Analysis of Selection, Mutation and Recombination in Genetic Algorithms

Genetic algorithms have been applied fairly successful to a number of optimization problems. Nevertheless, a common theory why and when they work is still missing. In this paper a theory is outlined which is based on the science of plant and animal breeding. A central part of the theory is the response to selection equation and the concept of heritability. A fundamental theorem states that the heritability is equal to the regression coefficient of parent to offspring. The theory is applied to analyze selection, mutation and recombination. The results are used in the Breeder Genetic Algorithm whose performance is shown to be superior to other genetic algorithms.

[1]  H. Grüneberg,et al.  Introduction to quantitative genetics , 1960 .

[2]  M. Kimura The Neutral Theory of Molecular Evolution: Introduction , 1983 .

[3]  Heinz Mühlenbein,et al.  The Science of Breeding and Its Application to the Breeder Genetic Algorithm (BGA) , 1993, Evolutionary Computation.

[4]  Kalyanmoy Deb,et al.  Messy Genetic Algorithms Revisited: Studies in Mixed Size and Scale , 1990, Complex Syst..

[5]  J. Davenport Editor , 1960 .

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

[7]  Schloss Birlinghoven Evolution in Time and Space -the Parallel Genetic Algorithm , 1991 .

[8]  Larry J. Eshelman,et al.  The CHC Adaptive Search Algorithm: How to Have Safe Search When Engaging in Nontraditional Genetic Recombination , 1990, FOGA.

[9]  R. Elston The mathematical theory of quantitative genetics , 1982 .

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

[11]  W. Vent,et al.  Rechenberg, Ingo, Evolutionsstrategie — Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. 170 S. mit 36 Abb. Frommann‐Holzboog‐Verlag. Stuttgart 1973. Broschiert , 1975 .

[12]  M. Kimura,et al.  An introduction to population genetics theory , 1971 .

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

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

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

[16]  R. A. Fisher,et al.  The Genetical Theory of Natural Selection , 1931 .

[17]  Thomas Bäck,et al.  A Survey of Evolution Strategies , 1991, ICGA.

[18]  M. Kimura,et al.  The neutral theory of molecular evolution. , 1983, Scientific American.

[19]  J. Crow Basic concepts in population, quantitative, and evolutionary genetics , 1986 .

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

[21]  Lashon B. Booker,et al.  Proceedings of the fourth international conference on Genetic algorithms , 1991 .

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

[23]  Heinz Mühlenbein,et al.  Evolution in Time and Space - The Parallel Genetic Algorithm , 1990, FOGA.

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

[25]  Thomas Bäck,et al.  An Overview of Evolutionary Algorithms for Parameter Optimization , 1993, Evolutionary Computation.

[26]  Heinz Mühlenbein,et al.  Evolution algorithms in combinatorial optimization , 1988, Parallel Comput..

[27]  Gilbert Syswerda,et al.  Uniform Crossover in Genetic Algorithms , 1989, ICGA.

[28]  J. David Schaffer,et al.  Proceedings of the third international conference on Genetic algorithms , 1989 .