ASYMPTOTIC CONVERGENCE PROPERTIES OF GENETIC ALGORITHMS AND EVOLUTIONARY PROGRAMMING: ANALYSIS AND EXPERIMENTS

The basic convergence properties of evolutionary optimization algorithms are investigated. Analysis indicates that the methods studied will asymptotically converge to global optima. The results also indicate that genetic algorithms may prematurely stagnate at solutions that may not even be locally optimal. Function optimization experiments are conducted that illustrate the mathematical properties. Evolutionary programming is seen to outperform genetic algorithms in searching two response surfaces that do not possess local optima. The results are statistically significant.

[1]  George E. P. Box,et al.  Evolutionary Operation: a Method for Increasing Industrial Productivity , 1957 .

[2]  Alex Fraser,et al.  Simulation of Genetic Systems by Automatic Digital Computers I. Introduction , 1957 .

[3]  Richard M. Friedberg,et al.  A Learning Machine: Part I , 1958, IBM J. Res. Dev..

[4]  A. Fraser.  Simulation of Genetic Systems by Automatic Digital Computers VI. Epistasis , 1960 .

[5]  H. H. Rosenbrock,et al.  An Automatic Method for Finding the Greatest or Least Value of a Function , 1960, Comput. J..

[6]  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 .

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

[8]  Kenneth Alan De Jong,et al.  An analysis of the behavior of a class of genetic adaptive systems. , 1975 .

[9]  R. Serfling.  Approximation Theorems of Mathematical Statistics , 1980 .

[10]  Hans-Paul Schwefel,et al.  Numerical Optimization of Computer Models , 1982 .

[11]  John J. Grefenstette,et al.  Optimization of Control Parameters for Genetic Algorithms , 1986, IEEE Transactions on Systems, Man, and Cybernetics.

[12]  Roe Goodman,et al.  Introduction to stochastic models , 1987 .

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

[14]  Lawrence. Davis,et al.  Handbook Of Genetic Algorithms , 1990 .

[15]  D. Fogel.  System Identification Through Simulated Evolution: A Machine Learning Approach to Modeling , 1991 .

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

[17]  Larry J. Eshelman,et al.  On Crossover as an Evolutionarily Viable Strategy , 1991, ICGA.

[18]  David B. Fogel,et al.  Evolving artificial intelligence , 1992 .

[19]  Z. Michalewicz,et al.  A modified genetic algorithm for optimal control problems , 1992 .