I try to find the optimal configuration of points on a grid, which has to fulfill some constraints. Solving a problem with points on a grid and finding the optimal configuration is a discrete optimization problem.
Since my current approach (using simulated annealing) is not working for more than 7 points, I thought it would be a nice try to translate this discrete problem into a continuous one:
Having N charged particles (I give them a charge in the hope that the solution can be easier transformed to the grid solution), each particle is connected by springs to other particles. I would like to find the optimal configuration such that the total energy is at its minimum. (Energy function has the repulsive part of the Coulomb potential and the attractive part by the springs).
How is it about sticking in local minima, have you any experience with a similar problem? So my question is, what are the problems I will have to deal with following this approach?
Here is a picture for illustration
