Adaptation in natural and artificial systems
Adaptation in natural and artificial systems
Genetic programming: on the programming of computers by means of natural selection
Genetic programming: on the programming of computers by means of natural selection
Genetic programming: an introduction: on the automatic evolution of computer programs and its applications
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
Genetic Programming and Evolvable Machines
Size Fair and Homologous Tree Crossovers for Tree Genetic Programming
Genetic Programming and Evolvable Machines
Effective Fitness as an Alternative Paradigm for Evolutionary Computation I: General Formalism
Genetic Programming and Evolvable Machines
Genetic Programming and Evolvable Machines
Complexity Compression and Evolution
Proceedings of the 6th International Conference on Genetic Algorithms
Proceedings of the European Conference on Genetic Programming
A Schema Theory Analysis of the Evolution of Size in Genetic Programming with Linear Representations
EuroGP '01 Proceedings of the 4th European Conference on Genetic Programming
General Schema Theory for Genetic Programming with Subtree-Swapping Crossover
EuroGP '01 Proceedings of the 4th European Conference on Genetic Programming
EuroGP '01 Proceedings of the 4th European Conference on Genetic Programming
A Review of Theoretical and Experimental Results on Schemata in Genetic Programming
EuroGP '98 Proceedings of the First European Workshop on Genetic Programming
The Schema Theorem and the Misallocation of Trials in the Presence of Stochastic Effects
EP '98 Proceedings of the 7th International Conference on Evolutionary Programming VII
Grammatical bias for evolutionary learning
Grammatical bias for evolutionary learning
Building Blocks, Cohort Genetic Algorithms, and Hyperplane-Defined Functions
Evolutionary Computation
Schema theory for genetic programming with one-point crossover and point mutation
Evolutionary Computation
Schemata evolution and building blocks
Evolutionary Computation
Schema processing under proportional selection in the presence ofrandom effects
IEEE Transactions on Evolutionary Computation
Some Considerations on the Reason for Bloat
Genetic Programming and Evolvable Machines
Genetic Programming Experiments with Standard and Homologous Crossover Methods
Genetic Programming and Evolvable Machines
General Schema Theory for Genetic Programming with Subtree-Swapping Crossover
EuroGP '01 Proceedings of the 4th European Conference on Genetic Programming
EuroGP '02 Proceedings of the 5th European Conference on Genetic Programming
General schema theory for genetic programming with subtree-swapping crossover: Part II
Evolutionary Computation
Genetic Programming and Evolvable Machines
Backward-chaining evolutionary algorithms
Artificial Intelligence
Understanding the biases of generalised recombination: part I
Evolutionary Computation
Evolutionary Computation
An Analysis About the Asymptotic Convergence of Evolutionary Algorithms
Computational Intelligence and Security
Backward-chaining evolutionary algorithms
Artificial Intelligence
Visualisation of building blocks in evolutionary algorithms
CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
Evolutionary Model Type Selection for Global Surrogate Modeling
The Journal of Machine Learning Research
EC theory: a unified viewpoint
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartII
About the limit behaviors of the transition operators associated with EAs
ISICA'07 Proceedings of the 2nd international conference on Advances in computation and intelligence
Why recombination should be adaptive
Proceedings of the 12th annual conference on Genetic and evolutionary computation
A probabilistic functional crossover operator for genetic programming
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Theoretical results in genetic programming: the next ten years?
Genetic Programming and Evolvable Machines
Practical performance models of algorithms in evolutionary program induction and other domains
Artificial Intelligence
An exact schema theorem for adaptive genetic algorithm and its application to machine cell formation
Expert Systems with Applications: An International Journal
Perturbation theory and the renormalization group in genetic dynamics
FOGA'05 Proceedings of the 8th international conference on Foundations of Genetic Algorithms
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A few schema theorems for genetic programming (GP) have been proposed in the literature in the last few years. Since they consider schema survival and disruption only, they can only provide a lower bound for the expected value of the number of instances of a given schema at the next generation rather than an exact value. This paper presents theoretical results for GP with one-point crossover which overcome this problem. First, we give an exact formulation for the expected number of instances of a schema at the next generation in terms of microscopic quantities. Due to this formulation we are then able to provide an improved version of an earlier GP schema theorem in which some (but not all) schema creation events are accounted for. Then, we extend this result to obtain an exact formulation in terms of macroscopic quantities which makes all the mechanisms of schema creation explicit. This theorem allows the exact formulation of the notion of effective fitness in GP and opens the way to future work on GP convergence, population sizing, operator biases, and bloat, to mention only some of the possibilities.