Hierarchically consistent test problems for genetic algorithms

The building-block hypothesis suggests that the genetic algorithm (GA) will perform well when it is able to identify above-average-fitness low-order schemata and recombine them to produce higher-order schemata of higher fitness. We suppose that the recombinative process continues recursively, combining schemata of successively higher orders as search progresses. Historically, attempts to illustrate this intuitively straight-forward process on abstract test problems, most notably the Royal Road problems, have been somewhat perplexing. More recent building-block test problems have abandoned the multi-level hierarchical structure of the Royal Roads, and thus departed from the original recursive aspects of the hypothesis. This paper defines the concept of hierarchical consistency, which captures the recursive nature of problems implied by the building-block hypothesis. We introduce several variants of problems that are hierarchically consistent and begin to explore aspects of problem difficulty with respect to these models