TY - JOUR

T1 - Macroscopic kinetic equation for a genetic algorithm

AU - Naitoh, Ken

PY - 1998/2

Y1 - 1998/2

N2 - A macroscopic kinetic equation of only four variables for a simple genetic algorithm (SGA) with an on-off type of replication operator and a crossover operator is developed and used to predict several types of evolutionary routes for a wide range of metabolic-rate-controlling parameters, initial conditions, string lengths, population sizes, and environments. The four variables correspond to the probabilities of the best-adapted species and three mutant groups into which degenerate and redundant strings are classified according to the Hamming distance (HD). The time-dependent frequency distribution along the fitness value is given by an implicit formulation. The environment is also defined in the HD-fitness value space as the frequency distribution of all the possible types of strings without redundancy. It is found that the SGA possesses the capability for exploring quasi-macroevolution.

AB - A macroscopic kinetic equation of only four variables for a simple genetic algorithm (SGA) with an on-off type of replication operator and a crossover operator is developed and used to predict several types of evolutionary routes for a wide range of metabolic-rate-controlling parameters, initial conditions, string lengths, population sizes, and environments. The four variables correspond to the probabilities of the best-adapted species and three mutant groups into which degenerate and redundant strings are classified according to the Hamming distance (HD). The time-dependent frequency distribution along the fitness value is given by an implicit formulation. The environment is also defined in the HD-fitness value space as the frequency distribution of all the possible types of strings without redundancy. It is found that the SGA possesses the capability for exploring quasi-macroevolution.

KW - Degeneracy structure

KW - Evolutionary stability

KW - Genetic algorithm

KW - Macroscopic kinetic equation

KW - Quasi-macroevolution

UR - http://www.scopus.com/inward/record.url?scp=0038955597&partnerID=8YFLogxK

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U2 - 10.1007/BF03167398

DO - 10.1007/BF03167398

M3 - Article

AN - SCOPUS:0038955597

VL - 15

SP - 87

EP - 133

JO - Japan Journal of Industrial and Applied Mathematics

JF - Japan Journal of Industrial and Applied Mathematics

SN - 0916-7005

IS - 1

ER -