The Simple Genetic Algorithm: Foundations and Theory
The Simple Genetic Algorithm: Foundations and Theory
Tracing the Behavior of Genetic Algorithms Using Expected Values of Bit and Walsh Products
Proceedings of the 6th International Conference on Genetic Algorithms
A Critical Examination of the Schema Theorem
A Critical Examination of the Schema Theorem
Genetic algorithms as function optimizers
Genetic algorithms as function optimizers
Evolutionary Computation
Simple genetic algorithms with linear fitness
Evolutionary Computation
Modeling simple genetic algorithms
Evolutionary Computation
General cardinality genetic algorithms
Evolutionary Computation
Form Invariance and Implicit Parallelism
Evolutionary Computation
Gene Expression and Fast Construction of Distributed Evolutionary Representation
Evolutionary Computation
Structural Search Spaces and Genetic Operators
Evolutionary Computation
A building-block royal road where crossover is provably essential
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Evolutionary Computation
The simple genetic algorithm and the walsh transform: Part ii, the inverse
Evolutionary Computation
Detecting the epistatic structure of generalized embedded landscape
Genetic Programming and Evolvable Machines
Theory of the simple genetic algorithm with α-selection
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Natural coding: a more efficient representation for evolutionary learning
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartI
Theory of the simple genetic algorithm with α-selection, uniform crossover and bitwise mutation
WSEAS TRANSACTIONS on SYSTEMS
On the movement of vertex fixed points in the simple GA
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
ICS'10 Proceedings of the 14th WSEAS international conference on Systems: part of the 14th WSEAS CSCC multiconference - Volume II
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This paper is the first part of a two-part series. It proves a number of direct relationships between the Fourier transform and the simple genetic algorithm. (For a binary representation, the Walsh transform is the Fourier transform.) The results are of a theoretical nature and are based on the analysis of mutation and crossover. The Fourier transform of the mixing matrix is shown to be sparse. An explicit formula is given for the spectrum of the differential of the mixing transformation. By using the Fourier representation and the fast Fourier transform, one generation of the infinite population simple genetic algorithm can be computed in time O(cl log2 3), where c is arity of the alphabet and l is the string length. This is in contrast to the time of O(c3l) for the algorithm as represented in the standard basis. There are two orthogonal decompositions of population space that are invariant under mixing. The sequel to this paper will apply the basic theoretical results obtained here to inverse problems and asymptotic behavior.