Structural difficulty in grammatical evolution versus genetic programming

Genetic programming (GP) has problems with structural difficulty as it is unable to search effectively for solutions requiring very full or very narrow trees. As a result of structural difficulty, GP has a bias towards narrow trees which means it searches effectively for solutions requiring narrow trees. This paper focuses on the structural difficulty of grammatical evolution (GE). In contrast to GP, GE works on variable-length binary strings and uses a grammar in Backus-Naur Form (BNF) to map linear genotypes to phenotype trees. The paper studies whether and how GE is affected by structural difficulty. For the analysis, we perform random walks through the search space and compare the structure of the visited solutions. In addition, we compare the performance of GE and GP for the Lid problem. Results show that GE representation is biased, this means it has problems with structural difficulty. For binary trees, GE has a bias towards narrow and deep structures; thus GE outperforms standard GP if optimal solutions are composed of very narrow and deep structures. In contrast, problems where optimal solutions require more dense trees are easier to solve for GP than for GE.