Clique-based crossover for solving the timetabling problem with GAs

The article describes an investigation and its results on a new crossover operator for solving the timetabling problem with genetic algorithms. Since a timetabling problem can be represented as a graph and then manipulated as a graph colouring problem, the central feature behind the approach presented here considers the presence of solved cliques in the mating parents. A clique is a maximally connected subgraph, that is, any node in it is joined by an edge with any other node of the subgraph. Although finding the clique in a graph is not an easy problem, in fact, it is an NP-complete type, real timetabling problems usually include cliques whose sizes, in relation to the total size of the problem, are still manageable. Results after experimentation with several test files show that the approach and its variations is advantageous under certain circumstances. The reasons why this is happening are explained. Also the ways that, despite the results, this research can lead to answering other interesting questions are outlined