Macroscopic kinetic equation for a genetic algorithm

Ken Naitoh*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)87-133
Number of pages47
JournalJapan Journal of Industrial and Applied Mathematics
Issue number1
Publication statusPublished - 1998 Feb
Externally publishedYes


  • Degeneracy structure
  • Evolutionary stability
  • Genetic algorithm
  • Macroscopic kinetic equation
  • Quasi-macroevolution

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics


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