### Abstract

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 language | English |
---|---|

Pages (from-to) | 87-133 |

Number of pages | 47 |

Journal | Japan Journal of Industrial and Applied Mathematics |

Volume | 15 |

Issue number | 1 |

Publication status | Published - 1998 Feb |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Macroscopic kinetic equation for a genetic algorithm.** / Naitoh, Ken.

Research output: Contribution to journal › Article

*Japan Journal of Industrial and Applied Mathematics*, vol. 15, no. 1, pp. 87-133.

}

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

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

M3 - Article

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 -