Generalizing the notion of schema in genetic algorithms
Artificial Intelligence
Genetic algorithms + data structures = evolution programs (3rd ed.)
Genetic algorithms + data structures = evolution programs (3rd ed.)
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Evolutionary Computation
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GECCO '02 Proceedings of the Genetic and Evolutionary Computation Conference
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Evolutionary Computation
Algebraic theory of recombination spaces
Evolutionary Computation
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Evolutionary Computation
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Evolutionary Computation
Comparing evolutionary computation techniques via their representation
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartI
An Extension of Geiringer's Theorem for a Wide Class of Evolutionary Search Algorithms.
Evolutionary Computation
Genetic Programming and Evolvable Machines
Saddles and barrier in landscapes of generalized search operators
FOGA'07 Proceedings of the 9th international conference on Foundations of genetic algorithms
Comparing evolutionary computation techniques via their representation
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartI
NP-Completeness of deciding binary genetic encodability
FOGA'05 Proceedings of the 8th international conference on Foundations of Genetic Algorithms
FOGA'05 Proceedings of the 8th international conference on Foundations of Genetic Algorithms
An extension of geiringer's theorem for a wide class of evolutionary search algorithms
Evolutionary Computation
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This paper addresses the relationship between schemata and crossover operators. In Appendix A a general mathematical framework is developed which reveals an interesting correspondence between the families of reproduction transformations and the corresponding collections of invariant subsets of the search space. On the basis of this mathematical apparatus it is proved that the family of masked crossovers is, for all practical purposes, the largest family of transformations whose corresponding collection of invariant subsets is the family of Antonisse's schemata. In the process, a number of other interesting facts are shown. It is proved that the full dynastic span of a given subset of the search space under either one of the traditional families of crossover transformations (one-point crossovers or masked crossovers) is obtained after [log2n] iterations where n is the dimension of the search space. The generalized notion of invariance introduced in the current paper unifies Radcliffe's notions of "respect" and "gene transmission". Besides providing basic tools for the theoretical analysis carried out in the current paper, the general facts established in Appendix A provide a way to extend Radcliffe's notion of "genetic representation function" to compare various evolutionary computation techniques via their representation.