Hierarchically-Consistent GA Test Problems

The Building-Block Hypothesis suggests that GAs perform well when they are able to identify above-averagefitness 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, and 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. Hierarchical consistency causes us to re-think some of the concepts of problem difficulty that have become established for example order-k delineation, and deception as defined with respect to a single global-optimum. We introduce several variants of problems that are hierarchically consistent, and discuss the concepts of problem difficulty with respect to these models. Experimental results begin to explore the effects that these variations have on GA performance.