A grouping hyper-heuristic framework: Application on graph colouring

Grouping problems are hard to solve combinatorial optimisation problems which require partitioning of objects into a minimum number of subsets while a given objective is simultaneously optimized. Selection hyper-heuristics are high level general purpose search methodologies that operate on a space formed by a set of low level heuristics rather than solutions. Most of the recently proposed selection hyper-heuristics are iterative and make use of two key methods which are employed successively; heuristic selection and move acceptance. At each step, a new solution is produced after a selected heuristic is applied to the solution in hand and then the move acceptance method is used to decide whether the resultant solution replaces the current one or not. In this study, we present a selection hyper-heuristic framework including a fixed set of low level heuristics specifically designed for grouping problems. The performance of different hyperheuristics using different components within the framework is investigated on a representative grouping problem of graph colouring. Additionally, the hyper-heuristic performing the best on graph colouring is applied to a benchmark of examination timetabling instances. The empirical results shows that the proposed grouping hyper-heuristic is not only sufficiently general, but also able to achieve high quality solutions for graph colouring and examination timetabling.