The Simple Genetic Algorithm: Foundations and Theory
The Simple Genetic Algorithm: Foundations and Theory
Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence
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
Schemata evolution and building blocks
Evolutionary Computation
Structural Search Spaces and Genetic Operators
Evolutionary Computation
Proceedings of the 8th annual conference on Genetic and evolutionary computation
Theory of the simple genetic algorithm with α-selection
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Introduction to Evolutionary Multiobjective Optimization
Multiobjective Optimization
Sufficient conditions for coarse-graining evolutionary dynamics
FOGA'07 Proceedings of the 9th international conference on Foundations of genetic algorithms
Theory of the simple genetic algorithm with α-selection, uniform crossover and bitwise mutation
WSEAS TRANSACTIONS on SYSTEMS
How crossover helps in pseudo-boolean optimization
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Understanding and protecting privacy: formal semantics and principled audit mechanisms
ICISS'11 Proceedings of the 7th international conference on Information Systems Security
When do evolutionary algorithms optimize separable functions in parallel?
Proceedings of the twelfth workshop on Foundations of genetic algorithms XII
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This paper assumes a search space of fixed-length strings, where the size of the alphabet can vary from position to position. Structural crossover is mask-based crossover, and thus includes n-point and uniform crossover. Structural mutation is mutation that commutes with a group operation on the search space. This paper shows that structural crossover and mutation project naturally onto competing families of schemata. In other words, the effect of crossover and mutation on a set of string positions can be specified by considering only what happens at those positions and ignoring other positions. However, it is not possible to do this for proportional selection except when fitness is constant on each schema of the family. One can write down an equation which includes selection which generalizes the Holland Schema theorem. However, like the Schema theorem, this equation cannot be applied over multiple time steps without keeping track of the frequency of every string in the search space.