Genetic programming: on the programming of computers by means of natural selection
Genetic programming: on the programming of computers by means of natural selection
The evolution of size and shape
Advances in genetic programming
Size Fair and Homologous Tree Crossovers for Tree Genetic Programming
Genetic Programming and Evolvable Machines
Some Considerations on the Reason for Bloat
Genetic Programming and Evolvable Machines
Accurate Replication in Genetic Programming
Proceedings of the 6th International Conference on Genetic Algorithms
Complexity Compression and Evolution
Proceedings of the 6th International Conference on Genetic Algorithms
Lexicographic Parsimony Pressure
GECCO '02 Proceedings of the Genetic and Evolutionary Computation Conference
Exons and Code Growth in Genetic Programming
EuroGP '02 Proceedings of the 5th European Conference on Genetic Programming
Avoiding the Bloat with Stochastic Grammar-Based Genetic Programming
Selected Papers from the 5th European Conference on Artificial Evolution
Fitness Causes Bloat: Mutation
EuroGP '98 Proceedings of the First European Workshop on Genetic Programming
A statistical learning theory approach of bloat
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Effects of code growth and parsimony pressure on populations in genetic programming
Evolutionary Computation
Dynamic maximum tree depth: a simple technique for avoiding bloat in tree-based GP
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartII
A statistical learning theory approach of bloat
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Genetic Programming and Evolvable Machines
Adaptation, Performance and Vapnik-Chervonenkis Dimension of Straight Line Programs
EuroGP '09 Proceedings of the 12th European Conference on Genetic Programming
VCD Bounds for some GP Genotypes
Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence
A survey and taxonomy of performance improvement of canonical genetic programming
Knowledge and Information Systems
Penalty functions for genetic programming algorithms
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part I
Hi-index | 0.00 |
Code bloat, the excessive increase of code size, is an important issue in Genetic Programming (GP). This paper proposes a theoretical analysis of code bloat in the framework of symbolic regression in GP, from the viewpoint of Statistical Learning Theory, a well grounded mathematical toolbox for Machine Learning. Two kinds of bloat must be distinguished in that context, depending whether the target function lies in the search space or not. Then, important mathematical results are proved using classical results from Statistical Learning. Namely, the Vapnik-Chervonenkis dimension of programs is computed, and further results from Statistical Learning allow to prove that a parsimonious fitness ensures Universal Consistency (the solution minimizing the empirical error does converge to the best possible error when the number of examples goes to infinity). However, it is proved that the standard method consisting in choosing a maximal program size depending on the number of examples might still result in programs of infinitely increasing size with their accuracy; a more complicated modification of the fitness is proposed that theoretically avoids unnecessary bloat while nevertheless preserving the Universal Consistency.