Teachers and Classes with Neural Networks

A convenient mapping and an efficient algorithm for solving scheduling problems within the neural network paradigm is presented. It is based on a reduced encoding scheme and a mean field annealing prescription which was recently successfully applied to TSP.

Most scheduling problems are characterized by a set of hard and soft constraints. The prime target of this work is the hard constraints. In this domain the algorithm persistently finds legal solutions for quite difficult problems. We also make some exploratory investigations by adding soft constraints with very encouraging results. Our numerical studies cover problem sizes up to O(105) degrees of freedom with no parameter tuning.

We stress the importance of adding self-coupling terms to the energy functions which are redundant from the encoding point of view but beneficial when it comes to ignoring local minima and to stabilizing the good solutions in the annealing process.