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.

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Abstract-Grouping problems are a class of combinatorial optimization problems in which the task is to search for the best partition of a set of objects into a collection of mutually disjoint subsets while satisfying a given set of constraints. Typical examples include data clustering, graph coloring and exam timetabling problems. Selection hyper-heuristics based on iterative search frameworks are high level general problem solving methodologies which operate on a set of low level heuristics to improve an initially generated solution via heuristic selection and move acceptance. In this paper, we describe a selection hyper-heuristic framework based on an efficient representation referred to as linear linkage encoding for multi-objective grouping problems. This framework provides the implementation of a fixed set of low level heuristics that can work on all grouping problems where a trade-off between a given objective and number of groups is sought. The empirical results on graph coloring problem indicates that the proposed grouping hyper-heuristic framework can indeed provide high quality solutions.