Runtime analysis of selection hyper-heuristics with classical learning mechanisms

The term selection hyper-heuristics refers to a randomised search technique used to solve computational problems by choosing and executing heuristics from a set of pre-defined low-level heuristic components. Selection hyper-heuristics have been successfully employed in many problem domains. Nevertheless, a theoretical foundation of these heuristics is largely missing. Gaining insight into the behaviour of selection hyper-heuristics is challenging due to the complexity and random design of these heuristics. This paper is one of the initial studies to analyse rigorously the runtime of selection hyper-heuristics with a number of the most commonly used learning mechanisms; namely, simple random, random gradient, greedy, and permutation. We derive the runtime of selection hyper-heuristic with these learning mechanisms not only on a classical example problem, but also on a general model of fitness landscapes. This in turn helps in understanding the behaviour of hyper-heuristics. Our results show that all the considered selections hyper-heuristics have roughly the same performance. This suggests that the learning mechanisms do not necessarily improve the performance of hyper-heuristics. A new learning mechanism that improves the performance of hyper-heuristic on our example problem is presented.