Adaptation in natural and artificial systems
Adaptation in natural and artificial systems
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
Group properties of crossover and mutation
Evolutionary Computation
Form Invariance and Implicit Parallelism
Evolutionary Computation
General cardinality genetic algorithms
Evolutionary Computation
The simple genetic algorithm and the walsh transform: Part i, theory
Evolutionary Computation
Schemata evolution and building blocks
Evolutionary Computation
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartII
An Extension of Geiringer's Theorem for a Wide Class of Evolutionary Search Algorithms.
Evolutionary Computation
Proceedings of the 8th annual conference on Genetic and evolutionary computation
Evolutionary Computation
Neighborhood graphs and symmetric genetic operators
FOGA'07 Proceedings of the 9th international conference on Foundations of genetic algorithms
Representation invariant genetic operators
Evolutionary Computation
FOGA'05 Proceedings of the 8th international conference on Foundations of Genetic Algorithms
Principal coordinate strategy: a novel adaptive control strategy for differential evolution
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
An extension of geiringer's theorem for a wide class of evolutionary search algorithms
Evolutionary Computation
Dilemmas in knowledge-based evolutionary computation for financial investing
Intelligent Decision Technologies
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In a previous paper (Rowe et al., 2002), aspects of the theory of genetic algorithms were generalised to the case where the search space, Ω, had an arbitrary group action defined on it. Conditions under which genetic operators respect certain subsets of Ω were identified, leading to a generalisation of the term schema. In this paper, search space groups with more detailed structure are examined. We define the class of structural crossover operators that respect certain schemata in these groups, which leads to a generalised schema theorem. Recent results concerning the Fourier (or Walsh) transform are generalised. In particular, it is shown that the matrix group representing Ω can be simultaneously diagonalised if and only if Ω is Abelian. Some results concerning structural crossover and mutation are given for this case.