How to analyse evolutionary algorithms

Many variants of evolutionary algorithms have been designed and applied. The experimental knowledge is immense. The rigorous analysis of evolutionary algorithms is difficult, but such a theory can help to understand, design, and teach evolutionary algorithms. In this survey, first the history of attempts to analyse evolutionary algorithms is described and then new methods for continuous as well as discrete search spaces are presented and discussed.

[1]  L. J. Eshelman,et al.  chapter Real-Coded Genetic Algorithms and Interval-Schemata , 1993 .

[2]  Thomas Jansen,et al.  On the analysis of the (1+1) evolutionary algorithm , 2002, Theor. Comput. Sci..

[3]  Rajeev Motwani,et al.  Randomized Algorithms , 1995, SIGA.

[4]  Hans-Georg Beyer,et al.  Analysis of the (/, )-ES on the Parabolic Ridge , 2000, Evolutionary Computation.

[5]  I. Wegener,et al.  Design and Management of Complex Technical Processes and Systems by means of Computational Intelligence Methods A Natural and Simple Function Which is Hard For All Evolutionary Algorithms , 2007 .

[6]  Dirk V. Arnold,et al.  Noisy Optimization With Evolution Strategies , 2002, Genetic Algorithms and Evolutionary Computation.

[7]  Kenneth A. De Jong,et al.  Are Genetic Algorithms Function Optimizers? , 1992, PPSN.

[8]  David B. Fogel,et al.  Evolutionary Computation: The Fossil Record , 1998 .

[9]  Thomas Jansen,et al.  A New Framework for the Valuation of Algorithms for Black-Box Optimization , 2002, FOGA.

[10]  David B. Fogel,et al.  Evolutionary Computation: Towards a New Philosophy of Machine Intelligence , 1995 .

[11]  Hans-Georg Beyer,et al.  Towards a Theory of 'Evolution Strategies': Results for (1, +λ)-Strategies on (Nearly) Arbitrary Fitness Functions , 1994, PPSN.

[12]  Hans-Georg Beyer,et al.  Local performance of the (1 + 1)-ES in a noisy environment , 2002, IEEE Trans. Evol. Comput..

[13]  Schloss Birlinghoven,et al.  How Genetic Algorithms Really Work I.mutation and Hillclimbing , 2022 .

[14]  Dipl. Ing. Karl Heinz Kellermayer.  NUMERISCHE OPTIMIERUNG VON COMPUTER-MODELLEN MITTELS DER EVOLUTIONSSTRATEGIE Hans-Paul Schwefel Birkhäuser, Basel and Stuttgart, 1977 370 pages Hardback SF/48 ISBN 3-7643-0876-1 , 1977 .

[15]  Lawrence J. Fogel,et al.  Artificial Intelligence through Simulated Evolution , 1966 .

[16]  Hans-Georg Beyer,et al.  Performance analysis of evolution strategies with multi-recombination in high-dimensional RN-search spaces disturbed by noise , 2002, Theor. Comput. Sci..

[17]  Melanie Mitchell,et al.  The royal road for genetic algorithms: Fitness landscapes and GA performance , 1991 .

[18]  Hans-Paul Schwefel,et al.  Evolution strategies – A comprehensive introduction , 2002, Natural Computing.

[19]  Georg Rappl,et al.  Konvergenzraten von Random-Search-Verfahren zur globalen Optimierung , 1984 .

[20]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[21]  John Maynard Smith,et al.  Models of evolution , 1983, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[22]  Kalyanmoy Deb,et al.  Long Path Problems , 1994, PPSN.

[23]  Thomas Jansen,et al.  Design and Management of Complex Technical Processes and Systems by means of Computational Intelligence Methods On the Choice of the Mutation Probability for the ( 1 + 1 ) EA , 2006 .

[24]  Thomas Jansen,et al.  Dynamic Parameter Control in Simple Evolutionary Algorithms , 2001, FOGA.

[25]  Marc Schoenauer,et al.  Rigorous Hitting Times for Binary Mutations , 1999, Evolutionary Computation.

[26]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[27]  Andrew Chi-Chih Yao,et al.  Probabilistic computations: Toward a unified measure of complexity , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[28]  Adam Prügel-Bennett,et al.  A Statistical Mechanical Formulation of the Dynamics of Genetic Algorithms , 1994, Evolutionary Computing, AISB Workshop.

[29]  Russell Beale,et al.  Handbook of Neural Computation , 1996 .

[30]  Michael Herdy,et al.  Reproductive Isolation as Strategy Parameter in Hierarichally Organized Evolution Strategies , 1992, PPSN.

[31]  Stefano Marsili-Libelli,et al.  Adaptive mutation in genetic algorithms , 2000, Soft Comput..

[32]  Ingo Wegener,et al.  Theoretical Aspects of Evolutionary Algorithms , 2001, ICALP.

[33]  Heinz Mühlenbein,et al.  Predictive Models for the Breeder Genetic Algorithm I. Continuous Parameter Optimization , 1993, Evolutionary Computation.

[34]  Ingo Rechenberg,et al.  Evolutionsstrategie '94 , 1994, Werkstatt Bionik und Evolutionstechnik.

[35]  Kennetb A. De.  Genetic Algorithms Are NOT Function Optimizers , 1992 .

[36]  Colin R. Reeves,et al.  Are Long Path Problems Hard for Genetic Algorithms? , 1996, PPSN.

[37]  A I Oyman,et al.  Analysis of the (1, )-ES on the Parabolic Ridge , 2000, Evolutionary Computation.

[38]  I. Good,et al.  The Maximum Entropy Formalism. , 1979 .

[39]  Nikolaus Hansen,et al.  Completely Derandomized Self-Adaptation in Evolution Strategies , 2001, Evolutionary Computation.

[40]  A. E. Eiben,et al.  Global Convergence of Genetic Algorithms: A Markov Chain Analysis , 1990, PPSN.

[41]  A. Sinclair,et al.  A computational view of population genetics , 1998 .

[42]  Hans-Georg Beyer,et al.  The Theory of Evolution Strategies , 2001, Natural Computing Series.

[43]  Heinz Mühlenbein,et al.  How Genetic Algorithms Really Work: Mutation and Hillclimbing , 1992, PPSN.

[44]  David E. Goldberg,et al.  The gambler''s ruin problem , 1997 .

[45]  Thomas Jansen,et al.  On the Optimization of Unimodal Functions with the (1 + 1) Evolutionary Algorithm , 1998, PPSN.

[46]  E. Cantu-Paz,et al.  The Gambler's Ruin Problem, Genetic Algorithms, and the Sizing of Populations , 1997, Evolutionary Computation.

[47]  Thomas Bäck,et al.  Evolutionary computation: Toward a new philosophy of machine intelligence , 1997, Complex..

[48]  J. Shapiro.  Statistical mechanics theory of genetic algorithms , 2001 .

[49]  H. Beyer.  An alternative explanation for the manner in which genetic algorithms operate. , 1997, Bio Systems.

[50]  John J. Grefenstette,et al.  Deception Considered Harmful , 1992, FOGA.

[51]  Hans-Paul Schwefel,et al.  Numerical optimization of computer models , 1981 .

[52]  Yuval Rabani,et al.  A computational view of population genetics , 1995, STOC '95.

[53]  Hans-Georg Beyer,et al.  Toward a Theory of Evolution Strategies: The (, )-Theory , 1994, Evolutionary Computation.

[54]  Hans-Georg Beyer,et al.  On the performance of (1, Lambda)-evolution strategies for the ridge function class , 2001, IEEE Trans. Evol. Comput..

[55]  Jarmo T. Alander,et al.  An Indexed Bibliography of Genetic Algorithms , 1995 .

[56]  Günter Rudolph,et al.  How Mutation and Selection Solve Long-Path Problems in Polynomial Expected Time , 1996, Evolutionary Computation.

[57]  Thomas Jansen,et al.  On the Analysis of Evolutionary Algorithms - A Proof That Crossover Really Can Help , 1999 .

[58]  E. T. Jaynes,et al.  Where do we Stand on Maximum Entropy , 1979 .

[59]  Kalyanmoy Deb,et al.  On self-adaptive features in real-parameter evolutionary algorithms , 2001, IEEE Trans. Evol. Comput..

[60]  Dan Boneh,et al.  On genetic algorithms , 1995, COLT '95.

[61]  Christos H. Papadimitriou,et al.  Computational complexity , 1993 .

[62]  G. Rappl.  On Linear Convergence of a Class of Random Search Algorithms , 1989 .

[63]  John H. Holland,et al.  When will a Genetic Algorithm Outperform Hill Climbing , 1993, NIPS.

[64]  Ingo Rechenberg,et al.  Evolutionsstrategie : Optimierung technischer Systeme nach Prinzipien der biologischen Evolution , 1973 .

[65]  Hans-Georg Beyer,et al.  On the performance of (1,l)-Evolution Strategies at the ridge function class , 2001 .

[66]  Hans-Georg Beyer,et al.  Fitness Noise and Localization Errors of the Optimum in General Quadratic Fitness Models , 1999, GECCO.

[67]  G. Unter Rudolph.  On Correlated Mutations in Evolution Strategies , 1992 .

[68]  José Carlos Príncipe,et al.  A Markov Chain Framework for the Simple Genetic Algorithm , 1993, Evolutionary Computation.

[69]  Hans-Georg Beyer,et al.  Toward a Theory of Evolution Strategies: Self-Adaptation , 1995, Evolutionary Computation.

[70]  Nikolaus Hansen,et al.  Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[71]  Hans-Paul Schwefel,et al.  Direct search for optimal parameters within simulation models , 1979 .

[72]  Ingo Wegener,et al.  On the utility of populations in evolutionary algorithms , 2001 .

[73]  Ahmet Irfan Oyman,et al.  Convergence behavior of evolution strategies on ridge functions , 1999 .

[74]  Kalyanmoy Deb,et al.  Genetic Algorithms, Noise, and the Sizing of Populations , 1992, Complex Syst..

[75]  Thomas Bäck,et al.  Evolutionary Algorithms: The Role of Mutation and Recombination , 2000 .

[76]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[77]  Zbigniew Michalewicz,et al.  Handbook of Evolutionary Computation , 1997 .

[78]  Thomas Bäck,et al.  Optimal Mutation Rates in Genetic Search , 1993, ICGA.

[79]  Hans-Georg Beyer,et al.  Local Performance of the (μ/μ, μ)-ES in a Noisy Environment , 2000, FOGA.

[80]  A. Prügel-Bennett,et al.  Modelling genetic algorithm dynamics , 2001 .

[81]  Michael D. Vose,et al.  The simple genetic algorithm - foundations and theory , 1999, Complex adaptive systems.

[82]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[83]  Prügel-Bennett,et al.  Analysis of genetic algorithms using statistical mechanics. , 1994, Physical review letters.