A grouping hyper-heuristic framework based on linear linkage encoding for graph coloring

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 the number of groups is sought. The empirical results on graph coloring problem indicate that the proposed grouping hyper-heuristic framework can indeed provide high quality solutions.