Adaptation in natural and artificial systems
Adaptation in natural and artificial systems
The evolution of evolvability in genetic programming
Advances in genetic programming
An introduction to genetic algorithms
An introduction to genetic algorithms
ALIFE Proceedings of the sixth international conference on Artificial life
Adaptation and the Modular Design of Organisms
Proceedings of the Third European Conference on Advances in Artificial Life
Intelligent Mutation Rate Control in Canonical Genetic Algorithms
ISMIS '96 Proceedings of the 9th International Symposium on Foundations of Intelligent Systems
Genome Growth and the Evolution of the Genotype-Phenotype Map
Evolution and Biocomputation, Computational Models of Evolution
Fast Reinforcement Learning through Eugenic Neuro-Evolution
Fast Reinforcement Learning through Eugenic Neuro-Evolution
The Estimation of Distributions and the Minimum Relative Entropy Principle
Evolutionary Computation
Speciation as automatic categorical modularization
IEEE Transactions on Evolutionary Computation
On a quantitative measure for modularity based on information theory
ECAL'05 Proceedings of the 8th European conference on Advances in Artificial Life
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The principle of modularization has proven to be extremely successful in the field of technical applications and particularly for Software Engineering purposes. The question to be answered within the present article is whether mechanisms can also be identified within the framework of Evolutionary Computation that cause a modularization of solutions. We will concentrate on processes, where modularization results only from the typical evolutionary operators, i.e. selection and variation by recombination and mutation (and not, e.g., from special modularization operators). This is what we call Self-Organized Modularization.Based on a combination of two formalizations by Radcliffe and Altenberg, some quantitative measures of modularity are introduced. Particularly, we distinguish Built-in Modularity as an inherent property of a genotype and Effective Modularity, which depends on the rest of the population. These measures can easily be applied to a wide range of present Evolutionary Computation models.It will be shown, both theoretically and by simulation, that under certain conditions, Effective Modularity (as defined within this paper) can be a selection factor. This causes Self-Organized Modularization to take place. The experimental observations emphasize the importance of Effective Modularity in comparison with Built-in Modularity. Although the experimental results have been obtained using a minimalist toy model, they can lead to a number of consequences for existing models as well as for future approaches.Furthermore, the results suggest a complex self-amplification of highly modular equivalence classes in the case of respected relations. Since the well-known Holland schemata are just the equivalence classes of respected relations in most Simple Genetic Algorithms, this observation emphasizes the role of schemata as Building Blocks (in comparison with arbitrary subsets of the search space).