considering a large number of particles. In this limit several minima have been found that have previously been missed by other authors using classical techniques.