Punctuated Equilibria in Genetic Search

A bstract. We introd uce a formaliza tion of a simple genetic algori thm. Mathemati cally, two mat rices F and M determine select ion and recombination operators. Fixed points and their stability for these operators ar e investiga ted in terms of the eigenvalues of the associated matrices. We apply our results to one-po int crossover wit h muta tion to illustrate how the interaction between the focusing operato r (select ion) and the disp ersion operato r (reco mbination) resul ts in the punct uated equilibrium frequentl y observed in genetic sea rch .