Fighting Bloat with Nonparametric Parsimony Pressure

Many forms of parsimony pressure are parametric, that is final fitness is a parametric model of the actual size and raw fitness values. The problem with parametric techniques is that they are hard to tune to prevent size from dominating fitness late in the evolutionary run, or to compensate for problem-dependent nonlinearities in the raw fitness function. In this paper we briefly discuss existing bloat-control techniques, then introduce two new kinds of non-parametric parsimony pressure, Direct and Proportional Tournament. As their names suggest, these techniques are based on simple modifications of tournament selection to consider both size and fitness, but not together as a combined parametric equation. We compare the techniques against, and in combination with, the most popular genetic programming bloat-control technique, Koza-style depth limiting, and show that they are effective in limiting size while still maintaining good bestfitness-of-run results.