Complex Systems

Punctuated Equilibria in Genetic Search Download PDF

Michael D. Vose
The University of Tennessee, Computer Science Department, 107 Ayres Hall,
Knoxville, TN 37996-1301

Gunar E. Liepins
Oak Ridge National Laboratory, MS 6360 Bldg. 6025, PO Box 2008,
Oak Ridge, TN 37831-6360


We introduce a formalization of a simple genetic algorithm. Mathematically, two matrices F and M determine selection and recombination operators. Fixed points and their stability for these operators are investigated in terms of the eigenvalues of the associated matrices. We apply our results to one-point crossover with mutation to illustrate how the interaction between the focusing operator (selection) and the dispersion operator (recombination) results in the punctuated equilibrium frequently observed in genetic search.