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 best-fitness-of-run results.

[1]  Stephen F. Smith,et al.  A learning system based on genetic adaptive algorithms , 1980 .

[2]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

[3]  Byoung-Tak Zhang,et al.  Balancing Accuracy and Parsimony in Genetic Programming , 1995, Evolutionary Computation.

[4]  Peter J. Angeline,et al.  Explicitly Defined Introns and Destructive Crossover in Genetic Programming , 1996 .

[5]  P. Nordin,et al.  Explicitly defined introns and destructive crossover in genetic programming , 1996 .

[6]  Terence Soule,et al.  Code growth in genetic programming , 1996 .

[7]  Annie S. Wu,et al.  Putting More Genetics into Genetic Algorithms , 1998, Evolutionary Computation.

[8]  Terence Soule,et al.  Removal bias: a new cause of code growth in tree based evolutionary programming , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[9]  Haynes.  Collective Adaptation: The Exchange of Coding Segments. , 1999, Evolutionary computation.

[10]  Sean Luke,et al.  Issues in Scaling Genetic Programming: Breeding Strategies, Tree Generation, and Bloat , 2000 .

[11]  Kenneth A. De Jong,et al.  Evolving Behaviors for Cooperating Agents , 2000, ISMIS.

[12]  Lothar Thiele,et al.  Multiobjective genetic programming: reducing bloat using SPEA2 , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[13]  Edwin D. de Jong,et al.  Reducing bloat and promoting diversity using multi-objective methods , 2001 .

[14]  Wolfgang Banzhaf,et al.  Explicit Control of Diversity and Effective Variation Distance in Linear Genetic Programming , 2002, EuroGP.

[15]  Sean Luke,et al.  Lexicographic Parsimony Pressure , 2002, GECCO.

[16]  Anikó Ekárt,et al.  Selection Based on the Pareto Nondomination Criterion for Controlling Code Growth in Genetic Programming , 2001, Genetic Programming and Evolvable Machines.