Rigorous Performance Analysis of Hyper-heuristics

Abstract

We provide an overview of the state-of-the-art in the time complexity analysis of selection hyper-heuristics for combinatorial optimisation. These algorithms aim at automating the optimisation process by using a set of low-level heuristics and a machine learning mechanism to decide online which heuristic is the most appropriate one at the current stage. We mainly focus on work that establishes the performance gains that simple and sophisticated hyper-heuristics can achieve compared to the low-level heuristics applied in isolation, and that compares the expected runtime of the hyper-heuristics against the best possible one achievable with the given set of low-level heuristics. We cover examples where mixing heuristics is necessary, as well as others where learning from the past performance of the applied heuristics is crucial for the algorithms to be efficient. We emphasise that simple and sophisticated hyper-heuristics from the literature can achieve optimal performance for some standard unimodal and multimodal benchmark functions. Problem characteristics are highlighted for which more or less machine learning sophistication is required, and insights are provided of how a rigorous theory can guide the design of more efficient hyper-heuristics.