The circular schema theorem for genetic algorithms and two-point crossover

The schema theorem is the classical formulation of the search strategy performed by genetic algorithms (adaptation procedures mimicking biological evolution and molecular genetics). The original schema theorem has been derived for single-point crossover assuming that the individual chromosomes are arranged as strings. This paper presents the novel circular schema theorem for the two-point crossover operator, the derivation of which is based on the definition of a circular schema length. This definition assumes that the individual chromosomes form rings instead of strings. With the help of the novel circular schema length an easily interpretable formulation is obtained. Experimental results are presented that confirm the theoretical analysis.