AbstractThis paper considers the combinatorial optimization problem in which the solution (sample) can be decomposed linearly into multiple schemata. Focusing on an arbitrary kind of schema, the schema preservation mechanism of the crossover in the genetic algorithm is discussed from the viewpoint of the increase or decrease of the number of samples (considered samples) containing the considered schema in the set of sample bit strings. It is shown that the change in the number of considered samples with time is divided into two kind of phases (stable and unstable phases), depending on whether or not there exists a point of equilibrium for increase and decrease in copying during the course of selection, and for degradation by destruction in crossover and mutation. It is shown that the transition between the stable phase and the unstable phase occurs according to the magnitude relation between the average fitness of the considered samples and the average fitness of the whole set of sample bit strings. By setting the crossover ratio as a higher value in the genetic algorithm, the schema is uniformly embedded in the whole set of sample bit strings, which increases the average fitness of the considered samples, and generates an equilibrium point that maintains a constant number of considered samples. Lastly, a computer simulation is performed, and it is shown that the discussion of the schema preservation mechanism of the crossover is adequate. © 2002 Scripta Technica, Syst Comp Jpn, 33(2): 64–76, 2002