Adaptation in natural and artificial systems
Adaptation in natural and artificial systems
Foundations of genetic programming
Foundations of genetic programming
The Simple Genetic Algorithm: Foundations and Theory
The Simple Genetic Algorithm: Foundations and Theory
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Effective Fitness as an Alternative Paradigm for Evolutionary Computation I: General Formalism
Genetic Programming and Evolvable Machines
Genetic Programming and Evolvable Machines
Group properties of crossover and mutation
Evolutionary Computation
Using Schema Theory To Explore Interactions Of Multiple Operators
GECCO '02 Proceedings of the Genetic and Evolutionary Computation Conference
General schema theory for genetic programming with subtree-swapping crossover: part I
Evolutionary Computation
General schema theory for genetic programming with subtree-swapping crossover: Part II
Evolutionary Computation
Genetic Programming and Evolvable Machines
Schemata evolution and building blocks
Evolutionary Computation
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
A simple but theoretically-motivated method to control bloat in genetic programming
EuroGP'03 Proceedings of the 6th European conference on Genetic programming
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This is the first part of a two-part paper where we propose, model theoretically and study a general notion of recombination for fixed-length strings, where homologous recombination, inversion, gene duplication, gene deletion, diploidy and more are just special cases. The analysis of the model reveals that the notion of schema emerges naturally from the model's equations. In Part I, after describing and characterising the notion of generalised recombination, we derive both microscopic and coarse-grained evolution equations for strings and schemata and illustrate their features with simple examples. Also, we explain the hierarchical nature of the schema evolution equations and show how the theory presented here generalises past work in evolutionary computation. In Part II, the study provides a variety of fixed points for evolution in the case where recombination is used alone, which generalise Geiringer's theorem, in addition, we numerically integrate the infinite-population schema equations for some interesting problems, where selection and recombination are used together to illustrate how these operators interact. Finally, to assess by how much genetic drift can make a system deviate from the infinite-population-model predictions we discuss the results of real GA runs for the same model problems with generalised recombination, selection and finite populations of different sizes.