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An Extension of Geiringer's Theorem for a Wide Class of Evolutionary Search Algorithms
2006
Evolutionary Computation
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This theorem not only implies the already existing versions of Geiringer's theorem, but also provides a recipe of how to obtain similar facts for a rather wide class of evolutionary algorithms. ...
The frequency with which various elements of the search space of a given evolutionary algorithm are sampled is affected by the family of recombination (reproduction) operators. ...
Acknowledgments The authors would like to thank the following for their advice and help with this paper: Andreas Blass, Divakar Viswanath, John Holland, Rick Riolo, and the University of Michigan complex ...
doi:10.1162/evco.2006.14.1.87
pmid:16536892
fatcat:nlxeigbbfvcl7kgdifvgbhkv54
An Extension of Geiringer's Theorem for a Wide Class of Evolutionary Search Algorithms
2006
Evolutionary Computation
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2008; you can also visit the original URL.
The file type is application/pdf.
This theorem not only implies the already existing versions of Geiringer's theorem, but also provides a recipe of how to obtain similar facts for a rather wide class of evolutionary algorithms. ...
The frequency with which various elements of the search space of a given evolutionary algorithm are sampled is affected by the family of recombination (reproduction) operators. ...
Acknowledgments The authors would like to thank the following for their advice and help with this paper: Andreas Blass, Divakar Viswanath, John Holland, Rick Riolo, and the University of Michigan complex ...
doi:10.1162/106365606776022805
pmid:16536892
fatcat:ty5zc4okbfbhxgdhi6rwn33vl4
Some results about the Markov chains associated to GPs and general EAs
2006
Theoretical Computer Science
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Moreover we prove an "anti-communism" theorem which applies to a wide class of EAs and says that for small enough mutation rate, the stationary distribution of the Markov chain modelling the EA cannot ...
Geiringer's theorem is a statement which tells us something about the limiting frequency of occurrence of a certain individual when a classical genetic algorithm is executed in the absence of selection ...
Boris Mitavskiy is very grateful to Professor Andreas Blass for his professional guidance and for the numerous educative advisor meetings during his (author's) years in graduate school. ...
doi:10.1016/j.tcs.2006.04.006
fatcat:3h5ruf7ryjawni34dvhtgcpqru
General Schema Theory for Genetic Programming with Subtree-Swapping Crossover: Part II
2003
Evolutionary Computation
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These include an exact definition of effective fitness and a size-evolution equation for GP with subtree-swapping crossover. ...
Like other recent GP schema theory results, the theory gives an exact formulation (rather than a lower bound) for the expected number of instances of a schema at the next generation. ...
Riccardo would like to thank the members of the NEC (Natural and Evolutionary Computation) group at Essex for helpful comments and discussion. ...
doi:10.1162/106365603766646825
pmid:12875668
fatcat:6t7tbuifazhrrj347okpsmnj6u
General Schema Theory for Genetic Programming with Subtree-Swapping Crossover: Part I
2003
Evolutionary Computation
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The file type is application/pdf.
These include an exact definition of effective fitness and a size-evolution equation for GP with subtree-swapping crossover. ...
Like other recent GP schema theory results, the theory gives an exact formulation (rather than a lower bound) for the expected number of instances of a schema at the next generation. ...
Riccardo would like to thank the members of the NEC (Natural and Evolutionary Computation) group at Essex for helpful comments and discussion. ...
doi:10.1162/106365603321829005
pmid:12804097
fatcat:2fylmow3zfcspo2rworxs26kya
Landscapes and Effective Fitness
2003
Comments on Theoretical Biology
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a particular coordinate transformation that provides an appropriate basis for illuminating the structure and consequences of recombination. ...
The concept of a fitness landscape arose in theoretical biology, while that of effective fitness has its origin in evolutionary computation. ...
CRS wishes to thank Riccardo Poli for many stimulating and productive discussions. ...
doi:10.1080/08948550302439
fatcat:yecb5chpvnenxleojnhdj3ipre