A runtime analysis of simple hyper-heuristics: To mix or not to mix operators

There is a growing body of work in the field of hyper-heuristics. Hyper-heuristics are high level search methodologies that operate on the space of heuristics to solve hard computational problems. A frequently used hyper-heuristic framework mixes a predefined set of low level heuristics during the search process. While most of the work on such selection hyper-heuristics in the literature are empirical, we analyse the runtime of hyper-heuristics rigorously. Our initial analysis shows that mixing heuristics could lead to exponentially faster search than individual (deterministically chosen) heuristics on chosen problems. Both mixing of variation operators and mixing of acceptance criteria are investigated on some selected problems. It is shown that mixing operators is only efficient with the right mixing distribution (parameter setting). Additionally, some of the existing adaptation mechanisms for mixing operators are also evaluated.