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An Extension of Geiringer's Theorem for a Wide Class of Evolutionary Search Algorithms

Boris Mitavskiy, Jonathan Rowe
2006 Evolutionary Computation  
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

Boris Mitavskiy, Jonathan Rowe
2006 Evolutionary Computation  
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

Boris Mitavskiy, Jonathan Rowe
2006 Theoretical Computer Science  
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

Riccardo Poli, Nicholas Freitag McPhee
2003 Evolutionary Computation  
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

Riccardo Poli, Nicholas Freitag McPhee
2003 Evolutionary Computation  
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

Peter F. Stadler, Christopher R. Stephens
2003 Comments on Theoretical Biology  
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