Foundations of genetic programming
Foundations of genetic programming
The Simple Genetic Algorithm: Foundations and Theory
The Simple Genetic Algorithm: Foundations and Theory
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
Genetic Algorithms: Principles and Perspectives: A Guide to GA Theory
Genetic Algorithms: Principles and Perspectives: A Guide to GA Theory
Genetic algorithms as function optimizers
Genetic algorithms as function optimizers
A theoretical analysis of the HIFF problem
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Form Invariance and Implicit Parallelism
Evolutionary Computation
Structural Search Spaces and Genetic Operators
Evolutionary Computation
General cardinality genetic algorithms
Evolutionary Computation
The simple genetic algorithm and the walsh transform: Part i, theory
Evolutionary Computation
The simple genetic algorithm and the walsh transform: Part ii, the inverse
Evolutionary Computation
Schemata evolution and building blocks
Evolutionary Computation
EC theory: a unified viewpoint
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartII
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We present a covariant form for the dynamics of a canonical GA of arbitrary cardinality, showing how each genetic operator can be uniquely represented by a mathematical object ---a tensor ---that transforms simply under a general linear coordinate transformation. For mutation and recombination these tensors can be written as tensor products of the analogous tensors for one-bit strings thus giving a greatly simplified formulation of the dynamics. We analyze the three most well known coordinate systems ---string, Walsh and Building Block ---discussing their relative advantages and disadvantages with respect to the different operators, showing how one may transform from one to the other, and that the associated coordinate transformation matrices can be written as a tensor product of the corresponding one-bit matrices. We also show that in the Building Block basis the dynamical equations for all Building Blocks can be generated from the equation for the most fine-grained block (string) by a certain projection (“zapping”).