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An Overview of Schema Theory [article]

David White
2014 arXiv   pre-print
Schema theory seeks to give a theoretical justification for the efficacy of the field of genetic algorithms, so readers who have studied genetic algorithms stand to gain the most from this paper.  ...  Because the mathematics behind the theorems in schema theory is relatively elementary, we focus more on the motivation and philosophy.  ...  The Exact Schema Theorem applies to both genetic programming and variable length genetic algorithms and so it answers the first major criticism of schema theory.  ... 
arXiv:1401.2651v1 fatcat:nj34scnoz5gpzh3hacmz3ukvyq

Exact Schema Theory and Markov Chain Models for Genetic Programming and Variable-length Genetic Algorithms with Homologous Crossover

Riccardo Poli, Nicholas Freitag McPhee, Jonathan E. Rowe
2004 Genetic Programming and Evolvable Machines  
Nic McPhee thanks The University of Birmingham School of Computer Science for graciously hosting him during his sabbatical, and various offices and individuals at the University of Minnesota, Morris, for  ...  Acknowledgments The authors would like to thank the anonymous reviewers and the Editor-in-Chief for their excellent suggestions for improving this manuscript.  ...  The development of theory for evolutionary algorithms operating on structures with variable size and shape is complex, and simply getting to the point of stating exact models for these algorithms requires  ... 
doi:10.1023/b:genp.0000017010.41337.a7 fatcat:iv7qycu7nrhqblxabc3b6jisxy

General Schema Theory for Genetic Programming with Subtree-Swapping Crossover: Part II

Riccardo Poli, Nicholas Freitag McPhee
2003 Evolutionary Computation  
This paper is the second part of a two-part paper which introduces a general schema theory for genetic programming (GP) with subtree-swapping crossover (Part I (Poli and McPhee, 2003)).  ...  These include an exact definition of effective fitness and a size-evolution equation for GP with subtree-swapping crossover.  ...  Langdon for useful discussions and comments on various parts of the work reported in this paper.  ... 
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  
This paper is the second part of a two-part paper which introduces a general schema theory for genetic programming (GP) with subtree-swapping crossover (Part I (Poli and McPhee, 2003)).  ...  These include an exact definition of effective fitness and a size-evolution equation for GP with subtree-swapping crossover.  ...  Langdon for useful discussions and comments on various parts of the work reported in this paper.  ... 
doi:10.1162/106365603321829005 pmid:12804097 fatcat:2fylmow3zfcspo2rworxs26kya

Geiringer theorems: from population genetics to computational intelligence, memory evolutive systems and Hebbian learning

Boris S. Mitavskiy, Elio Tuci, Chris Cannings, Jonathan Rowe, Jun He
2013 Natural Computing  
It has been adopted to the setting of evolutionary algorithms and, a lot more recently, reinforcement learning and Monte-Carlo tree search methodology to cope with a rather challenging question of action  ...  The theorem motivates novel dynamic parallel algorithms that are explicitly described in the current paper for the first time.  ...  Even more recent is the development of exact schema theorems for variable-length GAs, linear GP and tree-based GP.  ... 
doi:10.1007/s11047-013-9395-4 fatcat:y5q4t57frbh6hd2x2nwkhybky4

Allele Diffusion in Linear Genetic Programming and Variable-Length Genetic Algorithms with Subtree Crossover [chapter]

Riccardo Poli, Jonathan E. Rowe, Christopher R. Stephens, Alden H. Wright
2002 Lecture Notes in Computer Science  
In this paper we study, theoretically, the search biases produced by GP subtree crossover when applied to linear representations, such as those used in linear GP or in variable length GAs.  ...  This indicates the presence of a diffusion process by which, even in the absence of selective pressure and mutation, the alleles in a particular individual tend not just to be swapped with those of other  ...  JER, AHW and RP would like to thank EPSRC for their support.  ... 
doi:10.1007/3-540-45984-7_21 fatcat:73htixyuwfgjbf5w2jxelaibze

Behavior of finite population variable length genetic algorithms under random selection

Hal Stringer, Annie S. Wu
2005 Proceedings of the 2005 conference on Genetic and evolutionary computation - GECCO '05  
In this work we provide empirical evidence that shows how a variable-length genetic algorithm (GA) can naturally evolve shorter average size populations.  ...  This reduction in chromosome length appears to occur in finite population GAs when 1) selection is absent from the GA (random) or 2) when selection focuses on some other property not influenced by the  ...  The idea of exact schema was applied to Poli and Langdon's new schema theory in [5] to produce "a macroscopic exact schema theorem for genetic programming with one-point crossover."  ... 
doi:10.1145/1068009.1068213 dblp:conf/gecco/StringerW05 fatcat:4lwr47nmfrepdpxm26ibxvvnne

Genetic algorithms: a survey

M. Srinivas, L.M. Patnaik
1994 Computer  
Evolutionary ~t r a t e g i e s~.~ and genetic algorithm^,^.'^ on the other hand,  ...  The popularity of genetic algorithms is reflected in three biennial conferences, a new international journal, and an ever-increasing mass of literature devoted to the theory, practice, and applications  ...  In this article we introduce the art and science of genetic algorithms and survey current issues in G A theory and practice.  ... 
doi:10.1109/2.294849 fatcat:pwvpvkypcfcihh7rss6bfchkuy

A genetic algorithm approach to optimization of asynchronous automatic assembly systems

Mark A. Wellman, Douglas D. Gemmill
1995 International journal of flexible manufacturing systems  
The schema theory describes how a genetic algorithm allocates an increasing number of trials to low order, short defining length, above average schema.  ...  Therefore, the probability that a schema survives depends on the defining length of the schema and the length of the string.  ... 
doi:10.1007/bf01324878 fatcat:24klqftyo5cszoahatz23enida

A genetic algorithm tutorial

Darrell Whitley
1994 Statistics and computing  
The theoretical foundations of genetic algorithms are reviewed, include the schema theorem as well as recently developed exact models of the canonical genetic algorithm.  ...  This tutorial covers the canonical genetic algorithm as well as more experimental forms of genetic algorithms, including parallel island models and parallel cellular genetic algorithms.  ...  My thanks to the people in the genetic algorithm community who have educated me over the years. Any errors or errant i n terpretations of other works are my o wn.  ... 
doi:10.1007/bf00175354 fatcat:qgozsokcibcodktyhijsryubsy

Genetic Programming — Introduction, Applications, Theory and Open Issues [chapter]

Leonardo Vanneschi, Riccardo Poli
2012 Handbook of Natural Computing  
Congress on Evolutionary Computation  ...  Initially, these exact theories were only applicable to GP with one-point crossover (see > Sect. 2.5).  ...  The original equation was derived from the exact schema theory for GP.  ... 
doi:10.1007/978-3-540-92910-9_24 fatcat:gej2odib4nfo5l7snzxxbpprfi

Genetic algorithms: An overview

Melanie Mitchell
1995 Complexity  
Genetic algorithms (GAs) are computer programs that mimic the processes of biological evolution in order to solve problems and to model evolutionary systems.  ...  The paper concludes with a short introduction to the theory of GAs.  ...  Genetic Algorithms in Search, Optimization, and Machine Learning. Reading, MA: Addison-Wesley.  ... 
doi:10.1002/cplx.6130010108 fatcat:k3ywnqo72jaf3ayera6seq7zc4

Coarse-Grained Dynamics for Generalized Recombination

Christopher R. Stephens, Riccardo Poli
2007 IEEE Transactions on Evolutionary Computation  
An exact microscopic model for the dynamics of a genetic algorithm with generalized recombination is presented.  ...  We discuss how inferences from the two-locus results extend to the case of a recombinative genetic algorithm with selection and more than two loci providing evidence from an integration of the exact dynamical  ...  ACKNOWLEDGMENT The authors thank the referees for comments on the manuscript.  ... 
doi:10.1109/tevc.2006.884043 fatcat:44xtdgsxkffnbllrstaylxokru

EC Theory: A Unified Viewpoint [chapter]

Christopher R. Stephens, Adolfo Zamora
2003 Lecture Notes in Computer Science  
-link these different, disparate elements and alter the standard taxonomic classification of EC and different EC theories.  ...  As an illustration we emphasize one particular coordinate transformation between the standard string basis and the "Building Block" basis.  ...  CRS would like to thank Riccardo Poli and Peter Stadler for very fruitful collaborations and acknowledges support from DGAPA project ES100201 and Conacyt project 30422-E.  ... 
doi:10.1007/3-540-45110-2_13 fatcat:o52am4ie4vbrldggp6s3htpori

A Schema Theory Analysis of the Evolution of Size in Genetic Programming with Linear Representations [chapter]

Nicholas Freitag McPhee, Riccardo Poli
2001 Lecture Notes in Computer Science  
We also present two important theoretical results: An exact theory of bloat, and a general theory of how average size changes on flat landscapes with glitches.  ...  In this paper we use the schema theory presented in [20] to better understand the changes in size distribution when using GP with standard crossover and linear structures.  ...  We are also grateful for the valuable feedback provided by Bill Langdon and the anonymous reviewers.  ... 
doi:10.1007/3-540-45355-5_10 fatcat:b7p2ewraczgqvepefqdm7camku
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