On solving hierarchical problems with top down control

We review recent work on the Hierarchical-If-And-Only-If problem and present a new hierarchical problem, HIFF-M that does not fit with previous explanations for evolutionary difficulty on hierarchical problems decomposed by levels for RMHC2. RMHC2 is a hill climbing algorithm augmented with a multi-level selection scheme. When used with the "ideal" sieve for a problem, as is done in this paper, RMHC2 exerts top-down control on the evolutionary dynamics, in the sense that adaptation of higher levels are given priority over adaptation of lower levels, and creates stabilizing selection pressure with potential to increase evolvability. Through HIFF-M, we discovered that the summary statistic, Fitness Distance Correlation by level, is not a reliable indicator of when a hierarchical problem is solvable by RMHC2, and that the two properties proposed to explain search easiness for RMHC2 are inadequate. Our investigation of this anomaly led us to propose an additional property for hierarchical evolution difficulty under RMHC2: inter-level conflict. We also discuss how hierarchical control can be subverted through the information transfer capacity of the transposition operation.