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-ratecontrolling 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 quasimacroevolution.
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Naitoh, K. Macroscopic kinetic equation for a genetic algorithm. Japan J. Indust. Appl. Math. 15, 87–133 (1998). https://doi.org/10.1007/BF03167398
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DOI: https://doi.org/10.1007/BF03167398