Error Thresholds in Genetic Algorithms

The error threshold of replication is an important notion in the quasispecies evolution model; it is a critical mutation rate (error rate) beyond which structures obtained by an evolutionary process are destroyed more frequently than selection can reproduce them. With mutation rates above this critical value, an error catastrophe occurs and the genomic information is irretrievably lost. Therefore, studying the factors that alter this magnitude has important implications in the study of evolution. Here we use a genetic algorithm, instead of the quasispecies model, as the underlying model of evolution, and explore whether the phenomenon of error thresholds is found on finite populations of bit strings evolving on complex landscapes. Our empirical results verify the occurrence of error thresholds in genetic algorithms. In this way, this notion is brought from molecular evolution to evolutionary computation. We also study the effect of modifying the most prominent evolutionary parameters on the magnitude of this critical value, and found that error thresholds depend mainly on the selection pressure and genotype length.

[1]  M. Nowak,et al.  Error thresholds of replication in finite populations mutation frequencies and the onset of Muller's ratchet. , 1989, Journal of theoretical biology.

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

[3]  P. Schuster,et al.  A computer model of evolutionary optimization. , 1987, Biophysical chemistry.

[4]  Alden H. Wright,et al.  Bistability in a Gene Pool GA with Mutation , 2002, FOGA.

[5]  J. Crutchfield,et al.  Optimizing Epochal Evolutionary Search: Population-Size Dependent Theory , 1998, Machine-mediated learning.

[6]  Inman Harvey,et al.  Recombination and Error Thresholds in Finite Populations , 1998, FOGA.

[7]  Peter Schuster,et al.  Extended Molecular Evolutionary Biology: Artificial Life Bridging the Gap Between Chemistry and Biology , 1993, Artificial Life.

[8]  SAGAInman HarveyCSRP.  Species Adaptation Genetic Algorithms: A Basis for a Continuing SAGA , 1992 .

[9]  Gabriela Ochoa,et al.  Error thresholds and optimal mutation rates in genetic algorithms , 2000 .

[10]  Inman Harvey,et al.  Through the Labyrinth Evolution Finds a Way: A Silicon Ridge , 1996, ICES.

[11]  M. Eigen,et al.  The Hypercycle: A principle of natural self-organization , 2009 .

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

[13]  Reinhard Männer,et al.  Towards an Optimal Mutation Probability for Genetic Algorithms , 1990, PPSN.

[14]  M. Nowak,et al.  Viral quasi-species and recombination , 1996, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[15]  Thomas Bäck,et al.  An evolutionary heuristic for the maximum independent set problem , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[16]  Inman Harvey,et al.  Evolutionary robotics: the Sussex approach , 1997, Robotics Auton. Syst..

[17]  Christoph Adami,et al.  Viral evolution under the pressure of an adaptive immune system: Optimal mutation rates for viral escape , 2002, Complex..

[18]  James R. Neil,et al.  Analysis of the simple genetic algorithm on the single-peak and double-peak landscapes , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[19]  M. Huynen.  Exploring phenotype space through neutral evolution , 1996, Journal of Molecular Evolution.

[20]  Peter F. Stadler,et al.  Error Thresholds on Correlated Fitness Landscapes , 1993 .

[21]  Kalyanmoy Deb,et al.  A Comparative Analysis of Selection Schemes Used in Genetic Algorithms , 1990, FOGA.

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

[23]  Vesselin K. Vassilev,et al.  Digital circuit evolution and fitness landscapes , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

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

[25]  John E. Beasley,et al.  OR-Library: Distributing Test Problems by Electronic Mail , 1990 .

[26]  J. Maynard Smith.  Natural Selection and the Concept of a Protein Space , 1970 .

[27]  Inman Harvey,et al.  Genetic Convergence in a Species of Evolved Robot Control Architectures , 1993, ICGA.

[28]  Gabriela Ochoa,et al.  Consensus Sequence Plots and Error Thresholds: Tools for Visualising the Structure of Fitness Landscapes , 2000, PPSN.

[29]  J. Root,et al.  Open the box , 1986 .

[30]  D. Fogel.  Evolutionary algorithms in theory and practice , 1997, Complex..

[31]  Luca Peliti,et al.  Quasispecies evolution in general mean-field landscapes , 2001, cond-mat/0105379.

[32]  Thomas Bäck,et al.  The zero/one multiple knapsack problem and genetic algorithms , 1994, SAC '94.

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

[34]  Peter Schuster.  Extended molecular evolutionary biology: Artificial life bridging the gap between chemistry and biology , 1993 .

[35]  John Maynard Smith,et al.  Natural Selection and the Concept of a Protein Space , 1970, Nature.

[36]  Alden H. Wright,et al.  Continuous Dynamical System Models of Steady-State Genetic Algorithms , 2000, FOGA.

[37]  Phil Husbands,et al.  A Comparison of Search Techniques on a Wing-Box Optimisation Problem , 1996, PPSN.

[38]  Jim Smith,et al.  Self adaptation of mutation rates in a steady state genetic algorithm , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[39]  Thomas Bäck,et al.  Evolutionary algorithms in theory and practice - evolution strategies, evolutionary programming, genetic algorithms , 1996 .

[40]  Inman Harvey,et al.  Evolutionary robotics and SAGA: The case for hill crawling and tournament selection , 1994 .

[41]  Inman Harvey,et al.  Error Thresholds and Their Relation to Optimal Mutation Rates , 2022 .

[42]  J. Crutchfield,et al.  Optimizing Epochal Evolutionary Search: Population-Size Dependent Theory , 1998, Machine Learning.

[43]  Stuart A. Kauffman,et al.  The origins of order , 1993 .

[44]  Thomas Bäck,et al.  The Interaction of Mutation Rate, Selection, and Self-Adaptation Within a Genetic Algorithm , 1992, PPSN.

[45]  Rajarshi Das,et al.  A Study of Control Parameters Affecting Online Performance of Genetic Algorithms for Function Optimization , 1989, ICGA.

[46]  M Nowak,et al.  Oscillations in the evolution of reciprocity. , 1989, Journal of theoretical biology.

[47]  M. Eigen,et al.  What is a quasispecies? , 2006, Current topics in microbiology and immunology.