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.
|ジャーナル||Japan Journal of Industrial and Applied Mathematics|
|出版ステータス||Published - 1998 2|
ASJC Scopus subject areas
- Applied Mathematics