Automatic Scheduling for schools : Scalability of the Hopfield Neural Networks

Sammanfattning: This project is focused on evaluating, in terms of real time needed to find a solution, the scalability of Hopfield Neural Networks, a Machine Learning method, applied to a common problem that every educational institution has to deal with at least once in every academic year, timetabling. With this purpose, the problem is first introduced. And secondly, in the background, the concept of "constraint" is presented, to continue with a brief explanation of Artificial Neural Networks, the state of the art and more specifically, how Hopfield Neural Networks are characterized. The formulation, modifications used, and the algorithm are presented. This algorithm will be implemented in MATLAB, and it will be run on data sets of different sizes. The results obtained for the presented data sets are presented in a table and graphs, to later discuss these results. In this discussion, it is found that the time spent to get a solution could scale quadratically with respect to the size of the problem, but there is not statistical evidence to this hypothesis. Finally, the conclusion is that Hopfield Neural Networks could have a good scalability if the hypothesis worked for bigger data sets, and some future work in the field is presented, like using sparse matrices for the implementation of the problem, or studying the scalability of Hopfield Neural Networks in other kinds of scheduling.