Distributing Charges on a Sphere by means of Evolutionary Strategies

In this paper we try to approach a solution to a classic question in physics known as Thomson Problem, by means of evolutionary strategies. The Thomson problem consisting in distributing a number (n) of equal charges on a sphere. Charges repel each other, and the equilibrium state is attained when, for each particle, the total amounth of repulsion forces is null. This problem could be seen as the problem of finding the distribution that makes minimum the electrostatic potential function of the charges. The difficult of the problem consists in the complexity of the potential function. For instance, if for each charge we have three variables, as it is usual in the space, then the potential function, f(N), has 3N variables. In addition to the complexity of the problem, this function presents local minimal that grows exponentially with N. Until now there isn't a function that relates the minimum potential to the number of charges, although we can find some approaches to this function. The objective of this work is to find an algorithm that avoids these difficulties and allows us to calculate configurations for more charges with less computational cost. In this paper not only we introduce a way of getting good solutions, in non exponential time, automatically by means of evolutionary strategies, but we also develop a method that improves the standard evolutionary strategies to get even better results.