A new hybrid approach for tackling Thomson problem

Distributing N charged particles informally over the surface of a unit sphere is an old and largely unsolved problem, it is generally known as the Thomson problem and it is solved by finding the lowest energy configuration that minimizes the electrostatic energy of the system. The energy function is everywhere infinitely differentiable and has an exponential number of local minimizers that grows exponentially with N. We tackle the Thomson problem by a novel hybrid approach that combines a Nonmonotone Spectral Gradient Method, which has been intensively used in many applications, with a variant of particular swarm optimization called comprehensive learning PSO.