Operator Equalisation and Bloat Free GP

Research has shown that beyond a certain minimum program length the distributions of program functionality and fitness converge to a limit. Before that limit, however, there may be program-length classes with a higher or lower average fitness than that achieved beyond the limit. Ideally, therefore, GP search should be limited to program lengths that are within the limit and that can achieve optimum fitness. This has the dual benefits of providing the simplest/smallest solutions and preventing GP bloat thus shortening run times. Here we introduce a novel and simple technique, which we call Operator Equalisation, to control how GP will sample certain length classes. This allows us to finely and freely bias the search towards shorter or longer programs and also to search specific length classes during a GP run. This gives the user total control on the program length distribution, thereby completely freeing GP from bloat. Results show that we can automatically identify potentially optimal solution length classes quickly using small samples and that, for particular classes of problems, simple length biases can significantly improve the best fitness found during a GP run.