A genetic system based on simulated crossover of sequences of two-bit genes

We introduce a genetic model based on simulated crossover of fixed sequences of two-bit genes. Results are(1)a lower bound on population size is exhibited such that a transition takes the stochastic finite population genetic system near the next state of the deterministic infinite population genetic system (provided both begin in the same state);(2)states and dynamics of the deterministic infinite population genetic system are derived for arbitrary (finite) fitness functions (expressed in terms of multivariate polynomials);(3)in the case of quadratic fitness defined by weight matrices with m nonnull entries it is shown that each state transition can be implemented in time O(m+l), where l is the chromosome length;(4)the genetic algorithm (implementing the proposed infinite population system) is experimentally compared with the infinite population genetic algorithm with bit-based simulated crossover for the max-cut problem; the results show that the extension to sequences of genes with four alleles is useful to improve performances.