Representation and structural difficulty in genetic programming

Standard tree-based genetic programming suffers from a structural difficulty problem in that it is unable to search effectively for solutions requiring very full or very narrow trees. This deficiency has been variously explained as a consequence of restrictions imposed by the tree structure or as a result of the numerical distribution of tree shapes. We show that by using a different tree-based representation and local (insertion and deletion) structural modification operators, that this problem can be almost eliminated even with trivial (stochastic hill-climbing) search methods, thus eliminating the above explanations. We argue, instead, that structural difficulty is a consequence of the large step size of the operators in standard genetic programming, which is itself a consequence of the fixed-arity property embodied in its representation.