### 抄録

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.

元の言語 | English |
---|---|

ページ（範囲） | 87-133 |

ページ数 | 47 |

ジャーナル | Japan Journal of Industrial and Applied Mathematics |

巻 | 15 |

発行部数 | 1 |

出版物ステータス | Published - 1998 2 |

外部発表 | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### これを引用

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

研究成果: Article

*Japan Journal of Industrial and Applied Mathematics*, 巻. 15, 番号 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

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 -