Hyper-Heuristics: A Study On Increasing Primitive-Space

Practitioners often need to solve real world problems for which no custom search algorithms exist. In these cases they tend to use general-purpose solvers that have no guarantee to perform well on their specific problem. The relatively new field of hyper-heuristics provides an alternative to the potential pit-falls of general-purpose solvers, by allowing practitioners to generate a custom algorithm optimized for their problem of interest. Hyper-heuristics are meta-heuristics operating on algorithm space employing targeted primitives to compose algorithms. This paper explores the advantages and disadvantages of expanding a hyper-heuristic's primitive-space with additional primitives. This should allow for an increase in quality of evolved algorithms. However, increasing the search space of a meta-heuristic almost always results in longer time to convergence and lower quality results for the same amount of computational time, but also all too often lower quality results at convergence, potentially making a problem impractical to solve for a practitioner. This paper explores the scalability of hyper-heuristics as the primitive-space is increased, demonstrating significantly increased quality solutions at convergence with a corresponding increase in convergence time. Additionally, this paper explores the impact that the nature of the added primitives have on the performance of the hyper-heuristic.