GRAHF: A Hyper-Heuristic Framework for Evolving Heterogeneous Island Model Topologies

Jonathan Wurth, Helena Stegherr, Michael Heider, Jörg Hähner

Abstract: Practitioners frequently encounter the challenge of selecting the best optimization algorithm from a pool of options. However, why not, rather than selecting a single algorithm, let evolution determine the optimal combination of all algorithms? In this paper, we present an approach to algorithm design inspired by a well-known traditional method for coarse-grained hybridization: the heterogeneous island model. Our hyper-heuristic framework represents island models as graphs and identifies optimal island topologies and parameters for specific sets of problem instances. Since the framework operates at the level of metaheuristic algorithms rather than components and incorporates a configuration mechanism directly into the search, it combines concepts from algorithm design, selection, and configuration. The proposed framework is investigated on 24 training sets of varying difficulty and demonstrates its ability to discover complex hybrids. A post-evaluation on real-world constrained optimization problems shows a significant improvement over the algorithms on their own. These results suggest that it is a promising way to design hybrid metaheuristics with minimal manual intervention, given representative training instances, a set of optimization algorithms, and sufficient computational resources.