Analytical and numerical investigations of evolutionary algorithms in continuous spaces

Abstract

We investigate the biologically motivated selfreproduction strategies by numerical and analytical calculations. In the analytical part we show that each of these strategies can be reduced to an eigenvalue problem of Sturm-Liouville-type. The properties of the landscape and the dynamics of the optimization are encoded in the spectrum of the Hamiltonian, which is different in both cases. We discuss some model cases with exact solutions and compare them with simulations.