An investigation of hyper-heuristic search spaces

Hyper-heuristics or "heuristics that coordinate heuristics" are fast becoming popular for solving combinatorial optimisation problems. These methods do not search directly the solution space; they do it indirectly through the exploration of the space of heuristics and/or their combinations. This space is named the associated space. The task of finding the best element in the associated space is referred to as the associated problem. This paper presents a formal definition of the associated problem, and investigates several of its properties. An empirical study of the associated problem is performed using a production scheduling problem as experimental environment. Obtained results allow us to partly explain what are the advantages of hyper-heuristic solution representations over other traditional ones, and, to give recommendations on hyper-heuristic design.