Exploring heuristic interactions in constraint satisfaction problems: A closer look at the hyper-heuristic space

Variable ordering has been a recurrent topic of study in the field of constraint satisfaction because of its impact in the cost of the search. Various variable ordering heuristics have been proposed to help guiding the search under different situations. One important direction of the study about variable ordering is the use of distinct heuristics as the search progresses to reduce the cost of the search. Even though the idea of combining heuristics goes back to the 60's, only a few works that study which heuristics to use and how they interact with each other have been described. In this investigation, we analyse the interactions of four important variable ordering heuristics by combining them through hyper-heuristics that decide the heuristic to apply based on the depth of the nodes in the search tree. The paper does not include any specific model for generating such hyperheuristics; instead, it presents an analysis of the changes in the cost when different heuristics are applied during the search by using one simple hyper-heuristic representation. The results show that selectively applying distinct heuristics as the search progresses may lead to important reductions in the cost of the search with respect to the performance of the same heuristics used in isolation.