Abstract. We provide strong theoretical and experimental evidence that standard sub-tree crossover with uniform selection of crossover points pushes a population of a-ary GP trees towards a distribution of tree sizes of the form:where n is the number of internal nodes in a tree and pa is a constant. This result generalises the result previously reported for the case a = 1.

Abstract. We provide strong theoretical and experimental evidence that standard sub-tree crossover with uniform selection of crossover points pushes a population of a-ary GP trees towards a distribution of tree sizes of the form:where n is the number of internal nodes in a tree and pa is a constant. This result generalises the result previously reported for the case a = 1.

Bloat can be defined as an excess of code growth without a corresponding improvement in fitness. This problem has been one of the most intensively studied subjects since the beginnings of Genetic Programming. This paper begins by briefly reviewing the theories explaining bloat, and presenting a comprehensive survey and taxonomy of many of the bloat control methods published in the literature through the years. Particular attention is then given to the new Crossover Bias theory and the bloat control method it inspired, Operator Equalisation (OpEq). Two implementations of OpEq are described in detail. The results presented clearly show that Genetic Programming using OpEq is essentially bloat free. We discuss the advantages and shortcomings of each different implementation, and the unexpected effect of OpEq on overfitting. We observe the evolutionary dynamics of OpEq and address its potential to be extended and integrated into different elements of the evolutionary process.

No abstract

The neutral theory of molecular evolution and the associated notion of neutrality have interested many researchers in Evolutionary Computation. The hope is that the presence of neutrality can aid evolution. However, despite the vast number of publications on neutrality, there is still a big controversy on its effects. The aim of this paper is to clarify under what circumstances neutrality could aid Genetic Programming using the traditional representation (i.e. tree-like structures) . For this purpose, we use fitness distance correlation as a measure of hardness. In addition we have conducted extensive empirical experimentation to corroborate the fitness distance correlation predictions. This has been done using two test problems with very different landscape features that represent two extreme cases where the different effects of neutrality can be emphasised. Finally, we study the distances between individuals and global optimum to understand how neutrality affects evolution (at least with the one proposed in this paper).