HIFF-II: A Hierarchically Decomposable Problem with Inter-level Interdependency

A new test problem called HIFF-II is presented. We propose that HIFF-II discriminates evolutionary algorithms that use recombination from those that do not. HIFF-II is a variant of the hierarchical-if-and-only-if (HIFF) problem proposed by Watson (2006). HIFF-II differs from HIFF in one significant way. The dependency matrix for HIFF-II is sparser than that for HIFF. Two important consequences from this are HIFF-II has inter-level interdependencies and there are distinct sets of optimal solutions of the same cardinality at every level. We tested the performance of a random mutation hill climbing algorithm and a genetic algorithm on HIFF-II. This experiment was conducted under "ideal" circumstances for each algorithm on the HIFF-II problem. For the random mutation hill climbing algorithm, this involved using an altruistic selection scheme to induce progress at all levels simultaneously and using a reasonably low mutation rate. For the genetic algorithm, this meant using the gene-invariant genetic algorithm (GIGA) which preserves population diversity throughout a run and selecting pairs of parents that are close in aggregate fitness value. This experiment confirmed that random mutation hill climbers experienced more difficulty evolving an optimal solution for HIFF-II than a genetic algorithm. The disparity between the performances of the two algorithms became more apparent as the problem size increases